2.4: Analyzing Findings
Learning Objectives
- Explain what a correlation coefficient tells us about the relationship between variables
- Recognize that correlation does not indicate a cause-and-effect relationship between variables
- Discuss our tendency to look for relationships between variables that do not really exist
- Explain random sampling and assignment of participants into experimental and control groups
- Discuss how experimenter or participant bias could affect the results of an experiment
- Identify independent and dependent variables
Did you know that as sales in ice cream increase, so does the overall rate of crime? Is it possible that indulging in your favorite flavor of ice cream could send you on a crime spree? Or, after committing crime do you think you might decide to treat yourself to a cone? There is no question that a relationship exists between ice cream and crime (e.g., Harper, 2013), but it would be pretty foolish to decide that one thing actually caused the other to occur.
It is much more likely that both ice cream sales and crime rates are related to the temperature outside. When the temperature is warm, there are lots of people out of their houses, interacting with each other, getting annoyed with one another, and sometimes committing crimes. Also, when it is warm outside, we are more likely to seek a cool treat like ice cream. How do we determine if there is indeed a relationship between two things? And when there is a relationship, how can we discern whether it is attributable to coincidence or causation?
Correlational Research
Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from \(-1\) to \(+1\) that indicates the strength and direction of the relationship between variables. The correlation coefficient is usually represented by the letter r .
The number portion of the correlation coefficient indicates the strength of the relationship. The closer the number is to \(1\) (be it negative or positive), the more strongly related the variables are, and the more predictable changes in one variable will be as the other variable changes. The closer the number is to zero, the weaker the relationship, and the less predictable the relationships between the variables becomes. For instance, a correlation coefficient of \(0.9\) indicates a far stronger relationship than a correlation coefficient of \(0.3\). If the variables are not related to one another at all, the correlation coefficient is \(0\). The example above about ice cream and crime is an example of two variables that we might expect to have no relationship to each other.
The sign—positive or negative—of the correlation coefficient indicates the direction of the relationship. A positive correlation means that the variables move in the same direction. Put another way, it means that as one variable increases so does the other, and conversely, when one variable decreases so does the other. A negative correlation means that the variables move in opposite directions. If two variables are negatively correlated, a decrease in one variable is associated with an increase in the other and vice versa.
The example of ice cream and crime rates is a positive correlation because both variables increase when temperatures are warmer. Other examples of positive correlations are the relationship between an individual’s height and weight or the relationship between a person’s age and number of wrinkles. One might expect a negative correlation to exist between someone’s tiredness during the day and the number of hours they slept the previous night: the amount of sleep decreases as the feelings of tiredness increase. In a real-world example of negative correlation, student researchers at the University of Minnesota found a weak negative correlation (\(r = -0.29\)) between the average number of days per week that students got fewer than \(5\) hours of sleep and their GPA (Lowry, Dean, & Manders, 2010). Keep in mind that a negative correlation is not the same as no correlation. For example, we would probably find no correlation between hours of sleep and shoe size.
As mentioned earlier, correlations have predictive value. Imagine that you are on the admissions committee of a major university. You are faced with a huge number of applications, but you are able to accommodate only a small percentage of the applicant pool.  You might try to correlate your current students’ college GPA with their scores on standardized tests like the SAT or ACT. By observing which correlations were strongest for your current students, you could use this information to predict relative success of those students who have applied for admission into the university.
Correlation Does Not Indicate Causation
Correlational research is useful because it allows us to discover the strength and direction of relationships that exist between two variables. However, correlation is limited because establishing the existence of a relationship tells us little about cause and effect . While variables are sometimes correlated because one does cause the other, it could also be that some other factor, a confounding variable, is actually causing the systematic movement in our variables of interest. In the ice cream/crime rate example mentioned earlier, temperature is a confounding variable that could account for the relationship between the two variables.
Even when we cannot point to clear confounding variables, we should not assume that a correlation between two variables implies that one variable causes changes in another. This can be frustrating when a cause-and-effect relationship seems clear and intuitive. Think back to our discussion of the research done by the American Cancer Society and how their research projects were some of the first demonstrations of the link between smoking and cancer. It seems reasonable to assume that smoking causes cancer, but if we were limited to correlational research , we would be overstepping our bounds by making this assumption.
Unfortunately, people mistakenly make claims of causation as a function of correlations all the time. Such claims are especially common in advertisements and news stories.  Guess how the cereal companies report this finding. Does eating cereal really cause an individual to maintain a healthy weight, or are there other possible explanations, such as, someone at a healthy weight is more likely to regularly eat a healthy breakfast than someone who is obese or someone who avoids meals in an attempt to diet? While correlational research is invaluable in identifying relationships among variables, a major limitation is the inability to establish causality. Psychologists want to make statements about cause and effect, but the only way to do that is to conduct an experiment to answer a research question. The next section describes how scientific experiments incorporate methods that eliminate, or control for, alternative explanations, which allow researchers to explore how changes in one variable cause changes in another variable.
Illusory Correlations
The temptation to make erroneous cause-and-effect statements based on correlational research is not the only way we tend to misinterpret data. We also tend to make the mistake of illusory correlations, especially with unsystematic observations. Illusory correlations , or false correlations, occur when people believe that relationships exist between two things when no such relationship exists. One well-known illusory correlation is the supposed effect that the moon’s phases have on human behavior. Many people passionately assert that human behavior is affected by the phase of the moon, and specifically, that people act strangely when the moon is full.
There is no denying that the moon exerts a powerful influence on our planet. The ebb and flow of the ocean’s tides are tightly tied to the gravitational forces of the moon. Many people believe, therefore, that it is logical that we are affected by the moon as well. After all, our bodies are largely made up of water. A meta-analysis of nearly \(40\) studies consistently demonstrated, however, that the relationship between the moon and our behavior does not exist (Rotton & Kelly, 1985). While we may pay more attention to odd behavior during the full phase of the moon, the rates of odd behavior remain constant throughout the lunar cycle.
Why are we so apt to believe in illusory correlations like this? Often we read or hear about them and simply accept the information as valid. Or, we have a hunch about how something works and then look for evidence to support that hunch, ignoring evidence that would tell us our hunch is false; this is known as confirmation bias . Other times, we find illusory correlations based on the information that comes most easily to mind, even if that information is severely limited. And while we may feel confident that we can use these relationships to better understand and predict the world around us, illusory correlations can have significant drawbacks. For example, research suggests that illusory correlations—in which certain behaviors are inaccurately attributed to certain groups—are involved in the formation of prejudicial attitudes that can ultimately lead to discriminatory behavior (Fiedler, 2004).
Causality: Conducting Experiments and using the Data
As you’ve learned, the only way to establish that there is a cause-and-effect relationship between two variables is to conduct a scientific experiment . Experiment has a different meaning in the scientific context than in everyday life. In everyday conversation, we often use it to describe trying something for the first time, such as experimenting with a new hair style or a new food. However, in the scientific context, an experiment has precise requirements for design and implementation.
The Experimental Hypothesis
In order to conduct an experiment, a researcher must have a specific hypothesis to be tested. As you’ve learned, hypotheses can be formulated either through direct observation of the real world or after careful review of previous research. For example, if you think that children should not be allowed to watch violent programming on television because doing so would cause them to behave more violently, then you have basically formulated a hypothesis—namely, that watching violent television programs causes children to behave more violently. How might you have arrived at this particular hypothesis? You may have younger relatives who watch cartoons featuring characters using martial arts to save the world from evildoers, with an impressive array of punching, kicking, and defensive postures. You notice that after watching these programs for a while, your young relatives mimic the fighting behavior of the characters portrayed in the cartoon.
These sorts of personal observations are what often lead us to formulate a specific hypothesis, but we cannot use limited personal observations and anecdotal evidence to rigorously test our hypothesis. Instead, to find out if real-world data supports our hypothesis, we have to conduct an experiment.
Designing an Experiment
The most basic experimental design involves two groups: the experimental group and the control group. The two groups are designed to be the same except for one difference— experimental manipulation. The experimental group gets the experimental manipulation—that is, the treatment or variable being tested (in this case, violent TV images)—and the control group does not. Since experimental manipulation is the only difference between the experimental and control groups, we can be sure that any differences between the two are due to experimental manipulation rather than chance.
In our example of how violent television programming might affect violent behavior in children, we have the experimental group view violent television programming for a specified time and then measure their violent behavior. We measure the violent behavior in our control group after they watch nonviolent television programming for the same amount of time. It is important for the control group to be treated similarly to the experimental group, with the exception that the control group does not receive the experimental manipulation. Therefore, we have the control group watch non-violent television programming for the same amount of time as the experimental group.
We also need to precisely define, or operationalize, what is considered violent and nonviolent. An operational definition is a description of how we will measure our variables, and it is important in allowing others understand exactly how and what a researcher measures in a particular experiment. In operationalizing violent behavior, we might choose to count only physical acts like kicking or punching as instances of this behavior, or we also may choose to include angry verbal exchanges. Whatever we determine, it is important that we operationalize violent behavior in such a way that anyone who hears about our study for the first time knows exactly what we mean by violence. This aids peoples’ ability to interpret our data as well as their capacity to repeat our experiment should they choose to do so.
