|
Size: 2700
Comment:
|
Size: 2700
Comment:
|
| Deletions are marked like this. | Additions are marked like this. |
| Line 22: | Line 22: |
| Denoting the time points by –1,0 and 1 and regressing these on the observed proportions correct gives regression estimates of the above linear trend | Denoting the time points by –1,0 and 1 and regressing these on the observed proportions correct give regression estimates of the above linear trend. |
| Line 25: | Line 25: |
| ||||||||<25% style="VERTICAL-ALIGN: top"> Observed proportion correct ||<25% style="VERTICAL-ALIGN: top"> 0.33 ||<25% style="VERTICAL-ALIGN: top"> 0.50 ||<25% style="VERTICAL-ALIGN: top"> 0.83 || ||||||||<25% style="VERTICAL-ALIGN: top"> Expected proportion correct ||<25% style="VERTICAL-ALIGN: top"> 0.30 ||<25% style="VERTICAL-ALIGN: top"> 0.55 ||<25% style="VERTICAL-ALIGN: top"> 0.80 || ||||||||<25% style="VERTICAL-ALIGN: top"> (Fitting a linear trend) ||<25% style="VERTICAL-ALIGN: top"> ||<25% style="VERTICAL-ALIGN: top"> ||<25% style="VERTICAL-ALIGN: top"> || |
||||||||<70% style="VERTICAL-ALIGN: top"> Observed proportion correct ||<10% style="VERTICAL-ALIGN: top"> 0.33 ||<10% style="VERTICAL-ALIGN: top"> 0.50 ||<10% style="VERTICAL-ALIGN: top"> 0.83 || ||||||||<70% style="VERTICAL-ALIGN: top"> Expected proportion correct ||<10% style="VERTICAL-ALIGN: top"> 0.30 ||<10% style="VERTICAL-ALIGN: top"> 0.55 ||<10% style="VERTICAL-ALIGN: top"> 0.80 || ||||||||<70% style="VERTICAL-ALIGN: top"> (Fitting a linear trend) ||<10% style="VERTICAL-ALIGN: top"> ||<10% style="VERTICAL-ALIGN: top"> ||<10% 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 proportions correct give regression estimates of the above linear trend.
Observed proportion correct |
0.33 |
0.50 |
0.83 |
|||
Expected proportion correct |
0.30 |
0.55 |
0.80 |
|||
(Fitting a linear trend) |
|
|
|
|||