2.3: Beauty and Attractiveness
-
- Last updated
- Save as PDF
- Kelly L. Reddy-Best, Abbey K Elder, and Lesya Hassall
- Iowa State University via Iowa State University Digital Press
Module Learning Objectives (MLO)
In this chapter, you will
- MLO 10.1 Identify foundational concepts related to beauty, attractiveness, identity, appearance, and dress. [CLO 1]
- MLO 10.2 Identify the ways beauty and perceptions of attractiveness influence people’s experiences. [CLO 1]
- MLO 10.3 Identify the aspects of facial appearance that contribute to perceptions of attractiveness. [CLO 1]
- MLO 10.4 Identify how people alter their bodies when they do not think they are attractive or meet cultural beauty ideals. [CLO 1]
- MLO 10.5 Identify factors that influence why people alter their bodies when they do not think they are attractive or meet a specific beauty ideal. [CLO 1]
- MLO 10.6 Identify people’s experiences related to meeting the ideals of beauty or perceptions of attractiveness. [CLO 2]
- MLO 10.7 Examine social justice issues related to dress, appearance, and interpretations of beauty and attractiveness in the United States. [CLO 3]
- MLO 10.8 Analyze how dress, appearance, and concepts of beauty and attractiveness in the United States are represented in the fashion system (e.g., advertisements or retailers). [CLO 3]
- MLO 10.9 Deconstruct your own perspectives and approaches to understanding dress, appearance, beauty, and attractiveness in the United States. [CLO 4]
- MLO 10.10 Identify the driving forces of transformative social justice change in the fashion system related to beauty and attractiveness in the United States. [CLO 5]
“Beauty Is Good” Stereotype
In US society, as well as in many other cultures, attractive people are assumed to be
- sociable
- likable
- intelligent
- likely to succeed in a job
- likely to succeed in relationships
(Dion, Berscheid, & Walster, 1972).
Physical attractiveness seems to have a halo effect that influences perceivers to assume that an attractive person holds a network of positive qualities. In this case, a positive stereotype is applied. Research indicates that this positive halo for attractiveness is pervasive, or held throughout US society. Traits that are considered physically unattractive, such as obesity is currently defined, act as a stigma to elicit a stereotype of negative qualities. For example, research indicates that obese individuals are more likely to be perceived as
- lazy
- lacking in self-control
- not intelligent
and a host of other negative things (Jasper & Klassen, 1990). However, these qualities are not actually found to a greater extent in obese individuals.
According to Aronson (1965), the halo effect for attractiveness happens when
Beauty is a reward because it
- is aesthetically pleasing.
- is desirable to “possess.” Attractive women, in particular, are seen as rewards or trophies for successful men.
- reflects positively on associates or friends of an attractive person. Research finds that if an attractive person is willing to hang out with someone, the halo effect rubs off a little on the partner or friend of the attractive person—especially in cases in which a man is romantically connected with a beautiful woman: he is seen as more powerful or effective if he can attract such a woman.
Beauty lends power because it
- attracts.
- holds attention, though not always to what someone is saying.
- opens doors of Attractive people get invited places so that others can have the rewarding or aesthetic experience of being around them.
Beauty is possibly a self-fulfilling prophecy
- Positive reinforcement from others throughout society affects attractive people’s self-concept and esteem positively over time. It is helpful to one’s self-confidence to get so much positive feedback and validation of.
- There is some evidence that attractive people actually tend to be more sociable and outgoing and more self-confident than the average person.
- This does not mean that less attractive people cannot be self-confident and sociable. However, highly attractive people are given such positive responses by others that it may be easier for them to develop these traits.
Symbolic Interaction Process and Body Satisfaction
The people in our lives influence how we feel about our bodies. One study found that among older married couples, each spouses had a substantial impact on how the cother felt about their own attractiveness.
Oh and Damhorst (2009) studied 94 heterosexual married couples 60 years and older who lived in Florida. A good predictor of a man or woman’s body satisfaction was what he or she believed his or her spouse thought about his or her attractiveness. But the best predictor of the older men’s and women’s body satisfaction was what the spouse actually thought about his or her attractiveness.
Clearly, when someone takes on the role of the other to interpret how that other might think about the self, the interpretations can influence how one assesses or appraises the self. In a close relationship such as a long-term marriage, spouses serve as mirrors for each other to define, to some extent, the self. But even when a person is not totally aware of what the other thinks, the way a spouse acts nonverbally and verbally toward his or her mate over time has a profound influence on feelings of attractiveness and body satisfaction.
Cultural Influences on How We Think About the Body
Cheng (2000) studied 209 immigrant Chinese Americans living throughout the United States for body satisfaction and perceptions of attractiveness. In many Asian cultures, the spiritual and abstract qualities of personality and physical functioning are as important as or more important than appearance characteristics in assessing attractiveness. In the United States, emphasis on thinness for women and muscle development for men, as well as facial characteristics, are highly important standards for physical attractiveness. We emphasize surface qualities over internal qualities. As people acculturate to a new culture, they may adopt ways of thinking about attractiveness from the new culture.
Faces and Attraction
Faces convey a significant amount of information about a person, including their various identities, such as sex, gender, ethnicity, race, and mood or emotion. The face is also one avenue through which judgements are made. That is, we have first impression of people based on their faces, and we make these judgements within seconds of meeting a person. Based on our impression of someone, we change our attitude and behavior toward this person (Lennon, Johnson, & Rudd, 2017).
Overall, individuals perceived as attractive receive unearned advantages. And, conversely, unattractive people experience significant discrimination due to the sizes and shapes of their facial features. This result has been found repeatedly in numerous peer-reviewed studies. That is, attractive people are given more awards; make more money; are perceived as smarter, more competent, be more social-able, happier; are given more attention; are more likely to be elected to office; and generally have more positive interactions than those who aren’t seen as markedly attractive (Lennon, Johnson, & Rudd, 2017).
Theories of Attraction
The first theory of attraction is sexual dimorphism , which refers to the physical features that are determined to be associated with men or women or masculinity or femininity. In numerous studies, researchers found that women who have more feminine features are judged to be more attractive and men who have more masculine features (a hard jawline, for instance) are rated as more attractive (Rhode, 2006).
The second theory is the theory of average faces . In this theory, researchers found that those faces that are more average are judged to be more attractive. You can view an example of face that are more average on the Face Research website ( Faceresearch.org ).
The last theory refers to facial symmetry : those faces that are more symmetrical are rated as more attractive (Lennon, Johnson, & Rudd, 2017).
Attraction and the Beauty Industry
There is a significant amount of bias against people who do not meet the appearance attractiveness standard.
The bias toward appearing attractive, being treated better simply because the size and shape of one’s facial features, has created a multi-billion-dollar beauty industry. The cosmetic and plastic surgery industries have contributed to and upheld ideal beauty standards ( American Society of Plastic Surgeons, 2017 ; Rhode, 2010; Ridder, 2021 ). It is no surprise, then, that the fashion industry is aware of the advantage and has employed attractive models, as these models sell more products.
Abercrombie & Fitch
Abercrombie & Fitch is a fashion company that began in the 19th century ( Abercrombie & Fitch, 2021 ). It sells products in numerous categories, including menswear, womenswear, and childrenswear. The company has frequently, in the recent 21st century, been in the news for a variety of issues, including its risqué print catalog, which featured models in sexualized positions. Additionally, it has a history of discriminatory hiring practices ( Walters, 2016 ).
In 2006, Mike Jeffries, the company’s CEO, stated publicly, “A lot of people don’t belong [in our clothes]. . . .That’s why we hire good-looking people in our stores Good-looking people attract other good-looking people, and we want to market to cool, good-looking people. We don’t market to anyone other than that” ( The Fashion Law, 2018 ). Jeffries was hired to overhaul the brand after company went bankrupt in 1992. His tactics of hiring “beautiful” people were to help revamp the company ad increase sales. His strategy was a success; it increased sales and profit.
The company also instituted a looks policy; it regulated employees’ appearances, including length and color of hair, women’s makeup, and fingernail length. In other words, the company hired retail employees as it would models; it put employees in its retail stores based on their appearance rather than their ability to perform job functions. Any person of color (Asian, Black, and/or Latinx) was confined to the stockroom and not out on the selling floor, because they did not have a particular look. This issue is a complex one, and while we read the example in the facial attractiveness module, other intersecting identities certainly experiencing discrimination here, such as race and body size.
One or more interactive elements has been excluded from this version of the text. You can view them online here: https://iastate.pressbooks.pub/dressappearancediversity/?p=26#oembed-1
To view a transcript for the video above, download this file: 60 MIN Abercrombie & Fitch Racism Lookism Controversy Video Transcript [DOC]
Beauty and Attractiveness Case Study
Step One: Become familiar with the case study.
- The case study attached below is a Word document and can be downloaded. It includes the task, evaluation, and template for the case study:
Beauty and Attractiveness Case Study [DOC]
Step Two: Submit your complete assignment on Canvas.
- Format your document.
- Remember to check the submission against the rubric.
References
Aronson, E. (1965). The social animal (2nd ed.). San Francisco: W. H. Freeman.
Cheng, C.-Y. (2000). Acculturation and cultural value orientations of immigrant Chinese Americans: Effects on body image, aesthetics for appearance, and involvement in dress . Unpublished doctoral dissertation, Iowa State University, Ames.
Dion, K., Berscheid, E., & Walster, E. (1972). What is beautiful is good. Journal of Personality and Social Psychology, 24 , 285–290.
Fisher, S. (1968). Body image. In D. Sills (Ed.), International encyclopedia of the social sciences (Vol. 2). New York: Macmillan.
Giddon, D. B. (1985). Ethical considerations for the fashion industry. In M. R. Solomon (Ed.), The Psychology of Fashion (pp. 225–232). Lexington, MA: Lexington Books.
Goffman, E, (1968). Stigma Notes on the management of social identity . Harmondsworth: Penguin.
Jasper, C. R., & Klassen. M. L. (1990). Stereotypical beliefs about appearance: Implications for retailing and consumer issues. Perceptual and Motor Skills, 71 , 519–528.
Lennon, S., Johnson, K. K. P., & Rudd, N. (2017). Social psychology of dress . London: Bloomsbury.
Ogle, J. P., & Damhorst, M. L. (2004). Constructing and deconstructing the body malleable through mother–daughter interactions. Sociological Inquiry, 74 (2), 180-209.