Once we have operationalized what is considered violent television programming and what is considered violent behavior from our experiment participants, we need to establish how we will run our experiment. In this case, we might have participants watch a \(30\)-minute television program (either violent or nonviolent, depending on their group membership) before sending them out to a playground for an hour where their behavior is observed and the number and type of violent acts is recorded.
Ideally, the people who observe and record the children’s behavior are unaware of who was assigned to the experimental or control group, in order to control for experimenter bias. Experimenter bias refers to the possibility that a researcher’s expectations might skew the results of the study. Remember, conducting an experiment requires a lot of planning, and the people involved in the research project have a vested interest in supporting their hypotheses. If the observers knew which child was in which group, it might influence how much attention they paid to each child’s behavior as well as how they interpreted that behavior. By being blind to which child is in which group, we protect against those biases. This situation is a single-blind study , meaning that one of the groups (participants) are unaware as to which group they are in (experiment or control group) while the researcher who developed the experiment knows which participants are in each group.
In a double-blind study , both the researchers and the participants are blind to group assignments. Why would a researcher want to run a study where no one knows who is in which group? Because by doing so, we can control for both experimenter and participant expectations. If you are familiar with the phrase placebo effect , you already have some idea as to why this is an important consideration. The placebo effect occurs when people's expectations or beliefs influence or determine their experience in a given situation. In other words, simply expecting something to happen can actually make it happen.
The placebo effect is commonly described in terms of testing the effectiveness of a new medication. Imagine that you work in a pharmaceutical company, and you think you have a new drug that is effective in treating depression. To demonstrate that your medication is effective, you run an experiment with two groups: The experimental group receives the medication, and the control group does not. But you don’t want participants to know whether they received the drug or not.
Why is that?  Because you expect the pill to have an effect, you might feel better simply because you took the pill and not because of any drug actually contained in the pill—this is the placebo effect.
To make sure that any effects on mood are due to the drug and not due to expectations, the control group receives a placebo (in this case a sugar pill). Now everyone gets a pill, and once again neither the researcher nor the experimental participants know who got the drug and who got the sugar pill. Any differences in mood between the experimental and control groups can now be attributed to the drug itself rather than to experimenter bias or participant expectations.
Independent and Dependent Variables
In a research experiment, we strive to study whether changes in one thing cause changes in another. To achieve this, we must pay attention to two important variables, or things that can be changed, in any experimental study: the independent variable and the dependent variable. An independent variable is manipulated or controlled by the experimenter. In a well-designed experimental study, the independent variable is the only important difference between the experimental and control groups. In our example of how violent television programs affect children’s display of violent behavior, the independent variable is the type of program—violent or nonviolent—viewed by participants in the study. A dependent variable is what the researcher measures to see how much effect the independent variable had. In our example, the dependent variable is the number of violent acts displayed by the experimental participants.
We expect that the dependent variable will change as a function of the independent variable. In other words, the dependent variable depends on the independent variable. A good way to think about the relationship between the independent and dependent variables is with this question: What effect does the independent variable have on the dependent variable? Returning to our example, what effect does watching a half hour of violent television programming or nonviolent television programming have on the number of incidents of physical aggression displayed on the playground?
Selecting and Assigning Experimental Participants
Now that our study is designed, we need to obtain a sample of individuals to include in our experiment. Our study involves human participants so we need to determine who to include. Participants are the subjects of psychological research, and as the name implies, individuals who are involved in psychological research actively participate in the process. Often, psychological research projects rely on college students to serve as participants. In fact, the vast majority of research in psychology subfields has historically involved students as research participants (Sears, 1986; Arnett, 2008). But are college students truly representative of the general population? College students tend to be younger, more educated, more liberal, and less diverse than the general population. Although using students as test subjects is an accepted practice, relying on such a limited pool of research participants can be problematic because it is difficult to generalize findings to the larger population.
Our hypothetical experiment involves children, and we must first generate a sample of child participants. Samples are used because populations are usually too large to reasonably involve every member in our particular experiment. If possible, we should use a random sample (there are other types of samples, but for the purposes of this chapter, we will focus on random samples). A random sample is a subset of a larger population in which every member of the population has an equal chance of being selected. Random samples are preferred because if the sample is large enough we can be reasonably sure that the participating individuals are representative of the larger population. This means that the percentages of characteristics in the sample—sex, ethnicity, socioeconomic level, and any other characteristics that might affect the results—are close to those percentages in the larger population.
In our example, let’s say we decide our population of interest is fourth graders. But all fourth graders is a very large population, so we need to be more specific; instead we might say our population of interest is all fourth graders in a particular city. We should include students from various income brackets, family situations, races, ethnicities, religions, and geographic areas of town. With this more manageable population, we can work with the local schools in selecting a random sample of around \(200\) fourth graders who we want to participate in our experiment.
In summary, because we cannot test all of the fourth graders in a city, we want to find a group of about \(200\) that reflects the composition of that city. With a representative group, we can generalize our findings to the larger population without fear of our sample being biased in some way.
Now that we have a sample, the next step of the experimental process is to split the participants into experimental and control groups through random assignment. With random assignment , all participants have an equal chance of being assigned to either group. There is statistical software that will randomly assign each of the fourth graders in the sample to either the experimental or the control group.
Random assignment is critical for sound experimental design . With sufficiently large samples, random assignment makes it unlikely that there are systematic differences between the groups. So, for instance, it would be very unlikely that we would get one group composed entirely of males, a given ethnic identity, or a given religious ideology. This is important because if the groups were systematically different before the experiment began, we would not know the origin of any differences we find between the groups: Were the differences preexisting, or were they caused by manipulation of the independent variable? Random assignment allows us to assume that any differences observed between experimental and control groups result from the manipulation of the independent variable.
Issues to Consider
While experiments allow scientists to make cause-and-effect claims, they are not without problems. True experiments require the experimenter to manipulate an independent variable, and that can complicate many questions that psychologists might want to address. For instance, imagine that you want to know what effect sex (the independent variable) has on spatial memory (the dependent variable). Although you can certainly look for differences between males and females on a task that taps into spatial memory, you cannot directly control a person’s sex. We categorize this type of research approach as quasi-experimental and recognize that we cannot make cause-and-effect claims in these circumstances.
Experimenters are also limited by ethical constraints. For instance, you would not be able to conduct an experiment designed to determine if experiencing abuse as a child leads to lower levels of self-esteem among adults. To conduct such an experiment, you would need to randomly assign some experimental participants to a group that receives abuse, and that experiment would be unethical.
Interpreting Experimental Findings
Once data is collected from both the experimental and the control groups, a statistical analysis is conducted to find out if there are meaningful differences between the two groups. A statistical analysis determines how likely any difference found is due to chance (and thus not meaningful). In psychology, group differences are considered meaningful, or significant, if the odds that these differences occurred by chance alone are \(5\) percent or less. Stated another way, if we repeated this experiment \(100\) times, we would expect to find the same results at least \(95\) times out of \(100\).
The greatest strength of experiments is the ability to assert that any significant differences in the findings are caused by the independent variable. This occurs because random selection, random assignment, and a design that limits the effects of both experimenter bias and participant expectancy should create groups that are similar in composition and treatment. Therefore, any difference between the groups is attributable to the independent variable, and now we can finally make a causal statement. If we find that watching a violent television program results in more violent behavior than watching a nonviolent program, we can safely say that watching violent television programs causes an increase in the display of violent behavior.
Reporting Research
When psychologists complete a research project, they generally want to share their findings with other scientists. The American Psychological Association (APA) publishes a manual detailing how to write a paper for submission to scientific journals. Unlike an article that might be published in a magazine like Psychology Today, which targets a general audience with an interest in psychology, scientific journals generally publish peer-reviewed journal articles aimed at an audience of professionals and scholars who are actively involved in research themselves.
A peer-reviewed journal article is read by several other scientists (generally anonymously) with expertise in the subject matter. These peer reviewers provide feedback—to both the author and the journal editor—regarding the quality of the draft. Peer reviewers look for a strong rationale for the research being described, a clear description of how the research was conducted, and evidence that the research was conducted in an ethical manner. They also look for flaws in the study's design, methods, and statistical analyses. They check that the conclusions drawn by the authors seem reasonable given the observations made during the research. Peer reviewers also comment on how valuable the research is in advancing the discipline’s knowledge. This helps prevent unnecessary duplication of research findings in the scientific literature and, to some extent, ensures that each research article provides new information. Ultimately, the journal editor will compile all of the peer reviewer feedback and determine whether the article will be published in its current state (a rare occurrence), published with revisions, or not accepted for publication.
Peer review provides some degree of quality control for psychological research. Poorly conceived or executed studies can be weeded out, and even well-designed research can be improved by the revisions suggested. Peer review also ensures that the research is described clearly enough to allow other scientists to replicate it, meaning they can repeat the experiment using different samples to determine reliability. Sometimes replications involve additional measures that expand on the original finding. In any case, each replication serves to provide more evidence to support the original research findings. Successful replications of published research make scientists more apt to adopt those findings, while repeated failures tend to cast doubt on the legitimacy of the original article and lead scientists to look elsewhere. For example, it would be a major advancement in the medical field if a published study indicated that taking a new drug helped individuals achieve a healthy weight without changing their diet. But if other scientists could not replicate the results, the original study’s claims would be questioned.
