Statistical Analysis for Education and Psychology Researchers

8 19 18 18
9 12 19 11
10 9 20 22

S^2 (variance)*=25.733 S^2 (variance)=17.389

• The sample variance is calculated using formula 3.1 in Chapter 3 For Age 6,

and for age 7, S^2 ,

Separate Variance Estimate

To calculate a separate variance estimate for t′, three steps are involved, i) find the
difference in means between the two groups; ii) calculate the standard error of the
difference in means; and iii) evaluate t′ which is the ratio of the difference in means (i
above) to the standard error of this difference in means (ii above).

1 Difference in means

In this example the difference is

2 Standard error of the difference in means (separate variance estimate)
The standard error of the difference in means is,

Standard error of

difference in means

separate variance

estimate—8.17

The SEdiffin means for the data in Table 8.6 is,
3 t′-ratio

The t′-ratio is evaluated as diff in means, which gives the

value, t′=−3.0338

For the separate variance estimate the degrees of freedom are estimated using

equation 8.16,

Inferences involving continuous data 299