Oh, K., & Damhorst, M. L. (2009). Coorientation of body image among older married couples. Body Image, 6 , 43-47.
Rhode, D. L. (2010). The beauty bias: The injustice of appearance in life and law . Oxford: Oxford University Press.
Rhode, G. (2006). The evolutionary psychology of facial beauty. Annual Review Psychology, 57 , 199-226.


8.2A: Mars and a Biosphere
- Discuss the Martian biosphere
Mars is the fourth planet from the Sun and the second smallest planet in the Solar System. The planet can be seen from Earth with the naked eye. Mars has a thin atmosphere and its surface is very similar to the Earth’s moon (craters). Mars has volcanoes, valleys, deserts, and polar ice caps similar to Earth. Additionally, Mars rotates similarly to Earth and has a tilt that produces seasons.
Mars was first observed at close proximity in 1965 by the Mariner 4. This observation began decades of study and speculations about the structure of the surface of Mars. Scientists hypothesize that its surface is covered by liquid water. Scientists are still collecting and analyzing data concerning its surface. The planet is currently host to five functioning spacecraft: three in orbit—the Mars Odyssey, Mars Express, and Mars Reconnaissance Orbiter; and two on the surface—Mars Exploration Rover Opportunity and the Mars Science Laboratory Curiosity.
Biosphere
A biosphere is typically defined as the part of the Earth and its atmosphere capable of supporting life. A biosphere can also be thought of as an global ecological system that incorporates all living beings and their relationships with the lithosphere, hydrosphere, and atmosphere. Currently, a great deal of research is going into developing hypotheses on a Martian biosphere. This research overlaps greatly with Martian terraforming, which explores how humans might manipulate the Martian environment to make it stable for maintaining life. As mentioned above, scientists are still collecting a great deal of data on the structure and functioning of Mars. This is a burgeoning field of research.
Key Points
- Mars has a thin atmosphere and its surface is very similar to the Earth’s moon (craters) and has volcanoes, valleys, deserts, and polar ice caps similar to Earth itself. Mars rotates similarly to Earth and has a tilt that produces seasons.
- Mars was first observed at close proximity in 1965 by the Mariner 4. Scientists hypothesize that the surface of Mars is covered by liquid water.
- Scientists are still collecting and analyzing data concerning the surface of Mars. The planet is currently host to five functioning spacecraft.
- A biosphere is an global ecological system that incorporates all living beings and their relationships with the lithosphere, hydrosphere, and atmosphere. A great deal of research is going into developing hypotheses on Martian biosphere. Results are currently inconclusive.
Key Terms
- Solar System : The Sun and all the heavenly bodies that orbit around it, including the eight planets, their moons, the asteroids, and comets.
- Mars : The fourth planet in the solar system. Symbol:
- planet : A body which orbits the Sun directly and is massive enough to be in hydrostatic equilibrium (effectively meaning a spheroid) and to dominate its orbit. The eight planets in the Solar System are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. Pluto was considered a planet until 2006 and has now been reclassified as a dwarf planet.


8.3: Continuous Methods 2 - Lone Chooser and Last Diminisher Methods
The Lone Chooser method, like the Lone Divider method, is an extension of the Divider/Chooser method. The Lone Chooser method for three players involves two dividers and one chooser. It can be extended to N players with N-1 dividers and one chooser. We will focus on the three player Lone Chooser method in this book.
The Last Diminisher is a very different method from the Divider/Chooser methods we discuss in this book. In a sense, everyone is a divider and everyone is a chooser. The Last Diminisher method works well when many players must divide a continuous object like a cake or a piece of land.
Lone Chooser Method
In the Lone Chooser method for three players, there are two dividers and one chooser. The basic idea is that the two dividers use the Divider/Chooser method to divide the object into two pieces. At this point each of the dividers believes that he/she has at least half the value of the object. Next each divider divides his/her piece into three smaller pieces for a total of six pieces. The chooser then picks one piece from each of the dividers’ pieces leaving all three players with two pieces each.
- Randomly choose one player to be the chooser, C. The other two players are dividers, D1 and D2.
- The dividers D1 and D2 use the Divider/Chooser method to divide the object into two pieces.
- Each of the dividers D1 and D2 subdivide his/her piece into three pieces of equal value. Use the same ideas as we used in the Divider/Chooser method for determining the value of each piece.
- The chooser assigns a value to each of the six pieces according to his/her value system. The chooser then picks the piece with the greatest value from each of the dividers. Each of the dividers keep his/her other two pieces.
Fred, Gloria, and Harvey wish to split a three-flavored cake worth $36 that is one-third chocolate, one-third strawberry, and one-third vanilla. Fred does not like chocolate, but likes strawberry and vanilla equally well. Gloria likes chocolate twice as much as vanilla and likes strawberry three times as much as vanilla. Harvey likes chocolate and strawberry equally but likes vanilla twice as much as chocolate or strawberry. Use the Lone-Chooser method to find a fair division for the cake.
First let’s figure out how each player values each of the pieces of the cake.
Fred sees the chocolate part of the cake as having a value of $0 since he does not like chocolate. All of the value of the cake is in the strawberry and vanilla parts. Since he likes them equally well, the strawberry part and the vanilla part are both worth $36/2=$18.
For Gloria, let x = the value of the vanilla part of the cake. Then the chocolate part is worth 2x and the strawberry part is worth 3x.
To Gloria the vanilla part is worth $6, the chocolate part is worth $12 and the chocolate part is worth $18.
For Harvey, let y = the value of the chocolate part of the cake. Then the value of the strawberry part is also y and the value of the vanilla part is 2y.
To Harvey the chocolate and strawberry parts are each worth $9 and the vanilla part is worth $18.
Assume the players draw cards to pick the chooser and Henry wins. Then Fred and Gloria must first do the Divider/Chooser method on the cake. They draw cards again and Fred is chosen as the divider. He needs to divide the cake into two pieces each worth $18. There are many possible ways for Fred to cut the cake. Let’s assume he cuts it as shown in figure 8.3.2.
Before Gloria can choose a piece, she must find the value of each of Fred’s pieces in her value system.
Gloria should choose the strawberry and chocolate piece since it has the highest value to her.
Now Fred and Gloria independently divide their pieces into three pieces of equal value in their respective value systems. Remember that each flavor of cake takes up 120◦. Since Fred sees the chocolate as having no value, he needs to divide the 120◦ of vanilla into three equal pieces of 40◦, each worth $6. One of the pieces will also include the 60◦ of chocolate. Gloria’s piece is worth a total of $24 so she needs to divide it into three pieces each worth $8. Start with the Strawberry part. She cuts two pieces of strawberry that have an angle of 53.3◦. The remaining amount of strawberry is Combining the small strawberry piece with the chocolate piece gives a larger piece with an angle of 73.4◦ and a value of The pieces are numbered for convenience.
At this point, Harvey joins the game. He assigns a value to each piece according to his value system.
Harvey should pick the piece from each divider that he sees as having the greatest value. Fred and Gloria each keep the two pieces from their parts that Harvey does not pick. That gives each of the players two of the six pieces.
Now let’s look at the final division. Harvey gets pieces 3 and 4 for a total value of $16.00, more than a fair share to him. Gloria gets pieces 5 and 6 for a total value of $16, more than a fair share to her. The original divider Fred gets pieces 1 and 2 for a total value of $12, exactly a fair share to him.
Last Diminisher Method
The Last Diminisher method can be used to divide a continuous object among many players. The concept is fairly simple. A player cuts a piece of the object. Each of the other players gets to decide if the piece is a fair share or too big. Any player that thinks the piece is too big can cut it smaller (diminish it). The key to the method is that the last person to cut/diminish a piece has to keep it.
Summary of the Last Diminisher method
- The players use a random method to choose an order. The players continue in the same order throughout the game. Call the n players, in order, P1, P2, P3, …, Pn.
- Player 1 cuts a piece he/she considers a fair share. In order, each of the remaining players either passes (says the piece is a fair share and P1 can have it) or diminishes the piece. The last player to diminish the piece keeps the piece and leaves the game. If no one diminishes the piece, P1 keeps the piece and leaves the game.
- The lowest numbered player still in the game cuts a piece of the object. Each of the remaining players can either pass or diminish the piece. The last player to cut/diminish the piece keeps it and leaves the game.
- Repeat step three until only two players remain. These players use the Divider/Chooser method to finish the game.
Suppose six players want to divide a piece of land using the Last Diminisher method. They draw cards to choose an order. Assume the players in order are denoted P1, P2, P3, P4, P5, and P6.
In round one, P1 cuts a piece by drawing lines on a map of the land. Assume players P2 through P6 pass on the piece. Since P1 is the last player to cut or diminish the piece, P1 keeps the piece and leaves the game.
In round two, players P2 through P6 remain in the game. P2 is the lowest numbered player so P2 cuts a piece of the land. Assume that P3 and P4 pass on the piece. P5 thinks that the piece is more than a fair share so P5 diminishes the piece by redrawing the lines on the map to make the piece smaller. Assume P6 passes. Since P5 is the last player to diminish the piece, P5 keeps the piece and leaves the game.
In round three, players P2, P3, P4, and P6 remain in the game. P2 is still the lowest numbered player so P2 cuts a piece of the land. This time assume that P3 diminishes, P4 passes and P6 diminishes the piece. P6 keeps the piece and leaves the game.
In round four, players P2, P3, and P4 remain in the game. Once again P2 cuts a piece. Assume both P3 and P4 pass on the piece. P2 keeps the piece and leaves the game.
For round five, since only P3 and P4 are left, they do Divider/Chooser on the remaining land. P3 cuts and P4 chooses.
Eight players want to divide a piece of land using the Last Diminisher method. They draw straws to determine an order. Assume the players in order are denoted by P1, P2, P3, P4, P5, P6, P7, and P8. P3 and P5 are the only diminishers in round one. No one diminishes in rounds two, three and six. P8 is the only diminisher in round four. Both P4 and P6 diminish in round five. Describe the fair division round by round.
Round one: P1 cuts a piece, P2 passes, P3 diminishes, P4 passes, P5 diminishes, P6, P7, and P8 pass. P5 is the last diminisher so P5 keeps the piece and leaves the game.
Round two: P1 cuts a piece and everyone else passes so P1 keeps the piece and leaves the game.
