Statistical Analysis for Education and Psychology Researchers

We can now summarize these results in an ANOVA table:

Source of variation Degrees of freedom SS MS F

Between groups (Model) 2 10.583 5.292F=0.79; df2, 21

Within individuals (Error) 21 140.750 6.702

Corrected total 23 151.333

Interpretation

We can look up the significance of the F-statistic corresponding to our chosen alpha level
of 5 per cent, in Table 7 of Appendix A4. We enter the column at the top of the table with
numerator df of 2 and find where this intersects with a row or denominator df of 21. The
critical F-value in the body of the table is 3.47. The observed F-value does not fall
beyond this critical value and therefore we cannot reject the null hypothesis of equal
means, F=0.79, df 2,21. It therefore appears that pupils in the three religious groups have
similar attributions about the concept of probability.

Computer Analysis

The SAS procedure PROC GLM is used to perform an analysis of variance on the data
shown in Table 8.9. PROC GLM (general linear models) uses the method of least squares
analysis to fit statistical models to data. It is suitable for both balanced and unbalanced
designs and can be used for both univariate and multivariate analyses. To perform a One-
way ANOVA the following SAS code would be submitted:

proc glm data=a;

class religion;

model attrib1=religion;

output out=new r=res1 p=pred1;

run;

The class statement specifies the variable(s) that categorizes the data into subgroups. The
model statement specifies on the left of the equals sign the response variable(s) and on
the right of the sign the independent variables that you want to model. In this example we
want to determine the effects of different categories of the independent variable, religion
(different religions) on the response variable attrib1 (attribution score). The output
statement outputs the residuals and predicted values from the fitted statistical model to a
data set which is named new. The residual and predicted values are named res1 and pred1
respectively.
The summary ANOVA table produced by SAS is shown in Figure 8.14. Although
there are no missing values in this particular data set, PROC GLM can handle missing
data. The GLM procedure actually estimates values for the missing data points from the
fitted least squares solution such that the residuals sum to zero.
To check the model assumptions of normality and homogeneity of variance the fitted
residuals are ranked using PROC RANK, using the following SAS code.
General Linear Models Procedure
Class Level Information

Statistical analysis for education and psychology researchers 320