Statistical Analysis for Education and Psychology Researchers

again as the ratio of the mean difference 1) above to the standard error of the differences
3) above.

1 Mean difference

This is simply the average difference score (occasion 2-occasion 1) =3.7.

2 Standard deviation of the differences (SDdiff)

The standard deviation of the differences is calculated using the usual

formula:

3 Standard error of the differences

The standard error of the differences is simply the standard deviation

divided by the square root of the sample size, which is

=3.850.

The t-statistic is the mean difference divided by the standard error of the differences, t is
therefore (3.7/3.850)=0.961. The degrees of freedom are given by n−1, in this example
df=9. One degree of freedom is used in estimating the variance of difference scores in the
population which is estimated from the sample mean difference.

Interpretation

The critical value at the 5 per cent significance level from the t-table (Table 3, Appendix
A4) is 2.262. Since the observed t-value of 0.961 is less than this critical value we cannot
reject the null hypothesis and therefore we conclude that it is plausible that the mean
difference (occasion 2-occasion 1) speaker scores is not significantly different from zero.

Confidence Interval for the Mean Difference (paired measures)

To calculate a 95 per cent CI, t 1 −α/2 is required. With 9 degrees of freedom this value is
2.262. The 95 per cent CI is given by,

(^) 95 per cent CI
for mean
difference (paired
data)—8.19
which is 3.7 +/− (2.262×3.850)
Statistical analysis for education and psychology researchers 306