Round three: P2 is now the lowest numbered player so P2 cuts a piece. Everyone else passes so P2 keeps the piece and leaves the game.
Round four: P3 is now the lowest numbered player so P3 cuts a piece. P4, P6, and P7 pass. P8 diminishes the piece making P8 the last diminisher so P8 keeps the piece and leaves the game.
Round five: P3 is still the lowest numbered player so P3 cuts a piece. P4 and P6 both diminish the piece but P7 passes. P6 is the last diminisher so P6 keeps the piece and leaves the game.
Round six: P3 cuts a piece again and everyone else passes, so P3 keeps the piece and leaves the game.
Round seven: P4 and P7 are the only players left so they use the Divider/Chooser method to divide the remaining land. P4 divides and P7 chooses.


3.7: Cultural Assessment
After establishing a culturally sensitive environment, nurses should incorporate a cultural assessment when caring for all patients. There are many assessment guides used for patient interviews that are adaptable to a variety of health care settings and are designed to facilitate understanding and communication. The Four Cs of Culture model [1] is an example of a quick cultural assessment tool that asks questions about what the patient C onsiders to be a problem, the C ause of the problem, how they are C oping with the problem, and how C oncerned they are about the problem. See the following box for examples of sample answers to the four Cs assessment.
1. What do you think is wrong? What is worrying you? (In other words, discover what the patient C onsiders to be the problem and what they C all it.)
- A patient with a diagnosis of pneumonia believes his body is “unbalanced.”
2. What do you think C aused this problem? How did this happen?
- The patient believes this illness is a punishment for a misdeed.
- The patient avoids eating certain foods to treat the illness while also using home remedies such as herbal tea.
3. How serious is this problem for you? How C oncerned are you?
- A patient views the illness as being “God’s will” and states, “It’s in God’s hands.”
A more comprehensive cultural assessment tool, inspired by R. E. Spector’s Heritage Assessment interview, [3] is described in the following box.
- Where were you born? Where were your parents born?
- What pronoun do you use (he, she, they)?
- In what language are you most comfortable speaking and reading?
- Did you grow up in a city or a town or a rural setting?
- When you were growing up, who lived with you and your family?
- Are your friends from the same cultural background as you?
- What is your religious preference?
- Do you have any dietary preferences related to your religious or cultural beliefs?
- In your culture, how do you celebrate the birth of a baby? A wedding?
- When a woman is pregnant, are there any special customs she needs to follow? Any special foods?
- When someone in your family is ill, who cares for them? What foods are prepared? Is there anything the ill person should avoid or refrain from doing?
- What home remedies might be used if someone is ill?
- As a family member is approaching death, what actions do you find comforting?
- After a loved one dies, what rituals are performed?
- What do you think a nurse should know about your culture if a family member is hospitalized?
- Who makes the decisions in your family?
- How are elders viewed in your culture?
- Are there any special beliefs regarding organ donation or blood transfusions that are held in your culture?
- Is your culture known for any special customs (e.g., rites of passage, foods, holidays, etc.)?
- Galanti, G. A. (2014). Caring for patients from different cultures (5th ed.). University of Pennsylvania Press. ↵
- Galanti, G. A. (2014). Caring for patients from different cultures (5th ed.). University of Pennsylvania Press. ↵
- Spector, R. E. (2017). Cultural diversity in health and illness (9th ed.). Pearson Education. ↵
- Spector, R. E. (2017). Cultural diversity in health and illness (9th ed.). Pearson Education. ↵


13.4: Facts About the F Distribution
-
- Last updated
- Save as PDF
Here are some facts about the \(F\) distribution:
- The curve is not symmetrical but skewed to the right.
- There is a different curve for each set of \(dfs\).
- The \(F\) statistic is greater than or equal to zero.
- As the degrees of freedom for the numerator and for the denominator get larger, the curve approximates the normal.
- Other uses for the \(F\) distribution include comparing two variances and two-way Analysis of Variance. Two-Way Analysis is beyond the scope of this chapter.
Visualize how changing the numerator and denominator degrees of freedom changes the graph of the f-distribution
Move the sliders to change the degrees of freedom and the graph of the F-Distribution.
Numerator df = 5
Denominator df = 5
Example \(\PageIndex{1}\)
Let’s return to the slicing tomato exercise. The means of the tomato yields under the five mulching conditions are represented by \(\mu_{1}, \mu_{2}, \mu_{3}, \mu_{4}, \mu_{5}\). We will conduct a hypothesis test to determine if all means are the same or at least one is different. Using a significance level of 5%, test the null hypothesis that there is no difference in mean yields among the five groups against the alternative hypothesis that at least one mean is different from the rest.
Answer
The null and alternative hypotheses are:
- \(H_{0}: \mu_{1} = \mu_{2} = \mu_{3} = \mu_{4} = \mu_{5}\)
- \(H_{a}: \mu_{i} \neq \mu_{j}\) some \(i \neq j\)
The one-way \(ANOVA\) results are shown in Table
| Source of Variation | Sum of Squares (\(SS\)) | Degrees of Freedom (\(df\)) | Mean Square (\(MS\)) | \(F\) |
|---|---|---|---|---|
| Factor (Between) | 36,648,561 | \(5 - 1 = 4\) | \(\dfrac{36,648,561}{4} = 9,162,140\) |
\(\dfrac{9,162,140}{2,044,672.6} = 4.4810\) |
| Error (Within) | 20,446,726 | \(15 - 5 = 10\) |
\(\dfrac{20,446,726}{10} = 2,044,672.6\) |
|
| Total | 57,095,287 | \(15 - 1 = 14\) |
Distribution for the test: \(F_{4,10}\)
\[df(\text{num}) = 5 - 1 = 4\]
\[df(\text{denom}) = 15 - 5 = 10\]
Test statistic: \(F = 4.4810\)
Figure \(\PageIndex{2}\)Probability Statement: \(p\text{-value} = P(F > 4.481) = 0.0248\).
Compare \(\alpha\) and the \(p\text{-value}\) : \(\alpha = 0.05, p\text{-value} = 0.0248\)
Make a decision: Since \(\alpha > p\text{-value}\), we reject \(H_{0}\).
Conclusion: At the 5% significance level, we have reasonably strong evidence that differences in mean yields for slicing tomato plants grown under different mulching conditions are unlikely to be due to chance alone. We may conclude that at least some of mulches led to different mean yields.
To find these results on the LibreTexts ANOVA calculator:
Enter in the data, separated by commas, and hit Calculate. You will see the test statistic and the p -value of the test.
The calculator displays:
- \(F = 4.4810\)
- \(p = 0.0248\) (\(p\text{-value}\))
Exercise \(\PageIndex{1}\)
MRSA, or Staphylococcus aureus , can cause a serious bacterial infections in hospital patients. Table shows various colony counts from different patients who may or may not have MRSA.
| Conc = 0.6 | Conc = 0.8 | Conc = 1.0 | Conc = 1.2 | Conc = 1.4 |
|---|---|---|---|---|
| 9 | 16 | 22 | 30 | 27 |
| 66 | 93 | 147 | 199 | 168 |
| 98 | 82 | 120 | 148 | 132 |
Plot of the data for the different concentrations:
Figure \(\PageIndex{3}\)Test whether the mean number of colonies are the same or are different. Construct the \(ANOVA\) table (using the LibreTexts ANOVA calculator), find the p -value, and state your conclusion. Use a 5% significance level.
Answer
While there are differences in the spreads between the groups (Figure \(\PageIndex{1}\)), the differences do not appear to be big enough to cause concern.
We test for the equality of mean number of colonies:
\(H_{0}: \mu_{1} = \mu_{2} = \mu_{3} = \mu_{4} = \mu_{5}\)
\(H_{a}: \mu_{i} \neq \mu_{j}\) some \(i \neq j\)
The one-way \(ANOVA\) table results are shown in Table.
| Source of Variation | Sum of Squares (\(SS\)) | Degrees of Freedom (\(df\)) | Mean Square (\(MS\)) | \(F\) |
|---|---|---|---|---|
| Factor (Between) | 10,233 | \(5 - 1 = 4\) | \(\dfrac{10,233}{4} = 2,558.25\) | \(\dfrac{2,558.25}{4,194.9} = 0.6099\) |
| Error (Within) | 41,949 | \(15 - 5 = 10\) | ||
| Total | 52,182 | \(15 - 1 = 14\) | \(\dfrac{41,949}{10} = 4,194.9\) |
Figure \(\PageIndex{2}\)
Distribution for the test: \(F_{4,10}\)
Probability Statement: \(p\text{-value} = P(F > 0.6099) = 0.6649\).
Compare \(\alpha\) and the \(p\text{-value}\) : \(\alpha = 0.05, p\text{-value} = 0.669, \alpha > p\text{-value}\)
Make a decision: Since \(\alpha > p\text{-value}\), we do not reject \(H_{0}\).
Conclusion: At the 5% significance level, there is insufficient evidence from these data that diferent levels of tryptone is a factor in the number of bacterial colonies formed.
Example \(\PageIndex{2}\)
Four sororities took a random sample of sisters regarding their grade means for the past term. The results are shown in Table.
| Sorority 1 | Sorority 2 | Sorority 3 | Sorority 4 |
|---|---|---|---|
| 2.17 | 2.63 | 2.63 | 3.79 |
| 1.85 | 1.77 | 3.78 | 3.45 |
| 2.83 | 3.25 | 4.00 | 3.08 |
| 1.69 | 1.86 | 2.55 | 2.26 |
| 3.33 | 2.21 | 2.45 | 3.18 |
Using a significance level of 1%, is there a difference in mean grades among the sororities?
Answer
Let \(\mu_{1}, \mu_{2}, \mu_{3}, \mu_{4}\) be the population means of the sororities. Remember that the null hypothesis claims that the sorority groups are from the same normal distribution. The alternate hypothesis says that at least two of the sorority groups come from populations with different normal distributions. Notice that the four sample sizes are each five.
This is an example of a balanced design, because each factor (i.e., sorority) has the same number of observations.
\(H_{0}: \mu_{1} = \mu_{2} = \mu_{3} = \mu_{4}\)
\(H_{a}\): Not all of the means \(\mu_{1}, \mu_{2}, \mu_{3}, \mu_{4}\) are equal.
