Poweranalys : bestämmelse av urvalsstorlek genom linjära mixade modeller och ANOVA

Sammanfattning: In research where experiments on humans and animals is performed, it is in advance important to determine how many observations that is needed in a study to detect any effects in groups and to save time and costs. This could be examined by power analysis, in order to determine a sample size which is enough to detect any effects in a study, a so called “power”. Power is the probability to reject the null hypothesis when the null hypothesis is false. Mälardalen University and the Caroline Institute have in cooperation, formed a study (The Climate Friendly and Ecological Food on Microbiota) based on individual’s dietary intake. Every single individual have been assigned to a specific diet during 8 weeks, with the purpose to examine whether emissions of carbon dioxide, CO2, differs reliant to the specific diet each individuals follows. There are two groups, one treatment and one control group. Individuals assigned to the treatment group are supposed to follow a climatarian diet while the individuals in the control group follows a conventional diet. Each individual have been followed up during 8 weeks in total, with three different measurements occasions, 4 weeks apart. The different measurements are Baseline assessment, Midline assessment and End assessment. In the CLEAR-study there are a total of 18 individuals, with 9 individuals in each group. The amount of individuals are not enough to reach any statistical significance in a test and therefore the sample size shall be examined through power analysis. In terms of, data, every individual have three different measurements occasions that needs to be modeled through mixed-design ANOVA and linear mixed models. These two methods takes into account, each individual’s different measurements. The models which describes data are applied in the computations of sample sizes and power. All the analysis are done in the programming language R with means and standard deviations from the study and the models as a base. Sample sizes and power have been computed for two different linear mixed models and one ANOVA model. The linear mixed models required less individuals than ANOVA in terms of a desired power of 80 percent. 24 individuals in total were required by the linear mixed model that had the factors group, time, id and the covariate sex. 42 individuals were required by ANOVA that includes the variables id, group and time.