DIG DEEPER: The Vaccine-Autism Myth and Retraction of Published Studies
Some scientists have claimed that routine childhood vaccines cause some children to develop autism, and, in fact, several peer-reviewed publications published research making these claims. Since the initial reports, large-scale epidemiological research has suggested that vaccinations are not responsible for causing autism and that it is much safer to have your child vaccinated than not. Furthermore, several of the original studies making this claim have since been retracted.
A published piece of work can be rescinded when data is called into question because of falsification, fabrication, or serious research design problems. Once rescinded, the scientific community is informed that there are serious problems with the original publication. Retractions can be initiated by the researcher who led the study, by research collaborators, by the institution that employed the researcher, or by the editorial board of the journal in which the article was originally published. In the vaccine-autism case, the retraction was made because of a significant conflict of interest in which the leading researcher had a financial interest in establishing a link between childhood vaccines and autism (Offit, 2008). Unfortunately, the initial studies received so much media attention that many parents around the world became hesitant to have their children vaccinated ( Figure ). For more information about how the vaccine/autism story unfolded, as well as the repercussions of this story, take a look at Paul Offit’s book, Autism’s False Prophets: Bad Science, Risky Medicine, and the Search for a Cure.
Reliability and Validity
Reliability and validity are two important considerations that must be made with any type of data collection. Reliability refers to the ability to consistently produce a given result. In the context of psychological research, this would mean that any instruments or tools used to collect data do so in consistent, reproducible ways.
Unfortunately, being consistent in measurement does not necessarily mean that you have measured something correctly. To illustrate this concept, consider a kitchen scale that would be used to measure the weight of cereal that you eat in the morning. If the scale is not properly calibrated, it may consistently under- or overestimate the amount of cereal that’s being measured. While the scale is highly reliable in producing consistent results (e.g., the same amount of cereal poured onto the scale produces the same reading each time), those results are incorrect. This is where validity comes into play. Validity refers to the extent to which a given instrument or tool accurately measures what it’s supposed to measure. While any valid measure is by necessity reliable, the reverse is not necessarily true. Researchers strive to use instruments that are both highly reliable and valid.
EVERYDAY CONNECTION: How Valid Is the SAT?
Standardized tests like the SAT are supposed to measure an individual’s aptitude for a college education, but how reliable and valid are such tests? Research conducted by the College Board suggests that scores on the SAT have high predictive validity for first-year college students’ GPA (Kobrin, Patterson, Shaw, Mattern, & Barbuti, 2008). In this context, predictive validity refers to the test’s ability to effectively predict the GPA of college freshmen. Given that many institutions of higher education require the SAT for admission, this high degree of predictive validity might be comforting.
However, the emphasis placed on SAT scores in college admissions has generated some controversy on a number of fronts. For one, some researchers assert that the SAT is a biased test that places minority students at a disadvantage and unfairly reduces the likelihood of being admitted into a college (Santelices & Wilson, 2010). Additionally, some research has suggested that the predictive validity of the SAT is grossly exaggerated in how well it is able to predict the GPA of first-year college students. In fact, it has been suggested that the SAT’s predictive validity may be overestimated by as much as \(150\%\) (Rothstein, 2004). Many institutions of higher education are beginning to consider de-emphasizing the significance of SAT scores in making admission decisions (Rimer, 2008).
In 2014, College Board president David Coleman expressed his awareness of these problems, recognizing that college success is more accurately predicted by high school grades than by SAT scores. To address these concerns, he has called for significant changes to the SAT exam (Lewin, 2014).
Summary
A correlation is described with a correlation coefficient, \(r\), which ranges from \(-1\) to \(+1\). The correlation coefficient tells us about the nature (positive or negative) and the strength of the relationship between two or more variables. Correlations do not tell us anything about causation—regardless of how strong the relationship is between variables. In fact, the only way to demonstrate causation is by conducting an experiment. People often make the mistake of claiming that correlations exist when they really do not.
Researchers can test cause-and-effect hypotheses by conducting experiments. Ideally, experimental participants are randomly selected from the population of interest. Then, the participants are randomly assigned to their respective groups. Sometimes, the researcher and the participants are blind to group membership to prevent their expectations from influencing the results.
In ideal experimental design, the only difference between the experimental and control groups is whether participants are exposed to the experimental manipulation. Each group goes through all phases of the experiment, but each group will experience a different level of the independent variable: the experimental group is exposed to the experimental manipulation, and the control group is not exposed to the experimental manipulation. The researcher then measures the changes that are produced in the dependent variable in each group. Once data is collected from both groups, it is analyzed statistically to determine if there are meaningful differences between the groups.
Psychologists report their research findings in peer-reviewed journal articles. Research published in this format is checked by several other psychologists who serve as a filter separating ideas that are supported by evidence from ideas that are not. Replication has an important role in ensuring the legitimacy of published research. In the long run, only those findings that are capable of being replicated consistently will achieve consensus in the scientific community.
Glossary
- cause-and-effect relationship
- changes in one variable cause the changes in the other variable; can be determined only through an experimental research design
- confirmation bias
- tendency to ignore evidence that disproves ideas or beliefs
- confounding variable
- unanticipated outside factor that affects both variables of interest, often giving the false impression that changes in one variable causes changes in the other variable, when, in actuality, the outside factor causes changes in both variables
- control group
- serves as a basis for comparison and controls for chance factors that might influence the results of the study—by holding such factors constant across groups so that the experimental manipulation is the only difference between groups
- correlation
- relationship between two or more variables; when two variables are correlated, one variable changes as the other does
- correlation coefficient
- number from -1 to +1, indicating the strength and direction of the relationship between variables, and usually represented by r
- dependent variable
- variable that the researcher measures to see how much effect the independent variable had
- double-blind study
- experiment in which both the researchers and the participants are blind to group assignments
- experimental group
- group designed to answer the research question; experimental manipulation is the only difference between the experimental and control groups, so any differences between the two are due to experimental manipulation rather than chance
- experimenter bias
- researcher expectations skew the results of the study
- illusory correlation
- seeing relationships between two things when in reality no such relationship exists
- independent variable
- variable that is influenced or controlled by the experimenter; in a sound experimental study, the independent variable is the only important difference between the experimental and control group
- negative correlation
- two variables change in different directions, with one becoming larger as the other becomes smaller; a negative correlation is not the same thing as no correlation
- operational definition
- description of what actions and operations will be used to measure the dependent variables and manipulate the independent variables
- participants
- subjects of psychological research
- peer-reviewed journal article
- article read by several other scientists (usually anonymously) with expertise in the subject matter, who provide feedback regarding the quality of the manuscript before it is accepted for publication
- placebo effect
- people's expectations or beliefs influencing or determining their experience in a given situation
- positive correlation
- two variables change in the same direction, both becoming either larger or smaller
- random assignment
- method of experimental group assignment in which all participants have an equal chance of being assigned to either group
- random sample
- subset of a larger population in which every member of the population has an equal chance of being selected
- reliability
- consistency and reproducibility of a given result
- replicate
- repeating an experiment using different samples to determine the research’s reliability
- single-blind study
- experiment in which the researcher knows which participants are in the experimental group and which are in the control group
- statistical analysis
- determines how likely any difference between experimental groups is due to chance
- validity
- accuracy of a given result in measuring what it is designed to measure
Contributors and Attributions
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7.2: 5 Ways of Looking at a Thesis
1. A thesis says something a little strange.
Consider the following examples:
A: By telling the story of Westley and Buttercup’s triumph over evil, The Princess Bride affirms the power of true love.
B: Although the main plot of The Princess Bride rests on the natural power of true love, an examination of the way that fighting sticks—baseball bats, tree branches, and swords—link the frame story to the romance plot suggests that the grandson is being trained in true love, that love is not natural but socialized.
I would argue that both of these statements are perfectly correct, but they are not both strange. Only the second one says something, well, weird. Weird is good. Sentence A encourages the paper to produce precisely the evidence that The Princess Bride presents explicitly; sentence B ensures that the paper will talk about something new.
Romeo and Juliet concerns the dangers of family pride, Frankenstein the dangers of taking science too far. Yup. How can you make those things unusual? Good papers go out on a limb. They avoid ugly falls by reinforcing the limb with carefully chosen evidence and rigorous argumentation.
2. A thesis creates an argument that builds from one point to the next, giving the paper a direction that your reader can follow as the paper develops.
This point often separates the best theses from the pack. A good thesis can prevent the two weakest ways of organizing a critical paper: the pile of information and the plot summary with comments. A paper that presents a pile of information will frequently introduce new paragraphs with transitions that simply indicate the addition of more stuff. (“Another character who exhibits these traits is X,” for instance.) Consider these examples:
A: The Rules and Jane Austen’s Northanger Abbey both tell women how to act.
B: By looking at The Rules, a modern conduct book for women, we can see how Jane Austen’s Northanger Abbey is itself like a conduct book, questioning the rules for social success in her society and offering a new model.
Example A would almost inevitably lead to a paper organized as a pile of information. A plot summary with comments follows the chronological development of a text while picking out the same element of every segment; a transition in such a paper might read, “In the next scene, the color blue also figures prominently.” Both of these approaches constitute too much of a good thing. Papers must compile evidence, of course, and following the chronology of a text can sometimes help a reader keep track of a paper’s argument. The best papers, however, will develop according to a more complex logic articulated in a strong thesis. Example B above would lead a paper to organize its evidence according to the paper’s own logic.
