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Cindy is in the same class as Bill, Mary, and Pedro. On the mathematics test, she received a stanine score of9. Her mother wants to know just how high that score is-what percent of pupils perform less well than Cindy. Ms. Billingsley tells Cindy's mother that 96 percent of students in Cindy's grade performed less well than Cindy. Is this an accurate statement of Cindy's percentile rank?
No. The ninth stanine is not the 96th percentile. The lower limit of the ninth sta nine is the 96th percentile, but the upper limit is plus infinity. Any performance above the 96th percentile is the 9th stanine. Cindy may have scored far above the 96th percentile and received a stanine of 9. The same is true at the other end of the scale for a stanine of 1.A person with a stanine score of 1 may be as high as the 4th percentile, or very much lower.
Alfonso's stanine score is 7. Mr. Rivera is more familiar with standard scores than sta nines. He asked Ms. Billingsley how many standard deviations above the mean a stanine score of7 was. Ms. Billingsley imme diately responded, "One." Does Ms. Billingsley have a trick for remembering such things so well?
Yes. Three easy landmarks for relat ing stanines to standard scores ·are the mean and plus and minus one standard deviation. The mean is in the middle of the fifth stanine. Plus one standard deviation is in the middle of the seventh stanine. Minusone standard deviation is in the middle of the third stanine.
Mr. Rivera decided that Ms. Billingsley really knew her sta nines. So he pushed his luck and asked her what percent of students got stanine scores of7. Ms. Billingsley thought for a moment. Then she replied, "In a normal distribution, 12 per cent of the scores will be in the seventh stanine." Taken aback by the speed of her response, Mr. Rivera asked whether an other trick was involved. Was there?
Yes. Ms. Billingsley used the Rule of Four. With stanines, a close approxima tion to the distribution of scores can beremembered as starting with 4 percent in either stanine 1 or 9, then adding 4 percent for the next stanine each time up to stanine 5 and then subtracting 4 percent for each to the end of the scale. Thus, the percent of the scores that are assigned I, 2, 3, ...9 are verycloseto4,8, 12, 16,20, 16, 12,8,and4, respectively. So Ms. Billingsley said to her self, "Four percent for stanine 9, 8 percent for stanine 8, and 12 percent for stanine 7." Then she had her answer. She could have started with stanine 5, saying to herself,"Twenty percent in stanine 5, 16 percent in stanine 6, and 12 percent in stanine 7," reaching the same result.
Mr. Tatnall overheard the conversation between Ms. Bill ingsley and Mr. Rivera and decided to contribute another guide. He suggested that sta nines were the same as deciles. So, he said, the first stanine would be the same as the first decile, the second stanine and the second decile would be equivalent, and so on. Is Mr. Tatnall correct?
No. First, to be correct a decile is a point, not a range. The first decile is the score that separates the lowest scoring JO percent of scores from the highest scoring 90 percent, for example. The name for the lowest JO percent is the lowest tenth, or the first tenth, not the first decile. Beyond that, the first tenth is the lowest scoring JO per cent, but the first stanine is the lowest scor ing 4 percent, a much lower scoring group, on the average. In general, the only corres pondence between tenths of a distribution (or "deciles") and stanines is that tenths and stanines above 5 are high scoring and below 5 are low scoring. The differences between tenths and stanines reflect different as sumptions about the distribution of scores. Tenths are based on the assumption that scores have a rectangular or flat distribu tion. Stanines are based on the more realis tic assumption that scores are distributed normally.
Mr. Rivera decided to ask one more question. He has found that most of his students receive the same stanine scores in the fifth grade that they got in the fourth grade or even the third grade. He concluded that they are not making much pro gress in school. ls that correct?
No. Tests that use stanine scores refer these scores to students in a particular grade, not to students in general or to people in general. So a student who regularly receives stanine scores of 5 in a subject from year to year can be assumed to be making normal progress. He stays in the middle of the distribution. Another student who con tinually makes scores of stanine 7 stays about I standard deviation above the mean and makes normal progress also. Normal progress with stanines (or with percentiles or standard scores) is shown by earning the same score over time, not higher scores year by year.
Mr. Tatnall asked what should he do about Patricia, who went down from the fifth stanine last year to the fourth stanine this year in reading comprehension? Should Mr. Tatnall be worried about this?
No. Mr. Tatnall does not need to worry much about a change from one sta nine score to the adjacent stanine score. One question fewer correct could move a person one stanine down if his score was at the bottom of the range for that stanine. This is one of the problems with stanine scores. A person's performance can be anywhere in a range of scores but receive the same stanine. If Patricia scored at the lower edge of the fifth stanine, a trivial difference in performance could change her score to the next lower stanine.
Mr. Rivera then asked about his student, Elena, whose stanine score in reading com prehension went up from the fourth stanine to the sixth sta nine. Is that big a difference important?
Yes. When scores differ by two sta nines, we tend to think of there being a real difference, not an error of measurement. Other things being equal, for tests with satisfactory reliabilities (.90), such differen ces are expected to occur only about one time in ten. Therefore, differences that large deserve further investigation. Perhaps Elena has benefitted from some effective teaching, or she may have become more motivated, or she may have found more time to read, or something in her life that was impeding !}er progress may have been removed. A difference that large is unlikely to be an accident.
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