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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
The summary table

The Summary Table in ANOVA is the most important information to come from the analysis. You need to know what is going on and what each bit of information represents.

An example Summary Table

Source of variation

Sum of Squares

df

Mean Square

F

Sig.

Between Groups

351.520

4

87.880

9.085

.000

Within Groups

435.300

45

9.673

   

Total

786.820

49

     

You should understand what each entry in the above Table represents and the principles behind how each entry is calculated. You do not need to know how the Sums of Squares is actually calculated, however.

We earlier defined variance as based on two terms,

From the above table, the Between Groups variance is 351.52 (i.e., the SS) divided by 4 (the corresponding df). This gives 87.88. The error variance is determined by dividing 435.3 by 45. This gives 9.673.

You need to be able to recognise which term in the Summary table is the error term. In the Summary Table above, the "Within Groups" Mean Square is the error term. The easiest way to identify the error term for a particular F-value is that it is the denominator of the F-ratio that makes up the comparison of interest. The F-value in the above table is found by dividing the Between Groups variance by the error variance.

The error term is often labelled something like "Within groups" or "within-subjects" in the summary table printout. This reflects where it comes from. The variation within each group (e.g., the 10 values that make up the Counting group) must come from measurement error, random error, and individual differences that we cannot explain.

The F-value is found by dividing the Between Groups Mean Square by the Error Mean Square. The significant F-value tells us that the variance amongst our five means is significantly greater than what could be expected due to chance.

 

 

 

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