RESEARCH METHODS HANDBOOK

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Contents	Introduction	Descriptive	Hypothesis	Tables	Appendix

Example: ANOVA

Problem: You obtained the number of years of education from one random sample of 38 police officers from City A, the number of years of education from a second random sample of 30 police officers from City B, and the number of years of education from a third random sample of 45 police officers from City C. The average years of education for the sample from City A is 15 years with a standard deviation of 2 years. The average years of education for the sample from City B is 14 years with a standard deviation of 2.5 years. The average years of education for the sample from City C is 16 years with a standard deviation of 1.2 years. Is there a statistically significant difference between the education levels of police officers in City A, City B, and City C?

	City A	City B	City C
Mean (years)	15	14	16
Standard Deviation	2	2.5	1.2
S²(Variance)	4	6.25	1.44
N (number of cases)	38	30	45
Sum of Squares	152	187.5	64.8
Sum of Scores (mean*n)	570	420	720

State the Hypothesis

Ho: There is no statistically significant difference among the three cities in the mean years of education for police officers.

Ha: There is a statistically significant difference among the three cities in the mean years of education for police officers.

Set the Rejection Criteria Numerator Degrees of Freedom

df=k-1 where k=3 (number of independent samples)

df=2

Denominator Degrees of Freedom

df=n-k where n=113 (sum of n for all independent samples) df=110

Establish Critical Value

At alpha.05, df=(2,110)

Consult f-distribution, Fcv = 3.08

Compute the Test Statistic Estimate Grand Mean

Estimate F Statistic

Decide Results of Null Hypothesis Since the F-statistic (9.931) exceeds the F critical value (3.08), we reject the null hypothesis and conclude there is a statistically significant difference between the three cities in the mean years of education for police officers.