Question

SUMMARY
Groups	Count	Sum	Average	Variance
Dept. 1	10	340005	34000.5	31479782.94
Dept. 2	8	300391	37548.875	82885830.98
Dept. 3	7	284654	40664.85714	133792262.8
Dept. 4	21	907010	43190.95238	157721269.9
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	623553563.8	3	207851187.9	1.81088925	0.159863	2.827049
Within Groups	4820697839	42	114778520
Total	5444251403	45

Using this data, please answer if there are significant salary differences between the four departments? Please provide evidence to support your conclusion.

Answer 1

The given results are of a one-way ANOVA between 4 groups. The null hypothesis is that the population means for all the 4 groups are equal, and alternative hypothesis is that at least 2 means are different.

Looking at the results of the ANOVA and a significance level of 0.05 (or 5%), we see that the p-value is 0.15 > 0.05. Hence we cannot reject the null hypothesis at the 5% significance level.

Therefore, the mean salaries for the 4 departments are not same, i.e. statistically different. This is also clear looking at the huge differences between the mean salaries of the 4 departments, and the huge difference in the sample sizes.