The following results estimate the effects on test score of a number of different factors:- urban or rural school (URBAN), sex of child (SEX), standard or school year (YEAR) and, for the Chichewa test, whether Chichewa was the home language of the child (HOMEL). When analysing test scores in English the last of these variables (HOMEL) is inappropriate and is not included in the analysis.
Variable Codes
|
Variable |
Categories |
Codes |
|
YEAR |
3 |
3 4 6 |
|
SCHOOL |
5 |
M N P S W |
|
SEX |
2 |
B (boy) G (girl) |
|
URBAN |
2 |
R (rural) U (urban) |
|
HOMEL |
2 |
H (home language Chichewa) |
|
|
|
X (home language not Chichewa) |
The data in this study has a hierarchical structure, children within classes within schools, and this complicates the form of the analysis required. Each level in the hierarchy has its own degree of random variation which has to be taken into account. For example, a class may have a particularly good (or bad) teacher with the result that the scores of all the children in the class are better (or worse) than expected. This extra variation is over and above the usual child-to-child variation in scores. When comparing class types, i.e. years 3, 4 and 6, the extra variation should be estimated and taken into account, otherwise the differences between the years will be found to be more significant than they really should be. Similarly at the school level, when comparing urban and rural schools, the variation between schools needs to be used. The procedure MIXED in the computer package SAS is designed to deal with this type of data and has been used to produce the analyses.
Three sets of results are provided for each analysis:
1) estimates of variance parameters - these are the estimated values for the random sources of variation described above, child, class and school.2) estimates of fixed effects - these are the estimates of the effects of the factors listed above (year, sex, urban/rural). Since the analysis is concerned with differences due to the different categories in the factors then one category is taken as the base line and the difference between this and all other categories is presented, (eg for the factor "YEAR" the base line category is Year 6 at 0.0000 compared to which Year 4 gets -13.9642 or 13.9642 fewer marks than Year 6). In addition to the estimated effects an overall test of whether the factor has a significant effect is given.
3) least squares means - these are adjusted mean scores for each of the factors examined. Adjustment is made for all other factors in the analysis. Thus the least squares means for urban and rural schools are the scores to be expected in such schools if each class had the same number of pupils and equal numbers of boys and girls.
Significance Tests: Results
Section 1: English Word Find Test Scores.
Variance Parameter Estimates (REML)
|
Parameter |
Ratio |
Estimate |
Std Error |
Z |
P |
|
SCHOOL |
0.2917 |
12.7289 |
12.1475 |
1.05 |
0.2947 |
|
CLASS |
0.1088 |
4.7496 |
3.1947 |
1.49 |
0.1371 |
|
Residual |
1.0000 |
43.6297 |
2.8664 |
15.22 |
0.0000 |
Estimates for Fixed Effects
|
Parameter |
Estimate |
Std Error |
DF |
T Value |
P |
|
INTERCEPT |
29.8865 |
2.8786 |
464 |
10.38 |
0.0000 |
|
YEAR 3 |
-21.1943 |
1.5731 |
464 |
-13.47 |
0.0000 |
|
YEAR 4 |
-13.9642 |
1.5823 |
464 |
- 8.83 |
0.0000 |
|
YEAR 6 |
0.0000 |
|
|
|
|
|
SEX B |
1.9532 |
0.6088 |
464 |
3.21 |
0.0014 |
|
SEX G |
0.0000 |
|
|
|
|
|
URBAN R |
- 3.3313 |
3.5080 |
464 |
- 0.95 |
0.3428 |
|
URBAN U |
0.0000 |
|
|
|
|
Tests of Fixed Effects
|
Source |
NDF |
DDF |
Type III F |
Pr>F |
|
YEAR |
2 |
8 |
93.49 |
0.0000 |
|
SEX |
1 |
464 |
10.29 |
0.0014 |
|
URBAN |
1 |
3 |
0.90 |
0.4124 |
Least Squares Means
|
Level |
LSMEAN |
Std Error |
DF |
|
YEAR 3 |
8.0031 |
1.9701 |
464 |
|
YEAR 4 |
15.2332 |
1.9777 |
464 |
|
YEAR 6 |
29.1975 |
1.9792 |
464 |
|
SEX B |
18.4545 |
1.7774 |
464 |
|
SEX G |
16.5013 |
1.7830 |
464 |
|
URBAN R |
15.8122 |
2.2267 |
464 |
|
URBAN U |
19.1436 |
2.7106 |
464 |
Section 2. Chichewa Reading Test Scores
Variance Parameter Estimates (REML)
|
Parameter |
Ratio |
Estimate |
Std Error |
Z |
P |
|
SCHOOL |
0.1763 |
11.4064 |
11.9210 |
0.96 |
0.3387 |
|
CLASS |
0.1065 |
6.8892 |
4.4594 |
1.54 |
0.1224 |
|
Residual |
1.0000 |
64.6705 |
4.2491 |
15.22 |
0.0000 |
Estimates for Fixed Effects
|
Parameter |
Estimate |
Std Error |
DF |
T Value |
P |
|
INTERCEPT |
46.1624 |
3.0734 |
463 |
15.02 |
0.0000 |
|
YEAR 3 |
-29.1630 |
1.9062 |
463 |
-15.30 |
0.0000 |
|
YEAR 4 |
-15.8494 |
1.9131 |
463 |
-8.28 |
0.0000 |
|
YEAR 6 |
0.0000 |
|
|
|
|
|
SEX B |
1.2517 |
0.7425 |
463 |
1.69 |
0,0925 |
|
SEX G |
0.0000 |
|
|
|
|
|
URBAN R |
-4.6889 |
3.4665 |
463 |
-1.35 |
0.1768 |
|
URBAN U |
0.0000 |
|
|
|
|
|
HOMEL H |
1.3956 |
1.1562 |
463 |
1.21 |
0.2280 |
|
HOMEL X |
0.0000 |
|
|
|
|
Tests of Fixed Effects
|
Source |
NDF |
DDF |
Type III F |
Pr>F |
|
YEAR |
2 |
8 |
117.21 |
0.0000 |
|
SEX |
1 |
463 |
2.84 |
0.0925 |
|
URBAN |
1 |
3 |
1.83 |
0.2691 |
|
HOME L |
1 |
463 |
1.46 |
0.2280 |
Least Squares Means
|
Level |
LSMEAN |
Std Error |
DF |
|
YEAR 3 |
15.9785 |
2.0705 |
463 |
|
YEAR 4 |
29.2921 |
2.0929 |
463 |
|
YEAR 6 |
45.1416 |
2.1163 |
463 |
|
SEX B |
30.7633 |
1.8205 |
463 |
|
SEX G |
29.5115 |
1.8182 |
463 |
|
URBAN R |
27.7929 |
2.2607 |
463 |
|
URBAN U |
32.4819 |
2.6911 |
463 |
|
HOMEL H |
30.8353 |
1.7377 |
463 |
|
HOMEL X |
29.4396 |
1.9982 |
463 |