3. A thesis fits comfortably into the Magic Thesis Sentence (MTS).
The MTS: By looking at _____, we can see _____, which most readers don’t see; it is important to look at this aspect of the text because _____.
Try it out with the examples from the first point:
A: By telling the story of Westley and Buttercup’s triumph over evil, The Princess Bride affirms the power of true love.
B: Although the main plot of The Princess Bride rests on the natural power of true love, an examination of the way that fighting sticks–baseball bats, tree branches, and swords–link the frame story to the romance plot suggests that the grandson is being trained in true love, that love is not natural but socialized.
Notice that the MTS adds a new dimension to point number one above. The first part of the MTS asks you to find something strange (“which most readers don’t see”), and the second part asks you to think about the importance of the strangeness. Thesis A would not work at all in the MTS; one could not reasonably state that “most readers [or viewers] don’t see” that film’s affirmation of true love, and the statement does not even attempt to explain the importance of its claim. Thesis B, on the other hand, gives us a way to complete the MTS, as in “By looking at the way fighting sticks link the plot and frame of The Princess Bride , we can see the way the grandson is trained in true love, which most people don’t see; it is important to look at this aspect of the text because unlike the rest of the film, the fighting sticks suggest that love is not natural but socialized.” One does not need to write out the MTS in such a neat one-sentence form, of course, but thinking through the structure of the MTS can help refine thesis ideas.
4. A thesis says something about the text(s) you discuss exclusively .
If your thesis could describe many works equally well, it needs to be more specific. Let’s return to our examples from above:
A: By telling the story of Westley and Buttercup’s triumph over evil, The Princess Bride affirms the power of true love.
B: Although the main plot of The Princess Bride rests on the natural power of true love, an examination of the way that fighting sticks–baseball bats, tree branches, and swords–link the frame story to the romance plot suggests that the grandson is being trained in true love, that love is not natural but socialized.
Try substituting other works:
A: By telling the story of Darcy and Elizabeth’s triumph over evil, Pride and Prejudice affirms the power of true love.
Sure, that makes sense. Bad sign.
B: Although the main plot of Pride and Prejudice rests on the natural power of true love, an examination of the way that fighting sticks–baseball bats, tree branches, and swords–link the frame story to the romance plot suggests that the grandson is being trained in true love, that it is not natural but socialized.
Um, nope. Even if you have never read Pride and Prejudice , you can probably guess that such a precise thesis could hardly apply to other works. Good sign.
5. A thesis makes a lot of information irrelevant.
If your thesis is specific enough, it will make a point that focuses on only a small part of the text you are analyzing. You can and should ultimately apply that point to the work as a whole, but a thesis will call attention to specific parts of it. Let’s look at those examples again. (This is the last time, I promise.)
A: By telling the story of Westley and Buttercup’s triumph over evil, The Princess Bride affirms the power of true love.
B: Although the main plot of The Princess Bride rests on the natural power of true love, an examination of the way that fighting sticks–baseball bats, tree branches, and swords–link the frame story to the romance plot suggests that the grandson is being trained in true love, that love is not natural but socialized.
One way of spotting the problem with example A is to note that a simple plot summary would support its point. That is not of true example B, which tells the reader exactly what moments the paper will discuss and why.
If you find that your paper leads you to mark relevant passages on virtually every page of a long work, you need to find a thesis that helps you focus on a smaller portion of the text. As the MTS reminds us, the paper should still strive to show the reader something new about the text as a whole, but a specific area of concentration will help, not hinder, that effort.
Contributors and Attributions
- Five Ways of Looking at a Thesis. Authored by : Erik Simpson. Project : Kaleidoscope Open Course Initiative. License : CC BY: Attribution
- Image of pirate. Authored by : Taavi Burns. Located at : https://flic.kr/p/9oPPUY . License : CC BY-SA: Attribution-ShareAlike
- Image of Pride and Prejudice. Authored by : dawt. Located at : https://flic.kr/p/d1BRQy . License : CC BY-NC-ND: Attribution-NonCommercial-NoDerivatives


11.3: Temporal perspectives of the carbon cycle
Left unperturbed, the fast and slow carbon cycles maintain a relatively steady concentration of carbon in the atmosphere, land, plants, and ocean. But when anything changes the amount of carbon in one reservoir, the effect ripples through the others.
In Earth’s past, the carbon cycle has changed in response to climate change. Variations in Earth’s orbit alter the amount of energy Earth receives from the Sun and leads to a cycle of ice ages and warm periods like Earth’s current climate. (See Milutin Milankovitch. ) Ice ages developed when Northern Hemisphere summers cooled and ice built up on land, which in turn slowed the carbon cycle. Meanwhile, a number of factors including cooler temperatures and increased phytoplankton growth may have increased the amount of carbon the ocean took out of the atmosphere. The drop in atmospheric carbon caused additional cooling. Similarly, at the end of the last Ice Age, 10,000 years ago, carbon dioxide in the atmosphere rose dramatically as temperatures warmed.
Shifts in Earth’s orbit are happening constantly, in predictable cycles. In about 30,000 years, Earth’s orbit will have changed enough to reduce sunlight in the Northern Hemisphere to the levels that led to the last ice age.
Today, changes in the carbon cycle are happening because of people. We perturb the carbon cycle by burning fossil fuels and clearing land.
When we clear forests, we remove a dense growth of plants that had stored carbon in wood, stems, and leaves—biomass. By removing a forest, we eliminate plants that would otherwise take carbon out of the atmosphere as they grow. We tend to replace the dense growth with crops or pasture, which store less carbon. We also expose soil that vents carbon from decayed plant matter into the atmosphere. Humans are currently emitting just under a billion tons of carbon into the atmosphere per year through land use changes.
Without human interference, the carbon in fossil fuels would leak slowly into the atmosphere through volcanic activity over millions of years in the slow carbon cycle. By burning coal, oil, and natural gas, we accelerate the process, releasing vast amounts of carbon (carbon that took millions of years to accumulate) into the atmosphere every year. By doing so, we move the carbon from the slow cycle to the fast cycle. In 2009, humans released about 8.4 billion tons of carbon into the atmosphere by burning fossil fuel.
Since the beginning of the Industrial Revolution, when people first started burning fossil fuels, carbon dioxide concentrations in the atmosphere have risen from about 280 parts per million to 387 parts per million, a 39 percent increase. This means that for every million molecules in the atmosphere, 387 of them are now carbon dioxide—the highest concentration in two million years. Methane concentrations have risen from 715 parts per billion in 1750 to 1,774 parts per billion in 2005, the highest concentration in at least 650,000 years.
Effects of Changing the Carbon Cycle
All of this extra carbon needs to go somewhere. So far, land plants and the ocean have taken up about 55 percent of the extra carbon people have put into the atmosphere while about 45 percent has stayed in the atmosphere. Eventually, the land and oceans will take up most of the extra carbon dioxide, but as much as 20 percent may remain in the atmosphere for many thousands of years.
The changes in the carbon cycle impact each reservoir. Excess carbon in the atmosphere warms the planet and helps plants on land grow more. Excess carbon in the ocean makes the water more acidic, putting marine life in danger.
Atmosphere
It is significant that so much carbon dioxide stays in the atmosphere because CO 2 is the most important gas for controlling Earth’s temperature. Carbon dioxide, methane, and halocarbons are greenhouse gases that absorb a wide range of energy—including infrared energy (heat) emitted by the Earth—and then re-emit it. The re-emitted energy travels out in all directions, but some returns to Earth, where it heats the surface. Without greenhouse gases, Earth would be a frozen -18 degrees Celsius (0 degrees Fahrenheit). With too many greenhouse gases, Earth would be like Venus, where the greenhouse atmosphere keeps temperatures around 400 degrees Celsius (750 Fahrenheit).
Because scientists know which wavelengths of energy each greenhouse gas absorbs, and the concentration of the gases in the atmosphere, they can calculate how much each gas contributes to warming the planet. Carbon dioxide causes about 20 percent of Earth’s greenhouse effect; water vapor accounts for about 50 percent; and clouds account for 25 percent. The rest is caused by small particles (aerosols) and minor greenhouse gases like methane.
Water vapor concentrations in the air are controlled by Earth’s temperature. Warmer temperatures evaporate more water from the oceans, expand air masses, and lead to higher humidity. Cooling causes water vapor to condense and fall out as rain, sleet, or snow.
Carbon dioxide, on the other hand, remains a gas at a wider range of atmospheric temperatures than water. Carbon dioxide molecules provide the initial greenhouse heating needed to maintain water vapor concentrations. When carbon dioxide concentrations drop, Earth cools, some water vapor falls out of the atmosphere, and the greenhouse warming caused by water vapor drops. Likewise, when carbon dioxide concentrations rise, air temperatures go up, and more water vapor evaporates into the atmosphere—which then amplifies greenhouse heating.
So while carbon dioxide contributes less to the overall greenhouse effect than water vapor, scientists have found that carbon dioxide is the gas that sets the temperature. Carbon dioxide controls the amount of water vapor in the atmosphere and thus the size of the greenhouse effect.
Rising carbon dioxide concentrations are already causing the planet to heat up. At the same time that greenhouse gases have been increasing, average global temperatures have risen 0.8 degrees Celsius (1.4 degrees Fahrenheit) since 1880.
