IQ Testing

¶ … person is given a raw score on a particular test the person has no way of knowing how their score compares with other scores on the same test. For example, if a person got a raw score of 62 on a test of reading the person really does not know what that score means relative to the scores of other people who took the same test.

When people describe themselves or someone else being as scoring at a particular percentile on a certain ability or test they are referring to the percentile rank scored on a particular test. The percentile rank represents the number of people at or below a particular score on the test (Runyon, Coleman, & Pittenger, 2000). For instance, the statement such as, "My child is in the 75th percentile in reading," means that the child scored higher than 75% of other children who took the same test.

Percentile ranks simply allow for a comparison of a single score in a distribution relative to other scores in the same distribution of scores on the same measure (Cohen & Swerdlik, 2013). These are test result measurements; they are not general ability rankings. For example, scoring at the 75th percentile on a standardized reading test does not mean that one reads better than 75% of all people, just that one's score is at or above the scores of 75% of people in the same distribution on the same test (Huck, 2012).

Thus, it offers comparative information above and beyond reporting the raw score on a test. Percentile rankings are most often calculated for normal distributions where the measures of central tendency are equivalent are not valid comparisons in non-normal distributions. In a highly skewed distribution, such as measure of reaction time which is highly positively skewed, percentile ranks calculated by using the mean value as the 50th percentile are not meaningful (Cohen & Swerdlik, 2013).

When describing dispersion, or how the scores on the test are spread about the mean of the distribution, the most common statistic used is the standard deviation. The standard deviation is the square root of the variance (Runyon et al., 2000). The variance is a representation of the average distribution of scores around the mean of the distribution. The standard deviation describes how far particular score lies from the mean of the distribution (Huck, 2012).

When using the standard deviation as a descriptive statistics one implies that the distribution of scores is normal or near normal because the standard deviation is based on a distribution where the mean is at the 50th percentile (Cohen & Swerdlik, 2013). Thus, half of the scores in the distribution are above the mean and half of the scores in the distribution are below (all three measures of central tendency in a normal distribution are equal so this would apply to all measure of central tendency; Runyon et al., 2000).

When someone says that they scored one standard deviation below the mean they are telling you that they scored less than the 50th percentile (in this case a little more than 84% of.