I need some help on how to solve this question, what approach or rules to use? Im not really sure. Do I need to use hypothesis testing?
A company director took a sample of salaries of 13 employees in a big school during a certain time. she divided the wages into three groups according to the different jobs: teachers, assistants and coordinators as displayed in the table below. She wanted to find out whether or not the means of the salaries classified by the three jobs are significantly different. Let the level of significance be
(a) 5 % and
(b) 1 %.
Workers 1 2 3 4 5
Teachers 74 65 72 69 -
Assistants 75 78 74 76 72
Coordinators 56 55 53 52 -
You can solve this using ANOVA, followed by a post-hoc pair-wise comparison test if appropriate (e.g., Scheffè, Bonferroni, Tukey, etc...), or its nonparametric equivalent Kruskal-Wallis test. These tests provide the direct answer to the question of whether the mean salary differs between groups. Based on the p value that you obtain, you can determine whether differences are significant at the 5% (p<0.05) or also 1% level (p<0.01). In this case, considering the small sample size, I would suggest the KW test because it does not require normality assumptions. You have simply to input the three sequences of values in a statistical software and perform the test. In SPSS, you have to select Analyze - Nonparametric Tests - K Independent Samples. Just define the target variable, the grouping variable, the range, and click ok. You will obtain the p value that you are looking for.