This rise in temperature isn’t all the warming we will see based on current carbon dioxide concentrations. Greenhouse warming doesn’t happen right away because the ocean soaks up heat. This means that Earth’s temperature will increase at least another 0.6 degrees Celsius (1 degree Fahrenheit) because of carbon dioxide already in the atmosphere. The degree to which temperatures go up beyond that depends in part on how much more carbon humans release into the atmosphere in the future.
Ocean
About 30 percent of the carbon dioxide that people have put into the atmosphere has diffused into the ocean through the direct chemical exchange. Dissolving carbon dioxide in the ocean creates carbonic acid, which increases the acidity of the water. Or rather, a slightly alkaline ocean becomes a little less alkaline. Since 1750, the pH of the ocean’s surface has dropped by 0.1, a 30 percent change in acidity.
Ocean acidification affects marine organisms in two ways. First, carbonic acid reacts with carbonate ions in the water to form bicarbonate. However, those same carbonate ions are what shell-building animals like coral need to create calcium carbonate shells. With less carbonate available, the animals need to expend more energy to build their shells. As a result, the shells end up being thinner and more fragile.
Second, the more acidic water is, the better it dissolves calcium carbonate. In the long run, this reaction will allow the ocean to soak up excess carbon dioxide because more acidic water will dissolve more rock, release more carbonate ions, and increase the ocean’s capacity to absorb carbon dioxide. In the meantime, though, more acidic water will dissolve the carbonate shells of marine organisms, making them pitted and weak.
Warmer oceans—a product of the greenhouse effect—could also decrease the abundance of phytoplankton, which grow better in cool, nutrient-rich waters. This could limit the ocean’s ability to take carbon from the atmosphere through the fast carbon cycle.
On the other hand, carbon dioxide is essential for plant and phytoplankton growth. An increase in carbon dioxide could increase growth by fertilizing those few species of phytoplankton and ocean plants (like sea grasses) that take carbon dioxide directly from the water. However, most species are not helped by the increased availability of carbon dioxide.
Land
Plants on land have taken up approximately 25 percent of the carbon dioxide that humans have put into the atmosphere. The amount of carbon that plants take up varies greatly from year to year, but in general, the world’s plants have increased the amount of carbon dioxide they absorb since 1960. Only some of this increase occurred as a direct result of fossil fuel emissions.
With more atmospheric carbon dioxide available to convert to plant matter in photosynthesis, plants were able to grow more. This increased growth is referred to as carbon fertilization. Models predict that plants might grow anywhere from 12 to 76 percent more if atmospheric carbon dioxide is doubled, as long as nothing else, like water shortages, limits their growth. However, scientists don’t know how much carbon dioxide is increasing plant growth in the real world, because plants need more than carbon dioxide to grow.
Plants also need water, sunlight, and nutrients, especially nitrogen. If a plant doesn’t have one of these things, it won’t grow regardless of how abundant the other necessities are. There is a limit to how much carbon plants can take out of the atmosphere, and that limit varies from region to region. So far, it appears that carbon dioxide fertilization increases plant growth until the plant reaches a limit in the amount of water or nitrogen available.
Some of the changes in carbon absorption are the result of land use decisions. Agriculture has become much more intensive, so we can grow more food on less land. In high and mid-latitudes, abandoned farmland is reverting to forest, and these forests store much more carbon, both in wood and soil, than crops would. In many places, we prevent plant carbon from entering the atmosphere by extinguishing wildfires. This allows woody material (which stores carbon) to build up. All of these land use decisions are helping plants absorb human-released carbon in the Northern Hemisphere.
Changes in land cover—forests converted to fields and fields converted to forests—have a corresponding effect on the carbon cycle. In some Northern Hemisphere countries, many farms were abandoned in the early 20th century and the land reverted to forest. As a result, carbon was drawn out of the atmosphere and stored in trees on land.
In the tropics, however, forests are being removed, often through fire, and this releases carbon dioxide. As of 2008, deforestation accounted for about 12 percent of all human carbon dioxide emissions.
The biggest changes in the land carbon cycle are likely to come because of climate change. Carbon dioxide increases temperatures, extending the growing season and increasing humidity. Both factors have led to some additional plant growth. However, warmer temperatures also stress plants. With a longer, warmer growing season, plants need more water to survive. Scientists are already seeing evidence that plants in the Northern Hemisphere slow their growth in the summer because of warm temperatures and water shortages.
Dry, water-stressed plants are also more susceptible to fire and insects when growing seasons become longer. In the far north, where an increase in temperature has the greatest impact, the forests have already started to burn more, releasing carbon from the plants and the soil into the atmosphere. Tropical forests may also be extremely susceptible to drying.
The warming caused by rising greenhouse gases may also “bake” the soil, accelerating the rate at which carbon seeps out in some places. This is of particular concern in the far north, where frozen soil—permafrost—is thawing. Permafrost contains rich deposits of carbon from plant matter that has accumulated for thousands of years because the cold slows decay. When the soil warms, the organic matter decays and carbon—in the form of methane and carbon dioxide—seeps into the atmosphere.
Current research estimates that permafrost in the Northern Hemisphere holds 1,672 billion tons (Petagrams) of organic carbon. If just 10 percent of this permafrost were to thaw, it could release enough extra carbon dioxide to the atmosphere to raise temperatures an additional 0.7 degrees Celsius (1.3 degrees Fahrenheit) by 2100.
Excerpted from
Holli Riebeek, Design by Robert Simmon,
The Carbon Cycle, NASA, Earth Observatory Accessed December 2023
https://earthobservatory.nasa.gov/features/CarbonCycle/page1.php
, Public domain


9.1: Measurement and the United States System
- know what the word measurement means
- be familiar with United States system of measurement
- be able to convert from one unit of measure in the United States system to another unit of measure
Measurement
There are two major systems of measurement in use today. They are the United States system and the metric system . Before we describe these systems, let's gain a clear understanding of the concept of measurement.
Measurement is comparison to some standard.
The concept of measurement is based on the idea of direct comparison. This means that measurement is the result of the comparison of two quantities. The quantity that is used for comparison is called the standard unit of measure .
Over the years, standards have changed. Quite some time in the past, the standard unit of measure was determined by a king. For example,
1 inch was the distance between the tip of the thumb and the knuckle of the king.
1 inch was also the length of 16 barley grains placed end to end.
Today, standard units of measure rarely change. Standard units of measure are the responsibility of the Bureau of Standards in Washington D.C.
Some desirable properties of a standard are the following:
- Accessibility . We should have access to the standard so we can make comparisons.
- Invariance . We should be confident that the standard is not subject to change.
- Reproducibility . We should be able to reproduce the standard so that measurements are convenient and accessible to many people.
The United States System of Measurement
Some of the common units (along with their abbreviations) for the United States system of measurement are listed in the following table.
| Unit Conversion Table | |
| Length |
1 foot (ft) = 12 inches (in.)
1 yard (yd) = 3 feet (ft) 1 mile (mi) = 5,280 feet |
| Weight |
1 pound (lb) =16 ounces (oz)
1 ton (T) = 2,000 pounds |
| Liquid Volume |
1 tablespoon (tbsp) = 3 teaspoons (tsp)
1 fluid ounce (fl oz) = 2 tablespoons 1 cup (c) = 8 fluid ounces 1 pint (pt) = 2 cups 1 quart (qt) = 2 pints 1 gallon (gal) = 4 quarts |
| Time |
1 minute (min) = 60 seconds (sec)
1 hour ( hr) = 60 minutes 1 day (da) = 24 hours 1 week (wk) = 7 days |
Conversions in the United States System
It is often convenient or necessary to convert from one unit of measure to another. For example, it may be convenient to convert a measurement of length that is given in feet to one that is given in inches. Such conversions can be made using unit fractions .
A unit fraction is a fraction with a value of 1.
Unit fractions are formed by using two equal measurements. One measurement is placed in the numerator of the fraction, and the other in the denominator. Placement depends on the desired conversion .
Placement of
Units
Place the unit being converted
to
in the
numerator
.
Place the unit being converted
from
in the
denominator
.
For example,
| Equal Measurements | Unit Fraction |
| 1 ft = 12 in. | \(\dfrac{\text{1 ft}}{\text{12 in}}\) or \(\dfrac{\text{12 in}}{\text{1 ft}}\) |
| 1 pt = 16 fl oz | \(\dfrac{\text{1 pt}}{\text{16 fl oz}}\) or \(\dfrac{\text{16 fl oz}}{\text{1 pt}}\) |
| 1 wk = 7 da | \(\dfrac{\text{7 da}}{\text{1 wk}}\) or \(\dfrac{\text{1 wk}}{\text{7 da}}\) |
Make the following conversions. If a fraction occurs, convert it to a decimal rounded to two decimal places.
Convert 11 yards to feet.
Solution
Looking in the unit conversion table under length , we see that \(\text{1 yd = 3 ft}\). There are two corresponding unit fractions, \(\dfrac{\text{1 yd}}{\text{3 ft}}\) and \(\dfrac{\text{3 ft}}{\text{1 yd}}\). Which one should we use? Look to see which unit we wish to convert to. Choose the unit fraction with this unit in the numerator . We will choose \(\dfrac{\text{3 ft}}{\text{1 yd}}\) since this unit fraction has feet in the numerator. Now, multiply 11 yd by the unit fraction. Notice that since the unit fraction has the value of 1, multiplying by it does not change the value of 11 yd.
