Statistical Methods for Psychology

From Appendix t, we find that. Since is less than 2.262,

we will fail to reject and will decide that we have no evidence to suggest that the illu-

sion is affected by the elevation of the eyes.^8 (In fact, these data also include a second test

of Holway and Boring’s hypothesis since they would have predicted that there would not

be an illusion if subjects viewed the zenith moon with eyes level. On the contrary, the data

reveal a considerable illusion under this condition. A test of the significance of the illusion

with eyes level can be obtained by the methods discussed in the previous section, and the

illusion is statistically significant.)

Confidence Limits on Matched Samples

We can calculate confidence limits on matched samples in the same way we did for the

one-sample case, because in matched samples the data come down to a single column of

difference scores. Returning to Everitt’s data on anorexia we have

and thus

Notice that this confidence interval does not includemD 5 0.0, which is consistent with the

fact that we rejected the null hypothesis.

=3.57...m...10.95

CI.95=7.26 6 3.69

CI.95=7.26 6 2.12(1.74)

CI.95=D 6 t.05> 2 (sD)=D 6 t.025

sD

1 n

t=

D 20

sD

H 0

t.025(9)= 6 2.262 tobt=0.44

Section 7.4 Hypothesis Tests Applied to Means—Two Matched Samples 199

Table 7.4 Magnitude of the moon illusion when zenith moon is

viewed with eyes level and with eyes elevated

Observer Eyes Elevated Eyes Level Difference (D)

1 1.65 1.73 2 0.08

2 1.00 1.06 2 0.06

3 2.03 2.03 0.00

4 1.25 1.40 2 0.15

5 1.05 0.95 0.10

6 1.02 1.13 2 0.11

7 1.67 1.41 0.26

8 1.86 1.73 0.13

9 1.56 1.63 2 0.07

10 1.73 1.56 0.17

sD=0.043

sD=0.137

D=0.019

(^8) In the language favored by Jones and Tukey (2000), there probably is a difference between the two viewing
conditions, but we don’t have enough evidence to tell us the sign of the difference.