Distribution for the test: \(F_{3,16}\)
where \(k = 4\) groups and \(n = 20\) samples in total
\(df(\text{num}) = k - 1 = 4 - 1 = 3\)
\(df(\text{denom}) = n - k = 20 - 4 = 16\)
Calculate the test statistic: \(F = 2.23\)
Graph:
Figure \(\PageIndex{5}\)Probability statement: \(p\text{-value} = P(F > 2.23) = 0.1241\)
Compare \(\alpha\) and the \(p\text{-value}\) : \(\alpha = 0.01\)
\(p\text{-value} = 0.1241\)
\(\alpha < p\text{-value}\)
Make a decision: Since \(\alpha < p\text{-value}\), you cannot reject \(H_{0}\).
Conclusion: There is not sufficient evidence to conclude that there is a difference among the population mean grades for the sororities.
Enter in the data into the LibreTexts ANOVA calculator and hit Calculate.
The calculator displays the F statistic and the \(p\text{-value}\):
\(F = 2.2303\)
\(p = 0.1241\) (\(p\text{-value}\))
ANOVA Calculator
Enter the data values separated by commas, for example: 3,4,7,9,-2,8. Then hit Calculate and the F-statistic and the p-value will be generated for you.
Data1:
Data2:
Data3:
Data4:
Data5:
Data6:
Data7:
Data8:
| F: | p |
Exercise \(\PageIndex{2}\)
Four sports teams took a random sample of players regarding their GPAs for the last year. The results are shown in Table.
| Basketball | Baseball | Hockey | Lacrosse |
|---|---|---|---|
| 3.6 | 2.1 | 4.0 | 2.0 |
| 2.9 | 2.6 | 2.0 | 3.6 |
| 2.5 | 3.9 | 2.6 | 3.9 |
| 3.3 | 3.1 | 3.2 | 2.7 |
| 3.8 | 3.4 | 3.2 | 2.5 |
Use a significance level of 5%, and determine if there is a difference in GPA among the teams.
Answer
With a \(p\text{-value}\) of \(0.9271\), we decline to reject the null hypothesis. There is not sufficient evidence to conclude that there is a difference among the population mean GPAs for the sports teams.
Example \(\PageIndex{3}\)
A fourth grade class is studying the environment. One of the assignments is to grow bean plants in different soils. Tommy chose to grow his bean plants in soil found outside his classroom mixed with dryer lint. Tara chose to grow her bean plants in potting soil bought at the local nursery. Nick chose to grow his bean plants in soil from his mother's garden. No chemicals were used on the plants, only water. They were grown inside the classroom next to a large window. Each child grew five plants. At the end of the growing period, each plant was measured, producing the data (in inches) in Table \(\PageIndex{3}\).
| Tommy's Plants | Tara's Plants | Nick's Plants |
|---|---|---|
| 24 | 25 | 23 |
| 21 | 31 | 27 |
| 23 | 23 | 22 |
| 30 | 20 | 30 |
| 23 | 28 | 20 |
Does it appear that the three media in which the bean plants were grown produce the same mean height? Test at a 3% level of significance.
Answer
This time, we will perform the calculations that lead to the \(F'\) statistic. Notice that each group has the same number of plants, so we will use the formula
\[F' = \dfrac{n \cdot s_{\bar{x}}^{2}}{s^{2}_{\text{pooled}}}.\]
First, calculate the sample mean and sample variance of each group.
| Tommy's Plants | Tara's Plants | Nick's Plants | |
|---|---|---|---|
| Sample Mean | 24.2 | 25.4 | 24.4 |
| Sample Variance | 11.7 | 18.3 | 16.3 |
Next, calculate the variance of the three group means (Calculate the variance of 24.2, 25.4, and 24.4). Variance of the group means \(= 0.413 = s_{\bar{x}}^{2}\)
Then \(MS_{\text{between}} = ns_{\bar{x}}^{2} = (5)(0.413)\) where \(n = 5\) is the sample size (number of plants each child grew).
Calculate the mean of the three sample variances (Calculate the mean of 11.7, 18.3, and 16.3). Mean of the sample variances \(= 15.433 = s^{2}_{\text{pooled}}\)
Then \(MS_{\text{within}} = s^{2}_{\text{pooled}} = 15.433\).
The \(F\) statistic (or \(F\) ratio) is \(F = \dfrac{MS_{\text{between}}}{MS_{\text{within}}} = \dfrac{ns_{\bar{x}}^{2}}{s^{2}_{\text{pooled}}} = \dfrac{(5)(0.413)}{15.433} = 0.134\)
The \(dfs\) for the numerator \(= \text{the number of groups} - 1 = 3 - 1 = 2\).
The \(dfs\) for the denominator \(= \text{the total number of samples} - \text{the number of groups} = 15 - 3 = 12\)
The distribution for the test is \(F_{2,12}\) and the \(F\) statistic is \(F = 0.134\)
The \(p\text{-value}\) is \(P(F > 0.134) = 0.8759\).
Decision: Since \(\alpha = 0.03\) and the \(p\text{-value} = 0.8759\), do not reject \(H_{0}\). (Why?)
Conclusion: With a 3% level of significance, from the sample data, the evidence is not sufficient to conclude that the population mean heights of the bean plants are different.
Exercise \(\PageIndex{3}\)
Another fourth grader also grew bean plants, but this time in a jelly-like mass. The heights were (in inches) 24, 28, 25, 30, and 32. Do a one-way ANOVA test on the four groups. Are the heights of the bean plants different? Use the same method as shown in Example \(\PageIndex{3}\).
Answer
- \(F = 0.9496\)
- \(p\text{-value} = 0.4402\)
From the sample data, the evidence is not sufficient to conclude that the population mean heights of the bean plants are different.
COLLABORATIVE EXERCISE
From the class, create four groups of the same size as follows: men under 22, men at least 22, women under 22, women at least 22. Have each member of each group record the number of states in the United States he or she has visited. Run an ANOVA test to determine if the average number of states visited in the four groups are the same. Test at a 1% level of significance. Use one of the solution sheets in [link].
References
- Data from a fourth grade classroom in 1994 in a private K – 12 school in San Jose, CA.
- Hand, D.J., F. Daly, A.D. Lunn, K.J. McConway, and E. Ostrowski. A Handbook of Small Datasets: Data for Fruitfly Fecundity. London: Chapman & Hall, 1994.
- Hand, D.J., F. Daly, A.D. Lunn, K.J. McConway, and E. Ostrowski. A Handbook of Small Datasets. London: Chapman & Hall, 1994, pg. 50.
- Hand, D.J., F. Daly, A.D. Lunn, K.J. McConway, and E. Ostrowski. A Handbook of Small Datasets. London: Chapman & Hall, 1994, pg. 118.
- “MLB Standings – 2012.” Available online at http://espn.go.com/mlb/standings/_/year/2012 .
- Mackowiak, P. A., Wasserman, S. S., and Levine, M. M. (1992), "A Critical Appraisal of 98.6 Degrees F, the Upper Limit of the Normal Body Temperature, and Other Legacies of Carl Reinhold August Wunderlich," Journal of the American Medical Association , 268, 1578-1580.
Chapter Review
The graph of the \(F\) distribution is always positive and skewed right, though the shape can be mounded or exponential depending on the combination of numerator and denominator degrees of freedom. The \(F\) statistic is the ratio of a measure of the variation in the group means to a similar measure of the variation within the groups. If the null hypothesis is correct, then the numerator should be small compared to the denominator. A small \(F\) statistic will result, and the area under the \(F\) curve to the right will be large, representing a large \(p\text{-value}\). When the null hypothesis of equal group means is incorrect, then the numerator should be large compared to the denominator, giving a large \(F\) statistic and a small area (small \(p\text{-value}\)) to the right of the statistic under the \(F\) curve.
When the data have unequal group sizes (unbalanced data), then techniques discussed earlier need to be used for hand calculations. In the case of balanced data (the groups are the same size) however, simplified calculations based on group means and variances may be used. In practice, of course, software is usually employed in the analysis. As in any analysis, graphs of various sorts should be used in conjunction with numerical techniques. Always look of your data!
Contributors and Attributions
-
Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>.


8.2: Metamorphic Rock Identification
Metamorphic Rocks
Metamorphic Rock Identification
Introduction
Rocks are made of minerals. Rocks can be a mixture of different kinds of minerals, a mixture of many grains of the same kind of mineral, or a mixture of different grains of rocks. When you split a rock into very small pieces, the pieces are different from each other. For example, when you break granite apart, you get small pieces of quartz (clear), feldspar (pink or white), and mica (black). When you split a mineral into pieces, you still have pieces of the same mineral. If you break a big chunk of quartz into smaller pieces, you still have pieces of quartz.
There are three basic rock types: Igneous, sedimentary, and metamorphic.
Metamorphic Rocks
Metamorphic rocks (changed rocks) are made when existing rocks are subjected to high temperatures and high pressures for long periods of time. Metamorphism (meta = change, morph = form) happens when molten rock intrudes other rocks and bakes the contact zone where the molten rock touches the preexisting rock. Metamorphism also happens when rocks are buried deeply during the process of mountain building. The kind of metamorphic rock made depends on the kind of original rock; for example, sandstone is turned to quartzite, shale is turned to slate, and limestone is turned to marble. Other kinds of metamorphic rock are named for the kinds of minerals present, the size of the grains and other textures. For example, mica schist has very thin layers of mica, and garnet gneiss (pronounced like nice) has garnet crystals in thick layers of quartz and feldspar. The amount of time, amount of pressure, and highness of temperature determine what types of metamorphic rocks are made.
How Metamorphic Rocks are Made
- Pressure from the weight of overlying rocks or from stresses of mountain building rearranges the minerals in rocks into bands or rearranges the atoms of the minerals into new minerals.
- Heat from the intrusion of a large igneous mass can metamorphose a large area.
- Heat from the intrusion of a dike or sill or flow can bake the adjoining rocks in a contact metamorphic zone.
Composition
The mineral composition of the rock can be determined based on observations with a hand lens and if needed, physical or chemical tests. Start by identifying and list all visible minerals present in the rock.
