Contrasts and comparisons among means
This chapter is concerned with more specific tests among the means. It deals with the use of coefficients to formulate linear contrasts which specify the comparisons required by the researcher. The chapter discusses a posteriori tests of comparisons and presents a decision chart to assist in choosing the appropriate method. The Scheffe corrected F-test for a posteriori multi-mean comparisons and the Newman-Keuls test for a posteriori pair-wise comparisons. The researcher should start with the box labelled ‘type of comparison’ at the top. Multi-mean refers to a comparison or trend involving three or more means. The sum of squares for the contrast is the square of the difference between two weighted means, the mean of the means with negative coefficients and the mean of the means with positive coefficients. A more stringent criterion for rejection of the null hypothesis is required because contrasts showing, possibly by chance, large differences between means are more likely to attract the attention of the researcher.