Monday, November 10, 2008

Understanding the Numbers - II

I wanted to continue our discussion on statistics and interpreting test scores. Again, most of the information that you will read on this topic are from Jerome Sattler's "Measurement of Children."

Percentile ranks are the next norm-referenced measurement (an indication of average or typical performance of the specified group) that I want to discuss.

Percentile ranks are derived scores that permit us to determine an individual's position relative to the standardization sample (or any other specified sample). A percentile rank is a point in a distribution at or below which the scores of a given percentage of individuals fall. If 63 percent of the scores fall below a given score, then that score is at the 63rd percentile rank. Quartiles are percentile ranks that divide a distribution into four equal parts, with each part containing 25 percent of the norm group. Deciles, a less common percentile rank, contain 10 bands, with each band containing 10 percent of the norm group.

Interpretation of percentile ranks is simple and straightforward. For example, a person who obtains a percentile rank of 85 on an intelligence test has scored as well as or better than 85 percent of the people in the norm sample. However, the psychometric properties of percentile ranks limit their usefulness in data analysis. The primary difficulty is that all points along the percentile distribution do not represent equal units. Raw score differences between percentile ranks are smaller near the mean than at the extremes of the distribution. Thus percentile ranks must be normalized through conversion to another scale before they can be used in statistical tests.

[Remember: A norm group should be representative of the various demographic populations as a whole, the number of subjects in the the norm group (size) should also be large enough to ensure stability of the test scores, and it is always important to consider how relevant the norms are to the evaluation of the examinee.]

Remember to check out the "Labels" section of the blog where all posts are archived according to topics. This allows you to review previous posts and see what you might have missed! J.T.

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