Probable Parent Rocks
All metamorphic rocks are derived by the action of heat and/or pressure on pre-existing igneous, sedimentary, or metamorphic rocks. The pre-existing rock is called either the parent rock or the protolith. Your textbook incorrectly uses the term “source rocks” for the pre-existing rock. The term source rock used in sedimentary deposits to describe the rock from which petroleum is derived, or the rock that erodes to produce sediment and later sedimentary rock. Read the descriptions in your lab manual or textbook for the source rock of each of the metamorphic rocks that you identify. Indicate in the name(s) of the probable parent rock(s) in the last column of the metamorphic rock identification form.
Texture
The term texture refers to the size, shape, and boundary relationships of the minerals, particles, and other substances that make up a rock. There are two major textural groups in metamorphic rocks: Foliated and Non-Foliated.
| Texture | Characteristics | Rock Name |
|---|---|---|
| foliated (banded) | very thin layers | Slate |
| foliated (banded) | wavy layers with sheen | Phyllite |
| foliated (banded) | thin layers of mica | Schist |
| foliated (banded) | thick layers of quartz, feldspar, and mica | Gneiss |
| non-foliated (massive) | welded quartz sandstone | Quartzite |
| non-foliated (massive) | sugary to course crystals, fizzes in HCl acid | Marble |
| non-foliated (massive) | dense, black, fine grained, flint-like fracture | Hornfels |
Foliated (Banded) Metamorphic Rocks
In this texture, the mineral crystals in the rock are aligned with each other. This alignment may be displayed as parallel planes along which the rock splits, by overlapping sheets of platy minerals such as micas, by the parallel alignment of elongate minerals such as amphiboles, or by alternating layers of light and dark minerals. Foliated texture is further subdivided based on the presence or absence of pronounced color banding in the rock. Rocks without distinct alternating bands of light and dark minerals are described a nonlayered, whereas rocks with alternating bands of dark and light minerals are described as layered. Layered is also referred to as gneissic foliation. Foliated textures are further described on the basis of the grain (crystal) size in the rock. Examples of complete descriptions of foliated metamorphic rocks include: foliated, nonlayered, very fine grained for slate, foliated, layered, coarse grained for gneiss, and foliated, nonlayered, fine grained for phyllite. Foliated textures produced by shearing and breaking, such as in a fault zone or a meteor impact crater, are referred to as mylonitic.
| Characteristics | Minerals | Rock Name |
|---|---|---|
|
Very thin layers, like blackboards
Very fine-grained Smooth, flat surfaces, from slatey cleavage Separate grains not visible Dense, brittle, clinking sound |
Mica
Quartz Clay (microscopic) |
Slate |
|
Very, very thin, irregular layers of mica
Usually pale gray green Satin sheen to rock rather than individual flakes Fine to medium-grained Uneven surfaces Grains visible |
Mica
Quartz Other minerals |
Phyllite |
|
Thin, irregular layers of mica & platy minerals
Usually pale gray green Medium-grained Uneven surfaces Grains visible |
Mica (muscovite, biotite)
Chlorite Talc Hornblende Quartz Garnet Feldspar |
Schist |
| Thin, irregular layers of mica and platy minerals | Bluish color; mica, quartz | Blueschist |
| Thin, irregular layers of mica and platy minerals | Greenish color; mica, quartz, serpentine | Greenschist |
|
Thick bands, wavy, semi-continuous layers of white quartz, feldspar, and mica
Medium to coarse-grained Banded, coarsely crystalline Large, crystalline grains |
Feldspar
Quartz Mica Hornblende Garnet |
Gneiss |
Non-Foliated Metamorphic Rocks
In this texture the mineral crystals in the rock have grown in many directions and do not show alignment. As a result, nonfoliated rocks commonly appear massive and structureless, with only a few lines of impurities through the rock. These rocks may break across, rather than around, mineral grains to produce a scaly surface on the specimen. Nonfoliated textures are further described on the basis of the grain (crystal) size in the rock. Examples of complete descriptions of nonfoliated metamorphic rocks include nonfoliated, medium grained for quartzite, or nonfoliated, coarse grained for marble.
| Characteristics | Former Rock | Rock Name |
|---|---|---|
|
Very hard, smooth
Stretched and welded cobbles and pebbles – Fractures through grains, not around them as in rougher conglomerate Composed of rock fragments, quartz, chert |
Conglomerate |
Meta-
conglomerate |
|
Very hard, smooth
Welded sand grains – Fractures through grains, not around them as in rougher sandstone |
Sandstone | Quartzite |
|
Fizzes in dilute acid
Medium to coarse-grained Sugary to crystalline Composed of calcite (CaCO 3 ) |
Limestone | Marble |
|
Very hard, flint-like fracture
Smooth, very fine-grained Dark colored to black Very dense, compact |
Claystone
Slate Mudstone Shale |
Hornfels |
|
Black to brown
Dense, highly altered plant remains Carbon, opaque, non-crystalline |
Peat | Coal |


7.4: Cognitive Development
-
- Last updated
- Save as PDF
Beyond Formal Operational Thought: Post-formal Thought
In our last lesson, we discussed formal operational thought. The hallmark of this type of thinking is the ability to think abstractly or to consider possibilities and ideas about circumstances never directly experienced. Thinking abstractly is only one characteristic of adult thought, however. If you compare a 15 year old with someone in their late 30s, you would probably find that the later considers not only what is possible, but also what is likely. Why the change? The adult has gained experience and understands why possibilities do not always become realities. This difference in adult and adolescent thought can spark arguments between the generations. Here is an example. A student in her late 30s relayed such an argument she was having with her 14 year old son. The son had saved a considerable amount of money and wanted to buy an old car and store it in the garage until he was old enough to drive. He could sit in it; pretend he was driving, clean it up, and show it to his friends.  The mother, however, had practical objections. The car could just sit for several years without deteriorating. The son would certainly change his mind about the type of car he wanted before he was old enough to drive and they would be stuck with a car that would not run. Having a car nearby would be too much temptation and the son might decide to sneak it out for a quick run around the block, etc.
Postformal thought is practical, realistic and more individualistic. As a person approaches the late 30s, chances are they make decisions out of necessity or because of prior experience and are less influenced by what others think. Of course, this is particularly true in individualistic cultures such as the United States.
Dialectical Thought
In addition to moving toward more practical considerations, thinking in early adulthood may also become more flexible and balanced. Abstract ideas that the adolescent believes in firmly may become standards by which the adult evaluates reality. Adolescents tend to think in dichotomies; ideas are true or false; good or bad; right or wrong and there is no middle ground. However, with experience, the adult comes to recognize that there is some right and some wrong in each position, some good or some bad in a policy or approach, some truth and some falsity in a particular idea. This ability to bring together salient aspects of two opposing viewpoints or positions is referred to as dialectical thought and is considered one of the most advanced aspects of postformal thinking (Basseches, 1984). Such thinking is more realistic because very few positions, ideas, situations, or people are completely right or wrong. So, for example, parents who were considered angels or devils by the adolescent eventually become just people with strengths and weaknesses, endearing qualities and faults to the adult.
Educational Concerns
In 2005, 37 percent of people in the United States between 18 and 24 had some college or an associate degree; about 30 percent of people between 25 and 34 had completed an education at the bachelor’s level or higher (U. S. Bureau of the Census, 2005). Of current concern is the relationship between higher education and the workplace. Bok (2005), American educator and Harvard University President, calls for a closer alignment between the goals of educators and the demands of the economy. Companies outsource much of their work, not only to save costs, but to find workers with the skills they need. What is required to do well in today’s economy? Colleges and universities, he argues, need to promote global awareness, critical thinking skills, the ability to communicate, moral reasoning, and responsibility in their students (Bok, 2006). Regional accrediting agencies and state organizations provide similar guidelines for educators. Workers need skills in listening, reading, writing, speaking, global awareness, critical thinking, civility, and computer literacy-all skills that enhance success in the workplace. The U. S. Secretary of Education, Margaret Spellings challenges colleges and universities to demonstrate their effectiveness in providing these skills to students and to work toward increasing America’s competitiveness in the global economy (U. S. Department of Education, 2006).
A quality education is more than a credential. Being able to communicate and work well with others is crucial for success. There is some evidence to suggest that most workers who lose their jobs do so because of an inability to work with others, not because they do not know how to do their jobs (Cascio, in Berger 2005). Writing, reading, being able to work with a diverse work team, and having the social skills required to be successful in a career and in society are qualities that go beyond merely earning a credential to compete for a job. Employers must select employees who are not only degreed, but who will be successful in the work environment. Hopefully, students gain these skills as they pursue their degrees. Listen to this story about the lack of rigor in higher education and the problems students face as a result: A Lack Of Rigor Leaves Students ‘Adrift’ In College.


11.1: The Ideal Gas Equation
The concept of an ideal gas is a theoretical construct that allows for straightforward treatment and interpretation of gases’ behavior. As such, the ideal gas is a simplified model that we use to understand nature, and it does not correspond to any real system. The following two assumptions define the ideal gas model:
- The particles that compose an ideal gas do not occupy any volume.
- The particles that compose an ideal gas do not interact with each other.
Because of its simplicity, the ideal gas model has been the historical foundation of thermodynamics and of science in general. The first studies of the ideal gas behavior date back to the seventeenth century, and the scientists that performed them are among the founders of modern science.
Boyle’s Law
In 1662 Robert Boyle (1627–1691) found that the pressure and the volume of an ideal gas are inversely related at constant temperature. Boyle’s Law has the following mathematical description:
\[ P\propto\dfrac{1}{V}\quad\text{at const.}\;T, \label{11.1.1} \]
or, in other terms:
\[ PV=k_1\quad\text{at const.}\;T, \label{11.1.2} \]
which results in the familiar \(PV\) plots of Figure \(\PageIndex{1}\). As we already discussed in chapter 2 , each of the curves in Figure \(\PageIndex{1}\) is obtained at constant temperature, and it is therefore called “isotherm.”
Charles’s and Gay-Lussac’s Laws
It took scientists more than a century to expand Boyle’s work and study the relationship between volume and temperature. In 1787 Jacques Alexandre César Charles (1746–1823) wrote the relationship known as Charles’s Law:
\[ V\propto T\quad\text{at const.}\;P, \label{11.1.3} \]
or, in other terms:
\[ V=k_2 T\quad\text{at const.}\;P, \label{11.1.4} \]
which results in the plots of Figure \(\PageIndex{2}\). Each of the curves is obtained at constant pressure, and it is termed “isobar.”
