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| ||||||||<25% style="TEXT-ALIGN: center"> ||<25% style="TEXT-ALIGN: center"> '''Time 1''' ||<25% style="TEXT-ALIGN: center"> '''Time 2'''|| <25% style="TEXT-ALIGN: center"> '''Time 3''' || ||||||||<25% style="TEXT-ALIGN: center"> Correct ||<25% style="TEXT-ALIGN: center"> 3 ||<25% style="TEXT-ALIGN: center"> 6 || <25% style="TEXT-ALIGN: center"> 10 || ||||||||<25% style="TEXT-ALIGN: center"> Incorrect ||<25% style="TEXT-ALIGN: center"> 9 ||<25% style="TEXT-ALIGN: center"> 6 || <25% style="TEXT-ALIGN: center"> 2 || Time1 Time2 Time3 Correct 3 6 10 Incorrect 9 6 2 |
||||||||<25% style="TEXT-ALIGN: center"> ||<25% style="TEXT-ALIGN: center"> '''Time 1''' ||<25% style="TEXT-ALIGN: center"> '''Time 2'''||<25% style="TEXT-ALIGN: center"> '''Time 3''' || ||||||||<25% style="VERTICAL-ALIGN: top"> Correct ||<25% style="VERTICAL-ALIGN: top"> 3 ||<25% style="VERTICAL-ALIGN: top"> 6 ||<25% style="VERTICAL-ALIGN: top"> 10 || ||||||||<25% style="VERTICAL-ALIGN: top"> Incorrect ||<25% style="VERTICAL-ALIGN: top"> 9 ||<25% style="VERTICAL-ALIGN: top"> 6 ||<25% style="VERTICAL-ALIGN: top"> 2 || |
A more powerful form of chi-square specifically tests for a linear trend in proportions across groups. For example, proportion remembered correctly using a memory aid.
Example
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Time 1 |
Time 2 |
Time 3 |
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Correct |
3 |
6 |
10 |
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Incorrect |
9 |
6 |
2 |
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Does the proportion correct change linearly over time?
The chi-square testing the presence of a linear trend is outputted by SPSS CROSSTABS as the Linear-by-Linear association term. The lack of fit is the difference between the Pearson chi-square value and the linear-by-linear one.
Chi-square Degrees of Freedom
Linear 7.96 on 1 p=.005 Lack of fit 0.29 on 1 p=.130
Total 8.25 on 2 (Pearson chi-square)
So there is a linear trend providing a reasonable fit.
Denoting the time points by –1,0 and 1 and regressing these on the observed