A psychologist at a private psychiatric hospital was asked to determine whether there was any clear difference

Question:

A psychologist at a private psychiatric hospital was asked to determine whether there was any clear difference in the length of stay of patients with different categories of diagnosis. Looking at the last four patients in each of the three major categories, the results (in terms of weeks of stay) were as follows:

(a) Using the .05 level and the five steps of hypothesis testing, is there a significant difference in length of stay among diagnosis categories?
(b) Sketch the distributions involved.
(c) Figure the effect size for the study.
(d) Explain your answer to part (a) to someone who understands everything involved in conducting a t test for independent means but is unfamiliar with the analysis of variance.
(e) Test the significance of planned contrasts (using the .05 level without a Bonferroni correction) for affective disorders versus drug-related conditions
(f) Cognitive disorders versus drug-related conditions.
(g) Explain your answers to parts (e) and (f) to a person who understands analysis of variance but is unfamiliar with planned contrasts.