The interesting thing about isobars is that each line seems to converge to a specific point along the temperature line when we extrapolate them to \(V\rightarrow 0\). This led to the introduction of the absolute temperature scale, suggesting that the temperature will never get smaller than \(-273.15^\circ\mathrm{C}\).
It took an additional 21 years to write a formal relationship between pressure and temperature. The following relationships were proposed by Joseph Louis Gay-Lussac (1778–1850) in 1808:
\[ P\propto T\quad\text{at const.}\;V, \label{11.1.5} \]
or, in other terms:
\[ P=k_3 T\quad\text{at const.}\;V, \label{11.1.6} \]
which results in the plots of Figure \(\PageIndex{3}\). Each of the curves is obtained at constant volume, and it is termed “isochor.”
Avogadro’s Law
Ten years later, Amedeo Avogadro (1776–1856) discovered a seemingly unrelated principle by studying the composition of matter. His Avogadro’s Law encodes the relationship between the number of moles in an ideal gas and its volume as:
\[ V\propto n\quad\text{at const.}\;P,T, \label{11.1.7} \]
or in other terms:
\[ V=k_4 n\quad\text{at const.}\;P,T, \label{11.1.8} \]
The ideal gas Law
Despite all of the ingredients being available for more than 20 years, it’s only in 1834 that Benoît Paul Émile Clapeyron (1799–1864) was finally able to combine them into what is now known as the ideal gas Law . Using the same formulas obtained above, we can write:
\[ PV=\underbrace{k_3 T}_{\text{from Gay-Lussac's}} \cdot \underbrace{k_4 n,}_{\text{from Avogadro's}} \label{11.1.9} \]
which by renaming the product of the two constants \(k_3\) and \(k_4\) as \(R\), becomes:
\[ PV=nRT \label{11.1.10} \]
The value of the constant \(R\) can be determined experimentally by measuring the volume that 1 mol of an ideal gas occupies at a constant temperature (e.g., at \(T=0^\circ\mathrm{C}\)) and a constant pressure (e.g., atmospheric pressure \(P=1\;\mathrm{atm}\)). At those conditions, the volume is measured at 22.4 L, resulting in the following value of \(R\):
\[ R=\dfrac{VP}{nT}=\dfrac{22.4 \cdot 1}{1 \cdot 273}=0.082 \;\dfrac{\text{L atm}}{\text{mol K}}, \label{11.1.11} \]
which a simple conversion to SI units transforms into:
\[ R=8.31\;\dfrac{\text{J}}{\text{mol K}}. \label{11.1.12} \]


4.7E: The Golgi Apparatus
- Describe the structure of the Golgi apparatus and its role in protein modification and secretion
We have already mentioned that vesicles can bud from the ER and transport their contents elsewhere, but where do the vesicles go? Before reaching their final destination, the lipids or proteins within the transport vesicles still need to be sorted, packaged, and tagged so that they wind up in the right place. Sorting, tagging, packaging, and distribution of lipids and proteins takes place in the Golgi apparatus (also called the Golgi body), a series of flattened membranes.
The receiving side of the Golgi apparatus is called the cis face. The opposite side is called the trans face. The transport vesicles that formed from the ER travel to the cis face, fuse with it, and empty their contents into the lumen of the Golgi apparatus. As the proteins and lipids travel through the Golgi, they undergo further modifications that allow them to be sorted. The most frequent modification is the addition of short chains of sugar molecules. These newly-modified proteins and lipids are then tagged with phosphate groups or other small molecules so that they can be routed to their proper destinations.
Finally, the modified and tagged proteins are packaged into secretory vesicles that bud from the trans face of the Golgi. While some of these vesicles deposit their contents into other parts of the cell where they will be used, other secretory vesicles fuse with the plasma membrane and release their contents outside the cell.
In another example of form following function, cells that engage in a great deal of secretory activity (such as cells of the salivary glands that secrete digestive enzymes or cells of the immune system that secrete antibodies) have an abundance of Golgi. In plant cells, the Golgi apparatus has the additional role of synthesizing polysaccharides, some of which are incorporated into the cell wall and some of which are used in other parts of the cell.
LICENSES AND ATTRIBUTIONS
CC LICENSED CONTENT, SPECIFIC ATTRIBUTION
- OpenStax College, Biology. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest...ol11448/latest . License : CC BY: Attribution
- OpenStax College, Biology. October 21, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest...ol11448/latest . License : CC BY: Attribution
- histone. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/histone. License : CC BY-SA: Attribution-ShareAlike
- chromatin. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/chromatin. License : CC BY-SA: Attribution-ShareAlike
- Boundless. Provided by : Boundless Learning. Located at : www.boundless.com//biology/definition/nucleolus--2. License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Biology. October 23, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest...ol11448/latest . License : CC BY: Attribution
- OpenStax College, The Nucleus and DNA Replication. October 23, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m46073/latest/ . License : CC BY: Attribution
- OpenStax College, Biology. October 23, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest...ol11448/latest . License : CC BY: Attribution
- OpenStax College, Biology. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest/?collection=col11448/latest . License : CC BY: Attribution
- OpenStax College, Eukaryotic Origins. October 22, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44614/latest/ . License : CC BY: Attribution
- cofactor. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/cofactor. License : CC BY-SA: Attribution-ShareAlike
- adenosine triphosphate. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/adenosine%20triphosphate. License : CC BY-SA: Attribution-ShareAlike
- alpha-proteobacteria. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/alpha-proteobacteria. License : CC BY-SA: Attribution-ShareAlike
- Mitochondrion. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Mitochondrion. License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Biology. October 23, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest/?collection=col11448/latest . License : CC BY: Attribution
- OpenStax College, The Nucleus and DNA Replication. October 23, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m46073/latest/ . License : CC BY: Attribution
- OpenStax College, Biology. October 23, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest/?collection=col11448/latest . License : CC BY: Attribution
- OpenStax College, Eukaryotic Cells. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest...e_04_03_07.jpg . License : CC BY: Attribution
- OpenStax College, Biology. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest/?collection=col11448/latest . License : CC BY: Attribution
- protist. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/protist. License : CC BY-SA: Attribution-ShareAlike
- heterotroph. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/heterotroph. License : CC BY-SA: Attribution-ShareAlike
- autotroph. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/autotroph. License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Biology. October 23, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest/?collection=col11448/latest . License : CC BY: Attribution
- OpenStax College, The Nucleus and DNA Replication. October 23, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m46073/latest/ . License : CC BY: Attribution
- OpenStax College, Biology. October 23, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest/?collection=col11448/latest . License : CC BY: Attribution
- OpenStax College, Eukaryotic Cells. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest...e_04_03_07.jpg . License : CC BY: Attribution
- OpenStax College, Eukaryotic Cells. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest...e_04_03_08.jpg . License : CC BY: Attribution
- OpenStax College, Eukaryotic Cells. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest...e_04_03_10.jpg . License : CC BY: Attribution
- OpenStax College, Eukaryotic Cells. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest...e_04_03_09.jpg . License : CC BY: Attribution
- OpenStax College, Biology. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44435/latest...ol11448/latest . License : CC BY: Attribution
- reticulum. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/reticulum. License : CC BY-SA: Attribution-ShareAlike
- lumen. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/lumen. License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Biology. October 23, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest/?collection=col11448/latest . License : CC BY: Attribution
- OpenStax College, The Nucleus and DNA Replication. October 23, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m46073/latest/ . License : CC BY: Attribution
- OpenStax College, Biology. October 23, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest/?collection=col11448/latest . License : CC BY: Attribution
- OpenStax College, Eukaryotic Cells. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest/Figure_04_03_07.jpg . License : CC BY: Attribution
- OpenStax College, Eukaryotic Cells. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest...e_04_03_08.jpg . License : CC BY: Attribution
- OpenStax College, Eukaryotic Cells. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest...e_04_03_10.jpg . License : CC BY: Attribution
- OpenStax College, Eukaryotic Cells. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest...e_04_03_09.jpg . License : CC BY: Attribution
- OpenStax College, The Endomembrane System and Proteins. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44435/latest..._04_02_new.jpg . License : CC BY: Attribution
- OpenStax College, Biology. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44435/latest...ol11448/latest . License : CC BY: Attribution
- vesicle. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/vesicle. License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Biology. October 23, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest/?collection=col11448/latest . License : CC BY: Attribution
- OpenStax College, The Nucleus and DNA Replication. October 23, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m46073/latest/ . License : CC BY: Attribution
- OpenStax College, Biology. October 23, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest/?collection=col11448/latest . License : CC BY: Attribution
- OpenStax College, Eukaryotic Cells. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest/Figure_04_03_07.jpg . License : CC BY: Attribution
- OpenStax College, Eukaryotic Cells. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest...e_04_03_08.jpg . License : CC BY: Attribution
- OpenStax College, Eukaryotic Cells. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest...e_04_03_10.jpg . License : CC BY: Attribution
- OpenStax College, Eukaryotic Cells. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44407/latest...e_04_03_09.jpg . License : CC BY: Attribution
- OpenStax College, The Endomembrane System and Proteins. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44435/latest..._04_02_new.jpg . License : CC BY: Attribution
- OpenStax College, The Endomembrane System and Proteins. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44435/latest...e_04_04_03.jpg . License : CC BY: Attribution
Key Points
- The Golgi apparatus is a series of flattened sacs that sort and package cellular materials.
- The Golgi apparatus has a cis face on the ER side and a trans face opposite of the ER.
- The trans face secretes the materials into vesicles, which then fuse with the cell membrane for release from the cell.
Key Terms
- vesicle : A membrane-bound compartment found in a cell.


23.11: Conjugate Carbonyl Additions - The Michael Reaction
-
- Last updated
- Save as PDF
Objectives
After completing this section, you should be able to
- write an equation to illustrate the Michael reaction.
- write a detailed mechanism for a given typical Michael reaction.
- identify the product formed in a given Michael reaction.
- identify the reagents necessary to synthesize a given compound by a Michael reaction.
Key Terms
- Michael reaction
Study Notes
Before studying this section in detail, you should review conjugate addition to α , β ‑unsaturated carbonyl compounds (Section 19.13).
Notice the wide variety of compounds that can take part in a Michael reaction. As usual, you should not feel overwhelmed by the number of different compounds that can be used, just keep in mind that in all cases the mechanism is essentially the same.
