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Chapter 7: Analysing the Data |
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One-Way ANOVA
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Source of variation |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
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Between Groups |
351.520 |
4 |
87.880 |
9.085 |
.000 |
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Within Groups |
435.300 |
45 |
9.673 |
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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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