Anova

Objectives
The one-way analysis of variance (ANOVA) is used to determine whether there are any significant differences between the means of three or more independent (unrelated) groups. This guide will provide a brief introduction to the one-way ANOVA including the assumptions of the test and when you should use interpret the output. This guide will then go through the procedure for running this test in SPSS using an appropriate example, which options to choose and how to interpret the output. Should you wish to learn more about this test before doing the procedure in SPSS, please click here.
What does this test do?
The one-way ANOVA compares the means between the groups you are interested in and determines whether any of those means are significantly different from each other. Specifically, it tests the null hypothesis:

where µ = group mean and k = number of groups. If, however, the one-way ANOVA returns a significant result then we accept the alternative hypothesis (HA), which is that there are at least 2 group means that are significantly different from each other.
At this point, it is important to realise that the one-way ANOVA is an omnibus test statistic and cannot tell you which specific groups were significantly different from each other, only that at least two groups were. To determine which specific groups differed from each other you need to use a post-hoc test. Post-hoc tests are described later in this guide.
Assumptions
  * Independent variable consists of two or more categorical independent groups.
  * Dependent variable is either interval or ratio (continuous) (see our guide on Types of Variable).
  * Dependent variable is approximately normally distributed for each category of the independent variable (see our guide on Testing for Normality).
  * Equality of variances between the independent groups (homogeneity of variances).
  * Independence of cases.
Example
A manager wants to raise the productivity at his company by...