|
Size: 1367
Comment:
|
Size: 2047
Comment:
|
| Deletions are marked like this. | Additions are marked like this. |
| Line 13: | Line 13: |
| 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) |
||||||||<25% style="TEXT-ALIGN: center"> '''Model''' ||<25% style="TEXT-ALIGN: center"> '''Chi-square''' ||<25% style="TEXT-ALIGN: center"> '''Df'''||<25% style="TEXT-ALIGN: center"> '''p-value''' || ||||||||<25% style="VERTICAL-ALIGN: top"> Linear ||<25% style="VERTICAL-ALIGN: top"> 7.96 ||<25% style="VERTICAL-ALIGN: top"> 1 ||<25% style="VERTICAL-ALIGN: top"> 0.005 || ||||||||<25% style="VERTICAL-ALIGN: top"> Lack of Fit ||<25% style="VERTICAL-ALIGN: top"> 0.29 ||<25% style="VERTICAL-ALIGN: top"> 1 ||<25% style="VERTICAL-ALIGN: top"> 0.130 || ||||||||<25% style="VERTICAL-ALIGN: top"> Total ||<25% style="VERTICAL-ALIGN: top"> 8.25 ||<25% style="VERTICAL-ALIGN: top"> 2 ||<25% style="VERTICAL-ALIGN: top"> 0.004 || ||||||||<25% style="VERTICAL-ALIGN: top"> ||<25% style="VERTICAL-ALIGN: top"> (Pearson Chi-square) ||<25% style="VERTICAL-ALIGN: top"> ||<25% style="VERTICAL-ALIGN: top"> || |
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
|
Time 1 |
Time 2 |
Time 3 |
|||
Correct |
3 |
6 |
10 |
|||
Incorrect |
9 |
6 |
2 |
|||
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.
Model |
Chi-square |
Df |
p-value |
|||
Linear |
7.96 |
1 |
0.005 |
|||
Lack of Fit |
0.29 |
1 |
0.130 |
|||
Total |
8.25 |
2 |
0.004 |
|||
|
(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