How is a mean score determined?
To determine your child’s mean score (or average score), simply take the national percentile rank scores (NPR) in Reading (Total), Mathematics (Total), Language (Total), Science and Social Studies, add those five scores, and divide by five. Then determine which stanine that falls in on a bell curve. (See more details below.) If you test with CHEWV, we do all that for you! You’ll find both the mean and the stanine on the CHEWV Score Sheet.
While the composite score is more meaningful overall, the WV law references the mean, or average, of five scores. In fact, it was in the 1994 legislative session that the law’s wording was changed from “composite” to “mean” in order for parents to know exactly what their child’s reported score was. A composite score is based on weighted scores of the various subtests, and includes all subtests within a given achievement test – including some areas we are not required to report. The word mean was retained in the 2003 law and again in the 2016 revision. However, in 2016 the standard was changed from an NPR score to a stanine score.
Because the stanine rank is much less specific than the NPR, CHEWV continues to figure the mean from the NPR scores of the five required subjects. Those five NPR scores are averaged to obtain the mean and then we see where that mean falls within the stanine distribution.
If you do not test with CHEWV, you can still take the NPR for Reading Total, Language (or ELA) Total, Mathematics Total, Social Studies, and Science, add those five NPR scores together, and divide by 5. That will provide the arithmetic NPR mean. Then the NPR can be converted to a stanine value using a bell curve distribution such as the one below.
There seems to always be confusion in some counties about individual scores versus the mean score. Therefore, CHEWV began providing the arithmetic mean on our “Report to the Superintendent” beginning in 2011. Since the 2016 standard became a stanine number, it is hoped that counties will be less likely to mistakenly address individual scores.
Over the years, differing calculations have been used to determine the NPR mean. One method of calculation is simply to add the percentile scores in the required subject areas and divide by the number of scores (5) – resulting in the typical arithmetic average. However, because percentiles are not of equal intervals and thus cannot be added or subtracted with statistical significance, an alternative method can be used. Dr. Henry Marockie, the former State Superintendent of Schools, directed county superintendents to use Normal Curve Equivalent calculations to determine the mean scores several years back. In contrast to percentiles, NCE’s provide an equal interval scale.
Some counties may be using the NCE-calculated mean; others are using the arithmetic average and not being concerned about the accuracy of the score. There is not much difference between the two calculations except around the 40th percentile range. NCE-calculated mean scores are a little lower around the 40th percentile than are arithmetic averages. Because of this slight variance, you may want to know your child’s NCE-calculated mean score if your child scored around the 40th percentile.
Determining the NCE-calculated mean score
Refer to the tables below to determine the NCE-calculated mean. Use Table 1 to convert each percentile rank score to an NCE score for each of the five areas. For CHEWV students, this would be the individual scores found on the Report to the Superintendent.