I have a student satisfaction survey that measures satisfaction on a scale of five levels (1: extremely dissatisfied, 5: extremely satisfied). In the survey we report both the frequency distribution of the satisfaction levels and the average satisfaction level. The survey collects students' program os study besides other variables.
What is the best statistical test to use in order to do the following?
1. Compare the frequency distribution of students satisfaction in one department to the frequency distribution of students satisfaction in the whole institution.
2. Compare the average of students satisfaction in one department to the average of students satisfaction in the whole institution.
Since my data are considered categorical, I'm thinking of using non parametric tests like Kruskal Wallis test or Wilcoxon test to compare means. And use chi square test to compare distribution since this what I know in case of comparing multiple groups. But I'm not sure if comparing one group to the total is valid using the same tests.
Any suggestions?
To compare a part (one group mean) to a whole (total mean), you can use a one-sample t-test or a one-sample z-test, depending on the circumstances and assumptions.
Both tests provide a statistical comparison of the group mean to the total mean, indicating whether the difference is statistically significant or due to random chance. The choice between a one-sample t-test and a one-sample z-test depends on the sample size, the distribution of the variable, and the assumptions being met.
Additionally, it is important to consider whether the assumptions of the chosen test are satisfied in your data. Violations of assumptions, such as non-normality or non-independence, may require the use of alternative tests or nonparametric methods.
Remember to interpret the results of the test appropriately, taking into account the effect size, confidence intervals, and the practical significance of the difference between the group mean and the total mean.
There's a problem with this whole approach. You are comparing a subgroup with the whole sample which includes the subgroup itself. Clearly, the larger the subgroup, the less chance of finding a difference, since the subgroup largely determines the whole. You are asking something like "are women different to women and men combined?" which strikes me as weird question.
The appropriate test is to compare the subgroup with the rest. This tests a describable hypothesis, whereas your part versus whole does not.
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