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Wednesday, February 18, 2009
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 independentvariable. 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 I will use SPSS software to perform the statistical analysis for your dissertation results chapter. This service includes ample email and phone support to ensure that you get all the statistical help you need to fully understand and defend your results.
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To apply the test, assume random sampling of a variate with equal variances, independent errors, and a normal distribution. Let be the number of replicates (sets of identical observations) within each of factor levels (treatment groups), and be the th observation within factor level. Also assume that the ANOVA is "balanced" by restricting to be the same for each factor level.
Now define the sum of square terms
(1)
(2)
(3)
(4)
(5)
which are the total, treatment, and error sums of squares. Here, is the mean of observations within factor level, and is the "group" mean (i.e., mean of means). Compute the entries in the following table, obtaining the P-value corresponding to the calculated F-ratio of the mean squared values
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