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(No Variance Homogeneity) The following uses the same means and sample sizes from the example of two independent means with homogeneity of variance but the standard deviations (and hence variance) are significantly different (hint: verify the f-ratio is 4 with df=37,29). Problem: You have obtained the number of years of education from one random sample of 38 police officers from City A and the number of years of education from a second random sample of 30 police officers from City B. The average years of education for the sample from City A is 15 years with a standard deviation of 1 year. The average years of education for the sample from City B is 14 years with a standard deviation of 2 years. Is there a statistically significant difference between the education levels of police officers in City A and City B? Assumptions Independent samples Interval/ratio level data Organize data City A (labeled sample 1) City B (labeled sample 2) For a 2-tailed hypothesis test Ha: There is a statistically significant difference between the mean education level of police officers working in City A and the mean education level of police officers working in City B. For a 1-tailed hypothesis test Ha: The mean education level of police officers working in City A is significantly greater than the mean education level of police officers working in City B.
If using 2-tailed test
Test Statistic
There is a statistically significant difference between the mean years of education for police officers in City A and mean years of education for police officers in City B. (note: the test statistic 2.463 exceeds the critical value of 2.021 for a 2-tailed test and 1.684 for a 1 tailed-test.) If using 1-tailed test Same results |
Example: Two
Independent Sample
Means 
