Question

A study investigates whether the average time (in minutes) that Drexel students spend using different apps differs between App Types (1=Twitter, 2=iMessage, 3=Facebook, 4=Snapchat). Researchers survey a randomly selected group of Drexel students where 20 different participants are asked for each App Type (i.e., 20 people for App Type 1, 20 people for App type 2 etc., total of 80 people) about how much time (hours per week) they spend using the app.

Part a. Researchers want to test whether the average time spent using apps differ statistically significantly between App Types. Assume that the normality assumption of this test is violated. In this case, which statistical test would you recommend? Give the name of the test and explain your answer.

Part b. In general, why are non-parametric statistical tests more appropriate for sample data that has extreme outliers compared to parametric tests? Explain it in your own words. (Short answer, 1.5 points)

Answer 1

A. Since the assumption of normality is not valid we will use NON PARAMETRIC TEST- The kruskal Wallis test.

​​​​​​Kruskall-Wallis one way anova is a non parametric method for comparing k independent sample means. It is roughly equivalent to a parametric one way anova with the data replaced by their ranks.

Nonparametric analysis of variance is used almost as widely and frequently as parametric ANOVA. Its use is usually justified on the basis that assumptions for parametric ANOVA are not met.

If the researcher can make the assumptions of an identically shaped and scaled distribution for all groups except for any difference in medians then the null hypothesis is that the medians of all groups are equal and the alternative hypothesis is that at least one population median of one group is different from the population median of at least one other group

B.

Nonparametric statistical test are more appropriate for sample data that has extreme outliers because when we do one way anova which is a parametric test then we get a much larger within group variability, differences between groups when they are compared to the residuals/within variability do not appear to be significant causing the p-value to move just above the significance threshold.

one possible solution is to use a non parametric approach nonparametric techniques such as kruskal-wallis test are based on ranks and medians. Ranks represent the relative position of an individual in comparison to others but are not affected by extreme values where as a mean is sensitive to outliers values.

Ranks and medians are more robust to outliers.