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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

 

One-Way ANOVA
A word about SPSS.

Here, unfortunately, we run into a snag with SPSS. It readily calculates Post hoc tests for one-way between groups ANOVAs (as we are doing here) but for repeated measures and for some higher order ANOVAs, SPSS will not calculate them for you. I am still not sure why at this point. There are also ways of doing post hoc comparisons in SPSS without resorting to Tukey's. But for the sake of simplicity and consistency we are going to use Tukey's throughout. But this means . . .

You will have to be able to calculate Tukey's HSD by hand (i.e., calculator).

It is therefore very important that you learn how to calculate Tukey's HSD by hand (!) So we will go through the steps here even though in this case the computer will do them for us.

The formula for Tukey's HSD is not clearly given in Howell, but it is

Note the presence of the 'q'. You will have to be able to find this number in a table. Most statistics texts have a table of q- values. THE STUDENTIZED RANGE STATISTIC (q) can be found on page 680-681 in Howell. Howell explains the derivation and use of q on pages 370-372.

For our example, k = 5 (because five means are being compared), and the df for the error term is 45. This gives a q-value of 4.04 (taking the lower df = 40). Note that we will always use alpha  = .05 when using Tukey's HSD. If there were 10 observations making up each mean, the formula for the HSD value gives

A HSD value of 3.97 (i.e., a bit less than 4) represents the cut off point for deciding if two means are to be treated as significantly different or not. All differences between means that are greater than (or equal to) this critical value are considered significantly different.

 

 

 

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