\(\begin{array} {rcll} {\text{11 yd}} & = & {\dfrac{\text{11 yd}}{1} \cdot \dfrac{30}{\text{1 yd}}} & {\text{Divide out common units.}} \\ {} & = & {\dfrac{\text{11 } \cancel{\text{yd}}}{1} \cdot \dfrac{\text{3 ft}}{\text{1 } \cancel{\text{yd}}}} & {\text{(Units can be added, subtracted, multiplied, and divided, just as numbers can.)}} \\ {} & = & {\dfrac{11 \cdot 3 \text{ ft}}{1}} & {} \\ {} & = & {\text{33 ft}} & {} \end{array}\)
Thus, \(\text{11 yd = 33 ft}\).
Convert 36 fl oz to pints.
Solution
Looking in the unit conversion table under liquid volume , we see that \(\text{1 pt = 16 fl oz}\). Since we are to convert to pints, we will construct a unit fraction with pints in the numerator.
\(\begin{array} {rcll} {\text{36 fl oz}} & = & {\dfrac{\text{36 fl oz}}{1} \cdot \dfrac{1 pt}{\text{16 fl oz}}} & {\text{Divide out common units.}} \\ {} & = & {\dfrac{\text{36 } \cancel{\text{fl oz}}}{1} \cdot \dfrac{\text{1 pt}}{\text{16 } \cancel{\text{fl oz}}}} & {} \\ {} & = & {\dfrac{36 \cdot 1 \text{ pt}}{16}} & {} \\ {} & = & {\dfrac{\text{36 pt}}{16}} & {\text{Reduce}} \\ {} & = & {\dfrac{9}{4} \text{ pt}} & {\text{Convert to decimals: } \dfrac{9}{4} = 2.25} \end{array}\)
Thus, \(\text{36 fl oz = 2.25 pt}\).
Convert 2,016 hr to weeks.
Solution
Looking in the unit conversion table under time , we see that \(\text{1 wk = 7 da}\) and that \(\text{1 da = 24hr}\). To convert from hours to weeks, we must first convert from hours to days and then from days to weeks. We need two unit fractions.
The unit fraction needed for converting from hours to days is \(\dfrac{1 da}{24 hr}\). The unit fraction needed for converting from days to weeks is \(\dfrac{\text{1 wk}}{\text{7 da}}\).
\(\begin{array} {rcll} {\text{2,016 hr}} & = & {\dfrac{\text{2,016 hr}}{1} \cdot \dfrac{\text{1 da}}{\text{24 hr}} \cdot \dfrac{\text{1 wk}}{\text{7 da}}} & {\text{Divide out common units.}} \\ {} & = & {\dfrac{\text{2,016 } \cancel{\text{hr}}}{1} \cdot \dfrac{\text{1 } \cancel{\text{da}}}{\text{24 } \cancel{\text{hr}}} \cdot \dfrac{\text{1 wk}}{\text{7 } \cancel{\text{da}}}} & {} \\ {} & = & {\dfrac{2,016 \cdot 1 \text{ wk}}{24 \cdot 7}} & {\text{Reduce}} \\ {} & = & {\text{12 wk}} & {} \end{array}\)
Thus, \(\text{2,016 hr = 12 wk}\).
Practice Set A
Make the following conversions. If a fraction occurs, convert it to a decimal rounded to two decimal places.
Convert 18 ft to yards.
- Answer
-
6 yd
Practice Set A
Convert 2 mi to feet.
- Answer
-
10,560 ft
Practice Set A
Convert 26 ft to yards.
- Answer
-
8.67 yd
Practice Set A
Convert 9 qt to pints.
- Answer
-
18 pt
Practice Set A
Convert 52 min to hours.
- Answer
-
0.87 hr
Practice Set A
Convert 412 hr to weeks.
- Answer
-
2.45 wk
Exercises
Make each conversion using unit fractions. If fractions occur, convert them to decimals rounded to two decimal places.
Exercise \(\PageIndex{1}\)
14 yd to feet
- Answer
-
42 feet
Exercise \(\PageIndex{2}\)
3 mi to yards
Exercise \(\PageIndex{3}\)
8 mi to inches
- Answer
-
506,880 inches
Exercise \(\PageIndex{4}\)
2 mi to inches
Exercise \(\PageIndex{5}\)
18 in. to feet
- Answer
-
1.5 feet
Exercise \(\PageIndex{6}\)
84 in. to yards
Exercise \(\PageIndex{7}\)
5 in. to yards
- Answer
-
0.14 yard
Exercise \(\PageIndex{8}\)
106 ft to miles
Exercise \(\PageIndex{9}\)
62 in. to miles
- Answer
-
0.00 miles (to two decimal places)
Exercise \(\PageIndex{10}\)
0.4 in. to yards
Exercise \(\PageIndex{11}\)
3 qt to pints
- Answer
-
6 pints
Exercise \(\PageIndex{12}\)
5 lb to ounces
Exercise \(\PageIndex{13}\)
6 T to ounces
- Answer
-
192,000 ounces
Exercise \(\PageIndex{14}\)
4 oz to pounds
Exercise \(\PageIndex{15}\)
15,000 oz to pounds
- Answer
-
937.5 pounds
Exercise \(\PageIndex{16}\)
15,000 oz to tons
Exercise \(\PageIndex{17}\)
9 tbsp to teaspoons
- Answer
-
27 teaspoons
Exercise \(\PageIndex{18}\)
3 c to tablespoons
Exercise \(\PageIndex{19}\)
5 pt to fluid ounces
- Answer
-
80 fluid ounces
Exercise \(\PageIndex{20}\)
16 tsp to cups
Exercise \(\PageIndex{21}\)
5 fl oz to quarts
- Answer
-
0.16 quart
Exercise \(\PageIndex{22}\)
3 qt to gallons
Exercise \(\PageIndex{23}\)
5 pt to teaspoons
- Answer
-
480 teaspoons
Exercise \(\PageIndex{24}\)
3 qt to tablespoons
Exercise \(\PageIndex{25}\)
18 min to seconds
- Answer
-
1,080 seconds
Exercise \(\PageIndex{26}\)
4 days to hours
Exercise \(\PageIndex{27}\)
3 hr to days
- Answer
-
\(\dfrac{1}{8} = 0.125 \text{ day}\)
Exercise \(\PageIndex{28}\)
\(\dfrac{1}{2}\) hr to days
Exercise \(\PageIndex{29}\)
\(\dfrac{1}{2}\) da to weeks
- Answer
-
\(\dfrac{1}{14} = 0.0714 \text{ week}\)
Exercise \(\PageIndex{30}\)
\(3 \dfrac{1}{7}\) wk to seconds
Exercises for Review
Exercise \(\PageIndex{31}\)
Specify the digits by which 23,840 is divisible.
- Answer
-
1,2,4,5,8
Exercise \(\PageIndex{32}\)
Find \(2\dfrac{4}{5}\) of \(5 \dfrac{5}{6}\) of \(7 \dfrac{5}{7}\)
Exercise \(\PageIndex{33}\)
Convert \(0.3 \dfrac{2}{3}\) to a fraction.
- Answer
-
\(\dfrac{11}{30}\)
Exercise \(\PageIndex{34}\)
Use the clustering method to estimate the sum: \(53 + 82 + 79 + 49\).
Exercise \(\PageIndex{35}\)
Use the distributive property to compute the product: \(60 \cdot 46\).
- Answer
-
\(60 (50 - 4) = 3,000 - 240 = 2,760\)


26.6E: Extrauterine Effects of Estrogens and Progesterone
Estrogen and progesterone have several effects beyond their immediate roles in the menstrual cycle, pregnancy, and labor.
- Describe the functions of progesterone and estrogen
Key Points
- Estrogen promotes female secondary sex characteristics and has structural and metabolic functions, including bone formation, salt and water retention, and increased cortisol levels.
- The effects of progesterone are largely amplified by estrogen and include increases in core temperature, anti-inflammatory effects, increased use of fat for energy, and regulation of insulin release.
- Progesterone is sometimes called the ” hormone of pregnancy” as it has many roles relating to the fetal development, including preparing the uterus for implantation, increasing the amount of cervical mucus, and decreasing the maternal immune response.
Key Terms
- estrogen : A hormone responsible for the appearance of secondary sex characteristics of human females at puberty and for the maturation and maintenance of the reproductive organs in their mature functional state.
- aldosterone : A mineralocorticoid hormone secreted by the adrenal cortex that regulates the balance of sodium and potassium in the body.
- progesterone : A steroid hormone secreted by the ovaries that prepares the uterus for the implantation of a fertilized ovum and subsequent pregnancy.
Both estrogens and progesterone serve functions in the body beyond their roles in menstruation, pregnancy, and childbirth.
Estrogens Overview
Estradiol : One of the estrogens produced in the human body, predominant during a woman’s reproductive years.
Estrogens are a group of compounds named for their importance in the estrous cycle of humans and other animals. They are the primary female sex hormones, although they are found in males as well. The three major naturally occurring forms of estrogen in women are estrone (E1), estradiol (E2), and estriol (E3). Estetrol (E4) is produced only during pregnancy.
Natural estrogens are steroid hormones, while some synthetic versions are non-steroidal. Estrogens are synthesized in all vertebrates as well as some insects, and their presence in both suggests that they have an ancient evolutionary history. Like all steroid hormones, estrogen readily diffuses across the cell membrane. Once inside the cell, it binds to and activates estrogen receptors which in turn modulate the expression of many genes.
