4. Post hoc analysis

Suppose a researcher is interested in the potential connection between church attendance and social class in his community. He selects random samples of people from each social class and asks them to estimate the number of times they attend an organized religious service during a typical month. He performs a statistical analysis of the data, including ANOVA, and finds that the difference between the means is significant at less than 0.005. Results of the analysis are shown in the following table:

(Fictitious data)	Lower Class	Working Class	Middle Class	Upper Class	F ratio	Alpha
Mean	9.1	6.6	2.5	8.7	36.75	<0.005
Standard deviation	4.2	5.2	1.1	4.6
N =	51	56	75	25

His analysis indicates that the relationship between social class and church attendance is significant, but it does not provide any information about which differences between the sample means are the most significant. He can see by inspection of the table that the mean from middle class respondents is very different from the other means, but he does not know how significant the difference is, or what other differences might be important.

The researcher conducts a post hoc analysis to explore these questions. He constructs the following table showing the absolute values of the differences between the means from all possible pairs of categories, and which differences are significant at the 0.05 level:

Mean Differences	Working Class	Middle Class	Upper Class
Lower class	2.5*	6.6*	0.4
Working class		4.1*	2.1*
Middle class			6.2*

*Significant at 0.05 level, Modified Least Significant Difference Test

The largest difference is between the means from the class sample and the means from the class sample.

The smallest difference is between the means from the class sample and the means from the class sample.

The researcher's post hoc analysis finds that all of the mean differences are significant, except for the difference between class and class categories.

The finding of significant differences between all the other pairs of categories the researcher's conclusion that there is a significant relationship between social class and attendance at religious organizations.