Michael Reaction
Certain nucleophiles undergo conjugate addition with the alkene of an α, β-unsaturated carbonyl compounds rather than undergo direct nucleophilic addition with the carbonyl. During conjugate addition, a nucleophile adds to the electrophilic β-alkene carbon to from a C-Nuc bond. If the starting materials contains an ester the corresponding alkoxide is used as the base in the reaction. Otherwise a hydroxide base, such as sodium or potassium hydroxide, is commonly used.
When enolate nucleophiles undergo conjugate addition with an α, β-unsaturated carbonyl the process is called a Michael Reaction. The Michael reaction works best with particularly acidic enolate donors such as malonic esters, β-keto esters, etc. Enolates which are weaker acids tend to undergo nucleophilic addition to the carbonyl rather than conjugate addition. For example, malonic ester’s acidic alpha-hydrogens can be easily deprotonated by sodium ethoxide to form an enolate. The enolate adds to propenal to form the conjugate addition product.
Example \(\PageIndex{1}\)
Predicting the Product of a Michael Reaction
During the is reaction the C=C pi bond of the α, β-unsaturated carbonyl is broken. An C-H bond is formed on the carbon in the α-position from the carbonyl. An acidic hydrogen is removed from the nucleophile and then it is used to form a C-C bond with the carbon in the beta position from the carbonyl.
- In the first step, remove the double bond and add two single bonds
- Add a hydrogen to the bond adjacent to the carbonyl
- Add the nucleophile to the other end of the double bond (remember to remove a hydrogen from the nucleophile)
Worked Example \(\PageIndex{1}\)
What would be the product of the following conjugate addition?
Solution
- Break the double bond and add two single bonds
- Add a hydrogen to the bond adjacent to the carbonyl
- Remove a hydrogen from the nucleophile.
- Add the nucleophile to the other end of the double bond.
Mechanism of Michael Reaction
During a Michael reaction the enolate acts as a nucleophilic donor and the α, β-unsaturated carbonyl acts as the electrophilic acceptor. The mechanism is a mixture of an alpha-substitution for the enolate and a conjugate addition for the α, β-unsaturated carbonyl.
Notice that the Michael Reaction does not require the deprotonation of the product to push the reaction towards completion. The reaction is thermodynamically favorable because the C-C bond formed in the product is stronger than the C=C bond in the starting material. This means that, unlike the Claisen condensation, this reaction only requires a catalytic amount of reaction base.
Step 1: Deprotonation
The alkoxide base removes an alpha-hydrogen to from an enolate nucleophile.
Step 2: Nucleophilic attack on the carbon β to the carbonyl
The enolate nucleophile then adds to the electrophilic β-carbon of the α, β-unsaturated carbonyl. Conjugation pushes the C=C pi bond electrons onto the carbonyl oxygen, forming a new enolate enolate.
Step 3: Protonation
The alkoxide is protonated, forming an enol.
Step 4: Tautomerization
Tautomerization converts the enol back into a carbonyl forming the neutral conjugate addition product.
The Michael reaction can be performed with a wide variety of α, β-unsaturated carbonyl electrophilic acceptors and enolate donors. Michael acceptors such as α, β-unsaturated ketones, aldehydes, esters, amides, and nitro compounds can all participate in this reaction. Michael donors with particularly acidic α-hydrogens, such as β-diketones, β-keto esters, β-keto nitriles, α-nitro ketones, malonic esters, and nitro compounds can be used.
Table \(\PageIndex{1}\): Possible Donors and Acceptors Which can be used in a Michael Reaction
Stereochemical Consideration of Micheal Reactions
During a Michael reaction two sp 2 hybridized carbons are both converted to sp 3 hybridization. Both of them have the possibility of creating a chiral carbon. Michael reactions are often performed using an α, β-unsaturated carbonyl with only hydrogen substituents on the alkene to prevent the formation of chiral carbons. If either carbon in the alkene has an alkyl substituent it will likely form a chiral carbon in the Michael reaction product. The α-carbon of the enolate donor also has the possibility of forming a chiral carbon as discussed in Section 22-6.
Planning a Synthesis Using a Michael Reaction
The true utility of the Michael reaction is seen when considering it use in a synthesis. The reaction can be used to prepare aldehydes, ketones, esters, amides, nitriles, and nitro compounds. A target molecule can possibly be made using a Michael reaction if it contains one of these functional groups and an alkyl chain at least three carbons long. The key bond cleavage is a C-C bond between β and gamma carbons from a carbonyl-like group. The fragment with the Y group loses an α-hydrogen and then forms a C=C bond between the α and beta carbon. The carbon of the other fragment gains a hydrogen. This fragment should possess an acidic α-hydrogen and should be made up of Michael donor fragments such as those listed in Table \(\PageIndex{1}\) . In some cases, there may be more than one fragmentation variation. Each variation should be investigated and the possible starting materials compared for viability.
Example
How could the following molecule be synthesized using a Michael Reaction?
- Answer
-
Pathway 1
Starting Materials 1
Pathway 2
Starting Material 2
Solution
When comparing the two sets of possible starting materials of pathway 1 are preferred. The Michael enolate donor is particularly acidic because its conjugate base is stabilized by two carbonyls. The Michael enolate donor for pathway 2 does not have the same acidity. Consequently, the enolate would preferably undergo nucleophilic addition rather than conjugate addition. The makes the starting materials of pathway 1 preferred for the synthesis of the starting material.
In combination with alkylations and condensations, the Michael reaction may be used to construct a wide variety of complex molecules from relatively simple starting materials. The carbon nucleophiles used in the following examples include cyanide ion, sodium diethylmalonate and the conjugate base of cyclohexane-1,3-dione. These anions are sufficiently stable that their addition reactions may be presumed reversible. If this is so, the thermodynamic argument used for hetero-nucleophile additions would apply here as well, and would indicate preferential formation of 1,4-addition products. Cyanide addition does not always follow this rule, and aldehydes often give 1,2-products (cyanohydrins). In each case the initial reaction is a Michael addition, and the new carbon-carbon bond is colored magenta. Any subsequent bonds that are formed by other reactions are colored orange.
Exercise \(\PageIndex{1}\)
Provide the products of the following Michael additions:
- Answer
-
Exercise \(\PageIndex{2}\)
What would be the starting materials required to make the following molecule using a Michael reaction? Red = Oxygen, Grey = Carbon, White = Hydrogen, Blue = Nitrogen.
- Answers
-


8: Business Processes
Learning Objectives
Upon successful completion of this chapter, you will be able to:
- Define the term business process
- Identify different systems needed to support business processes in an organization
- Explain the value of an enterprise resource planning(ERP) system
- Explain how business process management and business process engineering work; and
- Understand how information technology combined with business processes can bring an organization competitive advantage.
Business processes are the essence of what a business does, and information systems play an important role in making them work. This chapter will discuss business process management, business process reengineering, and ERP systems.


8.7: The Immune System and Disease
-
- 8.7.1: Viruses
- Viruses are acellular, parasitic entities that are not classified within any domain because they are not considered alive. They have no plasma membrane, internal organelles, or metabolic processes, and they do not divide. Instead, they infect a host cell and use the host’s replication processes to produce progeny virus particles. Viruses infect all forms of organisms including bacteria, archaea, fungi, plants, and animals.
-
- 8.7.2: Innate Immunity
- Innate immunity is not caused by an infection or vaccination and depends initially on physical and chemical barriers that work on all pathogens, sometimes called the first line of defense. The second line of defense of the innate system includes chemical signals that produce inflammation and fever responses as well as mobilizing protective cells and other chemical defenses.
-
- 8.7.3: Adaptive Immunity
- The adaptive immune response is a slower-acting, longer-lasting, and more specific response than the innate response. However, the adaptive response requires information from the innate immune system to function. APCs display antigens on MHC molecules to naïve T cells. T cells with cell-surface receptors that bind a specific antigen will bind to that APC. In response, the T cells differentiate and proliferate.
-
- 8.7.4: Disruptions in the Immune System
- A functioning immune system is essential for survival, but even the sophisticated cellular and molecular defenses of the mammalian immune response can be defeated by pathogens at virtually every step. In the competition between immune protection and pathogen evasion, pathogens have the advantage of more rapid evolution because of their shorter generation time, large population sizes and often higher mutation rates. Thus pathogens have evolved a diverse array of immune escape mechanisms.
Thumbnail: The biohazard symbol was developed by the Dow Chemical Company in 1966 for their containment products. It is used in the labeling of biological materials that carry a significant health risk. (Public Domain; Silsor ).


5.2: Toggle Buttons (Activity Example)
The remainder of the instruction here is hands-on. You’ll be taking inaccessible widgets, like the example of toggle buttons described here, and making them accessible by adding appropriate WAI-ARIA and keyboard operability. The toggle buttons widget demonstrated here is provided as an example for the ten widgets you will be working on over the next three units, describing the Activity Elements you will find in each exercise.
Roles, states, and properties for toggle buttons
- role=”button”
- tabindex=”0″
- aria-label=”[button name]”
- aria-pressed=”[true|false]”
Activity Element: Each widget will have an inaccessible JSFiddle version provided, like the one below. You can examine the JavaScript and HTML to observe how the widget was created. Under the Result tab, view and try out the widget to see how it functions. CSS is also provided, though you will not be working with CSS as part of the activities. In the JSFiddle here, the accessibility elements are included but commented out so you can see how the code snippets below have been applied. In the activities that follow, the accessibility elements will not be present. Your task will be to apply the code snippets yourself to make the inaccessible version provided in the activity file accessible.
At the top right, you may choose to “Edit in JSFiddle” and test the code snippets that will be provided below, to understand how they add accessibility to the widget. You can start by uncommenting the accessibility elements for the toggle buttons, and testing the resulting version with ChromeVox.
The following JSFiddle presents a typical toggle button. Review the JavaScript and HTML markup. Test the buttons present under the Result tab with ChromeVox to understand how it functions without any accessibility features added (if it functions at all). You can work in JSFiddle itself by clicking “Edit in JSFiddle” and copying the accessibility/WAI-ARIA code described below to fix the accessibility of the toggle buttons, before completing the Activity on the page that follows (there is no activity that follows in this example case). Skip JSFiddle
Add a
tabindex
to each button to make them keyboard focusable, define the
role="button"
, and add a label with
aria-label="[button name]"
and set the default state to “not pressed” with
aria-pressed="false"
.
