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Chapter 7 - Analysing the Data Part IV - Analysis of Variance Chapter 1 - Behavioural Science and research Chapter 2 - Research Design Chapter 3 - Collecting the Data Chapter 4 - Analysing the Data Part I - Descriptive Statistics Chapter 5 - Analysing the Data Part II - Inferential Statistics Chapter 6 - Analysing the Data Part III - Common Statistical Tests


Chapter 7: Analysing the Data
Part IV : Analysis of Variance


Degrees of freedom

How the degrees of freedom are determined in the ANOVA Summary table is also worth knowing. This provides a way of checking if you have all the right bits in the table. In more complex designs, SPSS splits the output into Between groups effects and Within-subjects (i.e., repeated measures) effects. You need to be able to bring all the bits together.

An important point to keep in mind is that the Total degrees of freedom should be one less than the total number of observations making up the analysis. Here we had 50 bits of information, so the total degrees of freedom are 49. This 49 has been partitioned into two sources 4 from the number of means being compared (i.e., k-1 = 5 1 = 4) and n-1 from each sample. Here, with 5 samples of 10 people each, gives 9 degrees of freedom from each sample giving the df for the error term as 5 X 9 = 45.

Statistical hypotheses

Ho: µ1 = µ2 = µ3 = µ4

H1: µs not all equal

So, if we find that the test statistic (F, in this case) is too unlikely given the null hypothesis, we reject the null in favour of the alternative. In this case, accepting the alternative implies that there is a difference somewhere among our means. At least two of the means are significantly different to each other. If there are only two groups being compared we can automatically assume that they are significantly different to each other. However, if there are more than two we can never be sure exactly which means are significantly different to which other ones until we explore the findings further with post hoc tests.




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