A one-way ANOVA (Analysis of Variance) compares the means of three or more groups of data to determine if the groups are different. In a one-way ANOVA, the data for the X group is attribute, and the data for the Y group is variable.
The null hypothesis for a one-way ANOVA states that there is no difference between the groups. The alternative hypothesis states that there are significant differences between the groups.
According to Norusis (2004), the three assumptions for a one-way ANOVA are:
1. Samples are independent and random
2. The population is normally distributed
3. The population variances are equal
There are several reasons to determine if these assumptions are met. If the samples are not randomized, then bias can be introduced into the analysis. If the sample population is not normally distributed and small, then the mean and standard deviation can be negatively impacted. If the number of cases within the subgroups are different and are creating population variance, then the multiple comparison procedure should be used to ensure accurate analysis.
Sign up for our Gold-level, Lean Six Sigma training to learn more about the one-way ANOVA.
Norusis, M.J. (2004). SPSS 12.0 guide to data analysis. Upper Saddle River, NJ: Prentice-Hall.