The T-test tutorial page provides a good background for understanding ANOVA ("Analysis of Variance"). Like the two-sample t-test, ANOVA lets us test hypotheses about the mean (average) of a dependent variable across different groups.
While the t-test is used to compare the means between two groups, ANOVA is used to compare means between 3 or more groups.
There are several varieties of ANOVA, such as one-factor (or one-way) ANOVA, two-factor (or two-way) ANOVA, and so on, and also repeated measures ANOVA. The factors are the independent variables, each of which must be measured on a categorical scale - that is, levels of the independent variable must define separate groups.
One-Way ANOVA Example
One-factor ANOVA, also called one-way ANOVA is used when the study involves 3 or more levels of a single independent variable. For example we might look at average test scores for students exposed to one of three different teaching techniques (three levels of a single independent variable).
ANOVA Statistics
The null hypothesis for ANOVA is that the mean (average value of the dependent variable) is the same for all groups. The alternative or research hypothesis is that the average is not the same for all groups.
The ANOVA test procedure produces an F-statistic, which is used to calculate the p-value. As described in the topic on
Statistical Data Analysis if p < .05, we reject the null hypothesis. We can then conclude that the average of the dependent variable is not the same for all groups.
With ANOVA, if the null hypothesis is rejected, then all we know is that at least 2 groups are different from each other. In order to determine which groups are different from which, post-hoc t-tests are performed using some form of correction (such as the Bonferroni correction) to adjust for an inflated probability of a Type I error.
SPSS Anova Statistical Analysis
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The prior examples have assumed one line per unique subject/variable combination. This is not a typical way to enter data. A more typical way (found ., in Systat) is to have one row/subject. We need to "stack" the data to go from the standard input to the form preferred by the analysis of variance. Consider the following analyses of 27 subjects doing a memory study of the effect on recall of two presentation rates and two recall intervals. Each subject has two replications per condition. The first 8 columns are the raw data, the last 4 columns collapse across replications. The data are found in a file on the personality project server.

Mauchly’s test for sphericity can be run in the majority of statistical software, where it tends to be the default test for sphericity. Mauchly’s test is ideal for mid-size samples. It may fail to detect sphericity in small samples and it may over-detect in large samples.

If the test returns a small p-value (p ≤.05), this is an indication that your data has violated the assumption. The following picture of SPSS output for ANOVA shows that the significance “sig” attached to Mauchly’s is .274. This means that the assumption has not been violated for this set of data.