Statistical Methods for Psychology

From Figure 18.6 we can see that the median Avoidance score for the Success group

was 13, and the median for the Fail group was 17. The group who failed to improve exhib-

ited more avoidance behavior early in treatment. The difference in median avoidance is 2 4.

From the output you can also see that when we model the null hypothesis, 222 of the

resamples were greater than a difference of 4, 264 results were less than a difference of 2 4,

and 486 results were greater than 6 4. Out of 10,000 samples, this represents 486/10,000 5

4.86% of the cases. Thus only 4.9% of the resampling statistics were more extreme than

our result, and we can reject the null hypothesis at a5.05. We can conclude that those in

the Fail group experienced significantly more avoidance behavior early in treatment than

those who later were classed as successes.^5

18.5 Bootstrapping Confidence Limits on a Correlation Coefficient

The standard approach to correlation problems is to calculate a correlation coefficient and

then to apply a hypothesis test with the hope of showing that the correlation is significantly

different from 0.00. However, there are a lot of significant correlations that are so low that

they are not particularly important, even if they are significantly different from 0.00. Along

with the recent emphasis on effect, size measures should be an increase in the use of confi-

dence limits.

As we saw in Chapter 9, Fisher’s arcsine transformation

provides one way to adjust for the skewed sampling distribution of rwhen r 0. An

attractive alternative is to draw bootstrapped samples on the assumption that the bivariate

±

r¿=(0.5)loge^2

11 r

12 r

2

670 Chapter 18 Resampling and Nonparametric Approaches to Data

Value in MEDDIFF

–10 –7.5 –5 –2.5 0 2.5 5 7.5 10

Histogram of “MEDDIFF” in file “eppingmedians.sta”

Frequency

2000

1500

1000

500

Figure 18.7 Frequency distribution of median differences from Epping-Jordan

et al. (1994)

(^5) If we had run a standard ttest on the means of these data, that probability would have been .0397.