RESEARCH METHODS HANDBOOK

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Contents	Introduction	Descriptive	Hypothesis	Tables	Appendix

One-Way Analysis of Variance
(ANOVA)

Used to evaluate multiple means of one independent variable to avoid conducting multiple t-tests

Assumptions

Random sampling

Interval/ratio level data

Independent samples

State the Hypothesis Null Hypothesis (Ho): There is no difference between the means of __________________.

Alternative Hypothesis (Ha): There is a difference between the means of __________________.

Set the Rejection Criteria Determine the degrees of freedom for the F Distribution

df for numerator = K - 1 where K = number of groups/means tested

df for denominator = N - K where N = total number of scores

Determine the level of confidence -- alpha

Establish the F critical value (Fcv) from the F Distribution table

Compute the Test Statistic

= each group mean

= grand mean for all the groups = ( sum of all scores)/N

nk = number in each group

Note: F= Mean Squares between groups/ Mean Squares within groups

Sum of Squares between groups =

Sum of Squares within groups =

Decide Results of Null Hypothesis Compare the F statistic to the F critical value. If the F statistic (ratio) equals or exceeds the Fcv, the null hypothesis is rejected. This suggests that the population means of the groups sampled are not equal -- there is a difference between the group means.

Example