Functions of Estrogens
Estriol : Another one of the three main estrogens produced in humans.
While estrogens are present in both men and women, they are usually at significantly higher levels in women of reproductive age.  They are also involved in the thickening of the endometrium and other aspects of menstrual cycle regulation.
Other functions of and structural changes induced by estrogen include:
- Formation of female secondary sex characteristics
- Accelerating metabolism
- Increasing fat stores
- Stimulating endometrial growth
- Increasing uterine growth
- Increasing vaginal lubrication
- Thickening the vaginal wall
- Maintaining blood vessels and skin
- Reducing bone resorption, increasing bone formation
- Reducing muscle mass
Effect on Libido
Sex drive is dependent on androgen levels only in the presence of estrogen.  The sexual desire in these women can be restored by administration of estrogen through oral contraceptives.
Mental Health
Estrogen plays a significant role in women’s mental health. Sudden estrogen withdrawal, fluctuating estrogen, and periods of sustained low levels of estrogen correlate with significant mood changes. Restoration or stabilization of estrogen levels is clinically effective for recovery from postpartum, perimenopause, and postmenopause depression.
Progesterone Overview
Progesterone : Belongs to the progestogen class of hormones and is the predominant example in the human body.
Progesterone is a steroid hormone involved in the female menstrual cycle, pregnancy (supports gestation ), and embryogenesis of humans and other species.
Progesterone belongs to a class of hormones called progestogens and is the major naturally-occurring human form in this category. Progesterone exerts its primary action through the intracellular progesterone receptor, although a distinct, membrane-bound progesterone receptor has also been postulated.
Functions of Progesterone
Progesterone has a number of physiological effects that are amplified in the presence of estrogen. Estrogen, through estrogen receptors, upregulates the expression of progesterone receptors. Also, elevated levels of progesterone potently reduce the sodium-retaining activity of aldosterone, resulting in natriuresis and a reduction in extracellular fluid volume. Progesterone withdrawal, on the other hand, is associated with a temporary increase in sodium retention (reduced natriuresis, with an increase in extracellular fluid volume) due to the compensatory increase in aldosterone production. This combats the blockade of the mineralocorticoid receptor by the previously-elevated level of progesterone.
Progesterone has key effects via non-genomic signalling on human sperm as they migrate through the female tract before fertilization occurs, though the receptor(s) as yet remain unidentified. Detailed characterization of the events occurring in sperm in response to progesterone has shed light on intracellular calcium transients, maintained changes, and slow calcium oscillations, now thought to possibly regulate motility.
Progesterone is sometimes called the “hormone of pregnancy” and has many roles relating to fetal development. It converts the endometrium to its secretory stage to prepare the uterus for implantation. At the same time, it affects the vaginal epithelium and cervical mucus, making them thick and impenetrable to sperm.
If pregnancy does not occur, progesterone levels will decrease, leading to menstruation. Normal menstrual bleeding is progesterone-withdrawal bleeding. If ovulation does not occur and the corpus luteum does not develop, its levels may be low, leading to anovulatory dysfunctional uterine bleeding. During implantation and gestation, progesterone appears to decrease the maternal immune response to allow for the acceptance of the pregnancy and decrease contractility of the uterine smooth muscle.
In addition, progesterone inhibits lactation during pregnancy. A drop in its levels is facilitates the onset of labor. Another drop following delivery is one of the triggers for milk production. The fetus metabolizes placental progesterone in the production of adrenal steroids.


12.4: The Limits of Environmental Laws and Regulations
Despite all the efforts to protect biodiversity through laws and regulations, the scale of environmental crimes continues to increase year after year. Today, the US $91–258 billion environmental crime industry is the world’s fourth largest illegal enterprise, after drug smuggling, counterfeiting, and human trafficking (Nellemann et al., 2016). Increased financial support for environmental law enforcement could certainty help: current spending to combat environmental crimes, globally estimated at US $20–30 million a year, is a mere drop in the bucket compared to the losses incurred from these same crimes, which are 10,000 times greater (Nelleman et al., 2016). There is also a need to prevent environmental crimes before they happen, given that the damages incurred cannot always be undone by punishing the offenders.
Environmental crime is the world’s fourth largest illegal enterprise, after drug smuggling, counterfeiting, and human trafficking.
An important step towards reducing the scale of environmental crimes is to address the ineffectiveness of environmental regulations. That includes addressing the range of tactics that criminals use to facilitate non-compliance (Chapron et al., 2017), but also ensuring there are mechanisms that remove the incentives for people to engage in environmental crimes. In the following section, we look at some of the most prominent challenges that complicate environmental law enforcement.
Lack of capacity
The foremost reason why environmental laws fail is that authorities often lack the capacity for effective monitoring and enforcement. Lack of capacity is a major problem in the marine fisheries industry due to the size of the oceans and the cost of patrolling them. This is particularly prominent in West Africa’s oceanic waters (Figure 12.6), which experience the world’s highest levels of illegal and unregulated fishing (Agnew et al., 2009; Gremillet et al., 2015). Apprehending the environmental criminals operating in these and other areas requires resources and manpower, both in short supply.
Lack of capacity is exacerbated by law enforcement officers that turn a blind eye to actions they deem innocuous, or when prosecutors fail to indict criminals out of fear of reprisals. Regulatory controls may also no longer exist or be enforced in regions that experience substantial political instability, economic hardship, civil unrest, or war (Hanson et al., 2009; Beyers et al., 2011). But even in areas where regulatory controls exist, prosecution can be complex, and thus very hard, especially when the illegal activities cross international boundaries and different legal jurisdictions. Such a breakdown of legal mechanisms often leaves natural resources vulnerable to whoever can exploit them.
Conflicting government priorities
Clashing priorities between different government structures complicate the enforcement of environmental laws. We see this when agencies overseeing mining activities issue inappropriate permits because of pressure for economic development, or because of corrupt agreements between businesses and government officials (Mascia and Pailler, 2011). Another example of mixed priorities occurs when a national government gives permission to extractive companies to exploit protected areas (Section 13.7.3) or communal lands without first consulting and obtaining local input and consent. Such government-sanctioned violations are generally very difficult to prosecute and require an active and caring citizenry to take their governments to task.
One of the most popular methods for citizens to make themselves heard is activist activities, such as public protests. Concerned individuals can also launch petitions on websites such as https://www.change.org , http://www.greenpeace.org , and https://www.avaaz.org . There is even a website for whistle-blowers ( https://wildleaks.org ) who want to report environmental crimes anonymously. Another positive development is the growing number of successful lawsuits that concerned citizens and environmental justice organizations have brought against their governments for environmental violations (e.g. CER, 2017; Yende, 2017). The Kenyan conservation organization Wildlife Direct has taken this a step further; they are keeping citizens informed about lawsuits involving environmental crimes through a website dedicated to tracking and reporting on such cases ( https://wildlifedirect.org/legal-program-3 ).
Informal economies, traditional activities, and the law
Law enforcement can at times be counterproductive. This is true especially in areas where the separation between informal/unreported and illegal activities is blurred. For example, traditional people who graze their livestock, collect medicinal plants, or hunt and trap animals in protected areas that were established on ancestral land seldom have criminal intent. But because formal law systems seldom account for these informal activities, those people are engaging in illegal activities. Similarly, confusing terminology may also lead to unintended conflict. For example, in some parts of Cameroon, the cultural definition of a hunter describes someone who owns a gun and makes a living from hunting animals (Hofner et al., 2018). In this context, some people consider it within the law to trap animals with snares, or even to make sporadic “hunting” trips into a protected area where hunting is forbidden, given that it is not for commercial purposes.
When dealing with vulnerable people, conservation initiatives must also consider impacts on livelihoods and the potential for sustainable utilisation
When dealing with vulnerable peoples whose livelihoods are threatened, an approach that involves sensitivity and compassion generally offers more effective and enduring resolutions. Many conservation initiatives have not only failed but have also created long-lasting negative attitudes by preventing traditional peoples from sustaining their livelihoods. Before implementing new regulations, governments should carefully consider if they would disrupt livelihoods. If so, it might be wise to consider if some form of sustainable utilisation isn’t possible. For example, while pastoralist activities in Tanzania’s Ngorongoro Conservation Area may lead to wildlife declines (Boone et al., 2002, but see Ogutu et al., 2016), conservation authorities decided on a suitable compromise by allowing Maasai herders to graze their livestock in the area on the condition that they exit daily. (See also Section 13.5.2 for discussion on zoning.)
When banning activities which have become unsustainable, it helps to provide start-up resources and market access to help affected people comply with new restrictions.
