East Carolina University
Department of Psychology


Resampling Statistics

    These statistics may be appropriate in circumstances where you are uncomfortable with the normality assumption common to parametric inferential statistics, and perhaps in some other circumstances as well. David Howell is of the opinion that resampling statistics will replace the traditional nonparametric statistics, and perhaps the traditional parametric statistics, in time.

    Howell’s resampling software is available on Howell’s Resampling Statistics page. In addition to reading the material there, you should download the program, unzip it, and install it on your personal computer.

Bootstrapping

    With this approach, one constructs a sampling distribution by repeatedly sampling, with replacement, from the actual sample of data at hand. This is much like what we did back in PSYC 6430 when we employed Monte Carlo methods to construct sampling distributions of the mean, variance, standard deviation, z, and t, but then we sampled from mathematically defined populations (such as the standard normal population).

Confidence Interval for a Median

    Consider the example presented displayed on Figure 18.1 of David Howell's Statistical Methods for Psychology, 8th edition. The data at hand are 20 scores on a memory task.  We wish to construct an 95% confidence interval for the median. We chose the median because the distribution appears to be distinctly skewed. Here is how we construct the confidence interval:

    The sampling distribution obtained by Howell appears on page 662 of his textbook and indicates a 95% CI of [6, 10].

     Dr. Howell has provided us with resampling software which he has authored. I would like you to give it a try. Please complete the following exercise and those that follow:

Confidence Interval for Pearson r

    Consider the data on misanthropy, idealism, and attitude about animals, which we analyzed back in PSYC 6430. We found a significant correlation between misanthropy and attitude about animals for nonidealists but not for idealists. Let us now put a confidence interval on the correlation we obtained with the nonidealists. Here is how we construct the confidence interval:

    Let us use Howell's resampling program to construct this confidence interval:

    You know that the traditional independent samples t test is equivalent to a test of the null hypothesis that the point-biserial r is zero in the population. Accordingly, it might well make sense to use this correlation program for a bootstrapping test of the difference in means between two independent samples -- just code group membership with numbers (like 1 and 2) and run the program. If the confidence interval for the point biserial r does not include zero, then the two groups differ significantly.

Permutation/Randomization Tests

    With this approach one takes the data at hand, randomly assigns scores to groups (without replacement), and then computes, on the obtained sample(s), the relevant statistic. This procedure is repeated many times, obtaining a sampling distribution of the statistic of interest.

Two Independent Samples

    Consider the data on page 667 of Howell's textbook. We have a sample of 49 scores in the success group, and 18 in the fail group. Here is how we conduct a permutation/randomization test:

     Try using Howell's software to conduct this test:

Two Correlated Samples

    Consider the data on page 665 of Howell's textbook. We have paired data from 19 subjects, and 19 signed difference scores. Here is how we conduct a permutation/randomization test:

    Try using Howell's software to conduct to analyze these data:

Closing Comments

    The program will do more than what I have covered here. Feel free to play around with the other routines available there.

    Dr. Howell's program is designed as a teaching tool rather than a research tool. If you wish to conduct resampling statistics for research purposes, you might want to get a commercial package -- unless you are as frugal as am I.

    Thanks, Dave, for your work on this!

Statistics 101

    John Grosberg offers a giftware program he has written, Statistics101.  It executes the Resampling Stats language of Julian Simon and Peter Bruce.  I have not had a chance to evaluate it myself.

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This page most recently revised on the 7th of February, 2014.