2.8.3. Statistical Tests
SECONDARY, BROWN
Null hypothesisIn case of normal distribution, the null hypothesis was the following: There is no difference among the mean values of the Probiotic, Synbiotic and Placebo (control) groups concerning the primary, secondary or explorative parameters to be tested acc. to the parameter description in the study protocol. If data are not normally distributed, the null hypothesis assumes an equality of medians of the three groups concerning the parameters to be tested.Alternative hypothesisIn case of normal distribution, at least one of three mean values differs from the mean value of another group concerning the primary, secondary or explorative parameters to be tested acc. to the parameter description in the study protocol. If data are not normally distributed, at least one median differs from another median concerning the parameters to be tested.Testing of NormalityAll metric data were tested for normal distribution using the Shapiro–Wilk test at the 2.5% level with the following null hypothesis: data are normally distributed. If Homoscedasticity was investigated with the Brown–Forsythe equal variance test at the 2.5% level.Tests for Comparison of the Three GroupsIn case of normality and homoscedasticity, the parametric method one-way ANOVA was used for statistical analysis for comparing the three groups according to the 3-arm design at the significance level of 5%. Otherwise, Kruskal–Wallis ANOVA on ranks was performed.Post Hoc TestsPost hoc tests were performed at the overall significance level of 5% if the main ANOVA test (parametric or non-parametric) was significant. The Holm–Sidak method was used in case of normality, and the Dunn’s method was the choice if the normality test failed, respectively.Post hoc tests were performed focusing on comparisons versus the Placebo group only, based on the fact that this was the major focus for assessing efficacy.Descriptive StatisticsRegarding descriptive statistics, data were expressed as means, standard deviations (SDs), medians, 25th and 75th percentiles, and frequency of observation. In figure means ± SEMs are used for depicting the results.