A researcher uses analysis of variance to test for mean differences among three treatments with a sample of n = 12 in each treatment. The F-ratio for this analysis would have what df values?
To determine the degrees of freedom (df) values for an analysis of variance (ANOVA), we need to consider two aspects: the numerator degrees of freedom and the denominator degrees of freedom.
In this case, the numerator df is equal to the number of groups minus 1, which is 3 - 1 = 2. This represents the variability between the treatment means.
The denominator df is equal to the total sample size minus the number of groups, which is (n × k) - k, where n is the sample size per group (12) and k is the number of groups (3). Therefore, the denominator df would be (12 × 3) - 3 = 33. This represents the variability within the groups.
Hence, the F-ratio for this analysis would have numerator df = 2 and denominator df = 33.