Despite best intentions, sustainable utilisation is not always possible, and the actions of people engaging in environmentally detrimental activities are not compatible with conservation goals. In such cases, it is important to implement controls that enable those people to transition toward sustainable activities. Failing that, conservation activities may unintentionally force the affected people to resort to illegal activities such as poaching out of desperation to obtain food and income. When banning previously-allowed activities that have become unsustainable, it helps to provide affected people with start-up resources and market access to help them comply with new restrictions while also meeting broader societal needs. For example, to fulfil income and nutritional needs when bushmeat harvesting is banned, it might be necessary to help hunters transition to farming with animals that reproduce quickly in captivity. Raising poultry can be a good alternative to bushmeat because chickens grow quickly, provide eggs, feed on insect pests, and need little land for maintenance. Farming with locally-adapted wildlife, such as large snails (e.g. Carvalho et al., 2015) and cane rats (Thryonomys swinderianus, LC) (e.g. van Vliet et al., 2016), has also proven to be a profitable and sustainable alternative to the bushmeat trade (for a review on wildlife farming for conservation, see Tensen, 2016). Initially, many people may resist the risks involved in leaving behind familiar activities. It is, therefore, important to explain carefully the reasoning behind those changes (e.g. “bushmeat hunting drives away tourist dollars”, Rogan et al., 2017). It may also be beneficial to enable the affected individuals to travel to areas where they can see first-hand how more sustainable activities can benefit local people.
Trade embargoes and sanctions
The basic premise of CITES is that, so long as participating countries abide by agreed-upon regulations, trade involving species of concern will not be stopped, only monitored. However, when agreements are not met, or compliance falls short, then trade is banned in part or in whole. For example, in early 2016, following failures to comply with international trade regulations, CITES instituted blanket suspensions on trade of all CITES-regulated products against 14 African countries (CITES, 2016). Another example from 2016: after various high-profile environmental crimes that involved CITES-regulated species, the USA afforded protection to lions and elephants under their Endangered Species Act ( https://www.fws.gov/endangered ). Trophy hunters from the USA now face significant regulatory and logistical barriers which has all but eliminated hunting of these species for wealthy American hunters, threatening a US $500 million per year industry that supports over 53,000 jobs and protects over 1.4 million km 2 of land (SCIF, 2015). In both these examples, businesses operating within the law are unfortunately also impacted.
Many formerly destructive companies are now voluntarily pursuing opportunities to prove, through special certifications, that their products are harvested responsibly and sustainably.
To avoid scenarios such as these, it is much more advantageous for pressure to mount from within non-complying countries and industries before outside pressure takes effect. To that end, many formerly destructive companies are now voluntarily pursuing opportunities to prove, through special certifications, that their products are harvested responsibly and sustainably. Four prominent certification agencies operating in Africa are the Forest Stewardship Council (FSC) which sets guidelines for the responsible management of forests, the Marine Stewardship Council (MSC) which sets standards for sustainable fisheries, the Roundtable on Sustainable Palm Oil (RSPO) which promotes sustainable production of palm oil, and the Rainforest Alliance which promotes sustainable agriculture (For a more complete treatment of sustainability standards, see https://www.isealalliance.org , https://www.evidensia.eco , and https://www.iisd.org/ssi ). Given that most certification schemes were established relatively recently, they are not without their flaws, but collaborations with conservation biologists (e.g. Christian et al., 2013; WWF, 2013) play a major role in ensuring continued improvements.


9: Inferences with Two Samples
You have learned to conduct hypothesis tests on single means and single proportions. You will expand upon that in this chapter. You will compare two means or two proportions to each other. The general procedure is still the same, just expanded. To compare two means or two proportions, you work with two groups. The groups are classified either as independent or matched pairs. Independent groups consist of two samples that are independent, that is, sample values selected from one population are not related in any way to sample values selected from the other population. Matched pairs consist of two samples that are dependent. The parameter tested using matched pairs is the population mean. The parameters tested using independent groups are either population means or population proportions.
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- 9.1: Prelude to Hypothesis Testing with Two Samples
- This chapter deals with the following hypothesis tests: Independent groups (samples are independent) Test of two population means. Test of two population proportions. Matched or paired samples (samples are dependent) Test of the two population proportions by testing one population mean of differences.
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- 9.2: Inferences for Two Population Means- Large, Independent Samples
- Suppose we wish to compare the means of two distinct populations. Our goal is to use the information in the samples to estimate the difference in the means of the two populations and to make statistically valid inferences about it.
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- 9.3: Inferences for Two Population Means - Unknown Standard Deviations
- When one or the other of the sample sizes is small, as is often the case in practice, the Central Limit Theorem does not apply. We must then impose conditions on the population to give statistical validity to the test procedure. We will assume that both populations from which the samples are taken have a normal probability distribution and that their standard deviations are equal.
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- 9.4: Inferences for Two Population Means - Paired Samples
- A confidence interval for the difference in two population means using paired sampling is computed using a formula in the same fashion as was done for a single population mean. The same five-step procedure used to test hypotheses concerning a single population mean is used to test hypotheses concerning the difference between two population means using pair sampling. The only difference is in the formula for the standardized test statistic.
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- 9.5: Inferences for Two Population Proportions
- A confidence interval for the difference in two population proportions is computed using a formula in the same fashion as was done for a single population mean. The same five-step procedure used to test hypotheses concerning a single population proportion is used to test hypotheses concerning the difference between two population proportions. The only difference is in the formula for the standardized test statistic.
Contributors and Attributions
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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>.


3.5: Document Design
By the end of this section, you will be able to:
- Apply themes and styles to a document
- Use the Page Background command group
When creating your WorldCorp market trends report, you may choose to use custom formatting or existing formatting to add styles to your document. You can achieve this via the options on the Design tab, by using existing templates in Microsoft Word, or through combining those options to customize a template. Some companies may have existing templates with logos, fonts, or colors that are part of the company brand. The Design tab offers many options for quickly changing the graphical formatting of your document, applying styles across the entire document so you do not have to manually make each change. You can change the color scheme, fonts, and paragraphs, either manually or using the themes and styles in Word.
You may also opt to use a template. Templates are predesigned documents for a variety of purposes, including reports, résumés, flyers, invitations, posters, and more. The advantage of a template is that it already has a design applied. However, you need to ensure the template you select is appropriate for your audience and purpose, and that your content will fit well in the template.
Using Styles and Themes
Your supervisor has suggested that you apply a theme to the WorldCorp market trends report. A theme is a cohesive set of fonts, font sizes, and colors that can be applied to your whole document. However, before you apply a theme to your document, you must “code” your document’s style. Styles are preset formatting for font type and size, line spacing, and other formats that are used to change the appearance of text in a document. Generally, you choose the style for the document before beginning to input the text. By choosing the style, you are coding the document so that Word knows how to format various sections. These codes tell Word which parts of the text are body text, titles, subtitles, and so on. Without these style codes, the theme won’t know how to apply itself to your document.
Styles Pane
Before you can implement styles, you first must label, or code, all the styles in your document. This means selecting parts of the text and using the Styles pane on the Home tab to identify them. For example, all body text must be selected and the Normal style applied; all headings must be labeled as Heading 1, Heading 2, and so on. Once all your text has a style applied, then you will be able to use the themes and styles to full capacity.
You can change the default fonts and font styles in the Styles pane, as Figure 3.31 shows. For example, if the default Normal font is Times New Roman, you may want to change it to Calibri. Then, when you select a segment of text and choose the Normal style, it will make the font Calibri, not Times New Roman. In effect, you are telling the program what you consider as “Normal” text font in this instance.
This is the manual way of applying styles. But the real power in using styles is to simply use them as identifiers for your text so that themes can “read” and style the text properly. For example, it wouldn’t matter if you chose Calibri as your Normal font style; if you select the “Madison” theme, for instance, the new Normal font will automatically change to Arial, because that is what comes with the theme. Different themes have different Normal font settings. To see what font a theme uses, you will need to select the theme and see the fonts it uses. Now, let’s explore how to apply a theme and why it works so well with styles.
Applying Themes
Let’s revisit the different headings of the market trends report we worked on in Formatting Document Content in Microsoft Word. Go to the Design tab and select the drop-down menu called Themes . You’ll see that there are over a dozen default themes built into the software (Figure 3.32). As an exercise, choose the “Ion” theme for your document. Selecting “Ion” changes all the available styles in your document. If you want to further change the theme, you can change the color scheme using the Colors menu on the Design tab. There are many different color palettes to choose from. Word offers these preset palettes because designers have determined that the colors work together well to give documents a cohesive, professional appearance.
You can change the colors and fonts associated with the selected theme by choosing the menus on the Design tab. Choose the Green color group and Arial font and apply it to the report.
When you change the color and font, all headings and titles of the section will change in one step. There is no need to select each heading one by one because you already coded your document with the correct styles before you applied the theme, so the theme knows which text is which type of heading, and so forth. In the template, the current font of the Normal text is Corbel. By selecting the Fonts drop-down menu, you can change all of the Normal text and/or Headings font. Go to the bottom of the drop-down Fonts menu and select Customize Fonts. A new dialog box will appear with all the fonts installed in Office, as seen in Figure 3.33. Choose a new font and select Save and the headings will be changed.
Page Background Command Group
The Page Background command group on the Design tab allows users to apply a page border, page colors, and watermarks. A watermark is a lightly colored image, logo, or text that exists in the background of the document. Like changing the page background color, adding a watermark will apply to the whole document. Some companies choose to use watermarks to indicate the status of a document (e.g., “Draft”) or to imprint their company name on each page of the document. To insert a watermark, select the Watermark icon and choose Custom Watermark, as you can see in Figure 3.34.
As an example, let’s add a watermark to the market trends report to indicate that it is a private, internal document. Type “Confidential” into the Custom Watermark dialog box and have it run diagonally across the page. There are a few options to alter the text’s appearance on the page. For instance, if you want to change the text to be less visible, choose Semitransparent. You can even use an image, like a company logo, as a watermark.