Statistical Analysis for Education and Psychology Researchers

0.0 0.0049

SMATHS 0.83722 1.00000.

0.0049 0.0

RAVEN...

Interpretation

Notice that SAS treats the RAVEN variable as missing in the correlation matrix. The
partial correlation for MATHS and SMATHS corresponds with the value computed in the
worked example (allowing for rounding error). A researcher may want to test the
significance of a difference between two correlations from independent samples. A SAS
programme to do this is presented in Figure 16, Appendix A3.

8.4 Independent t-test (unrelated two sample procedure)

When to Use

The two-sample independent t-test (sometimes called unrelated t-test) is most frequently
used in survey and experimental (parallel group) designs when an investigator wants to
determine whether there is a significant difference between two independent group
means. For example, an educational researcher may want to know which of two
classroom activities, reading silently or teachers’ storytelling is most helpful in improving
childrens’ word meanings. A teacher compares the vocabulary scores of two independent
classroom groups, one which has followed a reading programme including teacher
storytelling and the other which followed the same reading programme but had periods of
silent reading in the reading corner instead of the storytelling. In another example, as part
of a research programme on employee motivation and productivity, a psychologist
compares personality scores on Catell’s Sixteen Personality Factor Test (16PF) for male
and female employees.
In the t-test procedure, sample means are used to estimate the unknown population
means (parameters). With the two-sample t-test a researcher is interested in whether any
observed difference in means represents a real difference (not attributable to chance
fluctuations) and therefore justifies the inference that the two samples represent two
distinct populations with different population means rather than one population. The t-
statistic (sometimes called a t-ratio) is an estimate of the difference between two
population means. The significance of this difference is evaluated by calculating the
difference between the two means divided by the standard error of this difference. The
idea of computing this ratio is to compare the variability in the predicted differences in
scores, simply the difference between the mean scores for the two groups, to the total
variability of all scores (in both samples). Think of it as a proportion of variability
predicted compared with total variability. The standard error of the difference between
means is a measure of this total variability. The standard deviation of a sampling
distribution is usually referred to as the standard error of that distribution. Thus the
standard deviation of the mean is called the standard error of the mean. The difference

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