Add in equivalent keyboard access where mouse access is provided, referencing the
onActivate()
function, described below, with jQuery
.on('keydown')
.
Set
aria-pressed="[true|false]"
for buttons when activated or deactivated to announce the button’s state to screen readers.
Adding Keyboard Operability
Keyboard access for the buttons is fairly simple, with no special key press events needing to be defined.
Keyboard Interaction for Toggle Buttons
When the button has focus:
- Space: Activates the button.
- Enter: Activates the button.
-
Following button activation, focus is set depending on the type of action the button performs. For example:
- If activating the button opens a dialog, the focus moves inside the dialog (see dialog pattern ).
- If activating the button closes a dialog, focus typically returns to the button that opened the dialog unless the function performed in the dialog context logically leads to a different element. For example, activating a cancel button in a dialog returns focus to the button that opened the dialog. However, if the dialog were confirming the action of deleting the page from which it was opened, the focus would logically move to a new context.
- If activating the button does not dismiss the current context, then focus typically remains on the button after activation, e.g., an Apply or Recalculate button.
- If the button action indicates a context change, such as move to next step in a wizard or add another search criteria, then it is often appropriate to move focus to the starting point for that action.
- If the button is activated with a shortcut key, the focus usually remains in the context from which the shortcut key was activated. For example, if Alt + U were assigned to an “Up” button that moves the currently focused item in a list one position higher in the list, pressing Alt + U when the focus is in the list would not move the focus from the list.
Source: W3C WAI-ARIA 1.1 Authoring Practices
No added keyboard interaction is required for the toggle buttons beyond the standard Space bar and Enter key defined in the ik_utils.js file. Reference to these key events is added to the
onActivate()
function.
Accessible Toggle Buttons in Action
The buttons are accessed initially with the Tab key, and the Tab key is used to move between buttons. The Space bar or Enter keys are used to activate and deactivate buttons. Aim to have the widget you edit in the associated activity function like that presented in the video (there is no associated activity for this example).
Video: Accessible Toggle Buttons


1.3.4: A Model of Organizational Behavior and Management
-
- Last updated
- Save as PDF
4. What is the role of the behavioral sciences in management and organizations?
A major responsibility—perhaps the major responsibility—of managers is to make organizations operate effectively. Bringing about effective performance, however, is no easy task. As Nadler and Tushman note:
Understanding one individual’s behavior is challenging in and of itself; understanding a group that’s made up of different individuals and comprehending the many relationships among those individuals is even more complex. Imagine, then, the mind-boggling complexity of a large organization made up of thousands of individuals and hundreds of groups with myriad relationships among these individuals and groups. 11
Despite this difficulty, however, organizations must be managed. Nadler and Tushman continue:
Ultimately the organization’s work gets done through people, individually or collectively, on their own or in collaboration with technology. Therefore, the management of organizational behavior is central to the management task—a task that involves the capacity to understand the behavior patterns of individuals, groups, and organizations, to predict what behavioral responses will be elicited by various managerial actions, and finally to use this understanding and these predictions to achieve control . 12
The work of society is accomplished largely through organizations, and the role of management is to see to it that organizations perform this work. Without it, the wheels of society would soon grind to a halt.
What is Organizational Behaviour?
the focus is on applying what we can learn from the social and behavioral sciences so we can better understand and predict human behavior at work. We examine such behavior on three levels—the individual, the group, and the organization as a whole. In all three cases, we seek to learn more about what causes people—individually or collectively—to behave as they do in organizational settings. What motivates people? What makes some employees leaders and others not? Why do groups often work in opposition to their employer? How do organizations respond to changes in their external environments? How do people communicate and make decisions? Questions such as these constitute the domain of organizational behavior and are the focus of this course.
To a large extent, we can apply what has been learned from psychology, sociology, and cultural anthropology. In addition, we can learn from economics and political science. All of these disciplines have something to say about life in organizations. However, what sets organizational behavior apart is its particular focus on the organization (not the discipline) in organizational analysis (see Exhibit 1.8 ). Thus, if we wish to examine a problem of employee motivation, for example, we can draw upon economic theories of wage structures in the workplace. At the same time, we can also draw on the psychological theories of motivation and incentives as they relate to work. We can bring in sociological treatments of social forces on behavior, and we can make use of anthropological studies of cultural influences on individual performance. It is this conceptual richness that establishes organizational behavior as a unique applied discipline. And throughout our analyses, we are continually concerned with the implications of what we learn for the quality of working life and organizational performance. We always look for management implications so the managers of the future can develop more humane and more competitive organizations for the future.
For convenience, we often differentiate between micro- and macro-organizational behavior. Micro- organizational behavior is primarily concerned with the behavior of individuals and groups, while macro- organizational behavior (also referred to as organization theory ) is concerned with organization-wide issues, such as organization design and the relations between an organization and its environment. Although there are times when this distinction is helpful, it is always important to remember that in most instances we learn the most when we take a comprehensive view of organizational behavior and integrate these two perspectives. That is, issues such as organization structure can influence employee motivation. Hence, by keeping these two realms separate we lose valuable information that can help us better understand how to manage organizations.
Building Blocks of Organizations
Understanding the behavior of people at work is fundamental to the effective management of an organization. Obviously, a number of factors come together to determine this behavior and its organizational consequences. In order to understand the origins and characteristics of these factors, it is necessary to have a model that organizes and simplifies the variables involved. We offer such a model here in the hope that it will bring some order to the study of this subject. The model can be considered in two parts (see Exhibit 1.10 ).
The first part of the model is the simple recognition of organizational inputs and outcomes. That is, organizations receive inputs from the external environment in the form of capital, raw materials, labor, community or government support, and so forth. In addition, organizations experience or produce certain outcomes, including (1) organizational goal attainment, (2) group performance and effectiveness, and (3) individual performance and effectiveness. Thus, organizations and the people in them exist in a constant state of flux, receiving and transforming inputs from the environment and returning those transformed inputs in the form of finished goods and services, return on stockholders’ equity, salaries that are paid to employees, and so forth. It is, in short, a dynamic system.
The second aspect of the model is the organization itself and all of its parts. One way to understand the complexity of organizations is to think of them simply as a set of building blocks, including:
Individuals and groups. Organizations are collectives of individuals and groups working to pursue common objectives. Their members come from various backgrounds and have varying abilities and skills, differing motivational levels, and different ambitions. Within the organizational context, these people must communicate, make decisions, show leadership, and handle power and organizational politics as they carry out their assigned activities.
Tasks and technology. In addition to variations among individuals and groups, we must recognize variations in the technology of the workplace. That is, how does the work actually get done? Technology includes both the actual design of jobs and the tools and techniques used in manufacture (e.g., robotics and expert systems).
Organization design. Putting together these factors—individuals and groups and tasks—is the subject of organization design . That is, how do we structure an organization so it effectively coordinates and controls employee behavior to facilitate performance?
Organizational processes. In addition to people, machines, and structure, we must recognize a series of organizational processes , such as leadership, communication, decision-making, power and politics, and so forth. The processes largely determine the nature and quality of interpersonal and intergroup relations within the workplace and, as such, influence ultimate organizational performance.
Management. Finally, the glue that holds these building blocks together is the character of management. Throughout this text, we shall see numerous examples of how the degree of managerial effectiveness and prowess have determined the success or failure of a venture. We shall take a managerial view throughout our survey of organizational behavior.
There have been many attempts to provide a differentiation between leadership and management over time. While they are not the same thing, they are necessarily linked, and complementary. Any effort to separate the two is likely to cause more problems than it solves and as business evolved the content of leadership and management has changed. The emergence of the “knowledge worker,” and the profound differences that this causes the way business is organized. With the rise of the knowledge worker, one does not ‘manage’ people, and instead the task is to lead people and the goal is to make productive the specific strengths and knowledge of every individual.
These five variables, then, will constitute the primary ingredients of this book. We shall proceed sequentially, beginning with individual behavior and moving to group and intergroup behavior and finally to organization design and structure. On the basis of this, we will turn to a consideration of several of the more important organizational processes. Finally, we will look to the future and examine ways that organizations can continue to develop and improve their workforces and the organization as a whole. Throughout, the roles of technology and management will be considered. Also, throughout, we will blend theory with research and practice.
Concept Check
1. Discuss the role of management in the larger societal context.
2. What do you think the managers of the future will be like?
3. Identify what you think are the critical issues facing contemporary management. Explain.
11 D. Nadler and M. Tushman, “A Model for Diagnosing Organizational Behavior,” Organizational Dynamics, 1980, p. 35.
12 Ibid.
Exhibit 1.8 (Attribution: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license)
Exhibit 1.9 Xinyu Liu was hired as the studio as a designer at Invo, a Massachusetts-based firm. Prior to joining Invo, she was a user experience researcher at Samsung, where she investigated how to apply future technologies in everyday living. Changing behavior for good was a key component of the R&D work, leveraging invisible sensing tech, devising emotional effects, and crafting just-in-time graphic communication. Her wide-ranging skills, from analyzing social behavior to 3D modeling to electronics to UI design, are well-suited for the multi- domain projects at Invo. As part of the employee selection process, the hiring managers at Invo needed to recognize that their employees come from various backgrounds and have varying abilities and skills, differing motivational levels, and different ambitions. Within the organizational context, they needed to consider how Xinyu would fit on the team in the areas of communication, decision-making, and leadership, and how she would handle power and organizational politics as she carried out her responsibilities. (Credit: Juhan Sonin/ flickr/ Attribution 2.0 Generic (CC BY 2.0))
Exhibit 1.10 (Attribution: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license)


2.14: Introduction to Dotplots
What you’ll learn to do: Describe the distribution of quantitative data using a dotplot.
When we conduct statistical experiments, we often work with large tables that present each individual’s information. To analyze the data, we look to summarize information and patterns about the group as a whole, not just on the individual level. A dotplot is a simple and powerful tool to display the distribution of the data: showing the center, spread, skew, and possible outliers. In this next section, we shall see how to construct and interpret dotplots as well as build basic vocabulary to talk about the distribution (aka shape) of the data.
Contributors and Attributions
CC licensed content, Shared previously
- Concepts in Statistics. Provided by : Open Learning Initiative. Located at : http://oli.cmu.edu . License : CC BY: Attribution