In the ed biz, I believe this is called "just in time teaching." That is, learn the statistics when you need them. Well, if you've got educational or psychological testing results sitting in front of you, you need a crash course in stats.
It takes some practice and understanding of statistics to understand most standardized test scores. This applies to almost any achievement or cognitive ability test your child takes, including a wide variety of other tests your child might encounter if you head out for a private evaluation.
Our school likes to spring a boat load of test results on parents during IEP and IEP-qualification meetings. This isn't useful as it takes time to understand and digest information. One solution is to understand the scores in general, and come prepared with the means to understand them quickly.
Scores come expressed in a variety of ways, scaled scores, (“standard scores” for subtest results), percentiles, stanines, t-scores, and grade-level equivalents. It's truly a dizzying array of numbers, and unnecessarily complicated.
Scaled scores, standard scores, t-scores and stanines all are numbers that are derived assuming that a population’s performance on the test follows a normal distribution, or, something that falls on a bell curve. For traits that fall on a bell curve, most of the population is near the average. How tightly or broadly grouped a population is about the average is quantified by the standard deviation. For a normal distribution, 2/3 of the population will be within one standard deviation in either way about the average.
Scaled scores, the scores used for IQ scores and a variety of psychometric tests are all scaled such that average is 100, and the standard deviation is about 15 (some are 14-16, and the standard deviation is often easily located online with google if it’s not part of the report). Therefore, 2/3 of the population is between 85-115. Therefore, someone with an IQ of 115 scores better than about 87% of the population, or is in the 87th percentile. When you see 87% on a test report, this number therefore has nothing to do with the number of right or wrong answers, but is a percentile rank. The percent of the population that the child performs above is the percentile.
t-scores tend to have an average of 50 and standard deviation of 10, and standard scores have an average of 10 and standard deviation of 3. Stanines are generally tied to percentiles divided by ten (so 90th percentile is generally 9th stanine).
The grade-level equivalent represents the grade level of the mythical average child that would have performed the same as your child. This piece of information is generally least useful for children significantly above or below the average for a given skill. Don’t get distracted by these scores as they tend to be wildly misleading.
Key pieces of information to understand when looking at test results:
*What is population assumed? (particularly important if your school's population isn't typical)
*Is it age mates or grade mates? (particularly important for kids old- or young- for grade)
*Is it relative to a national normalization (“national norm”) or is it normed to kids in your school district, state, or similar socio-economic level?
Two standard deviations from the mean is generally what is taken to indicate that a child’s needs are different for the norm. An IQ score of 130 is just about the 98th percentile. Such a child, therefore, would be expected to be found in a typical population at a rate of about 2 in 100.
Because 2 individuals isn’t enough to discuss trends, let’s expand the population size to 10,000 individuals. Generally for things normed in the style of IQ tests, that means that you are comparing this child to 10,000 other children within about 3 months of age as your child. If the child is in the 98th percentile, this means that the child is scoring in the top 200 of those 10,000. If, however, you look at a child three standard deviations from the mean, or 145, then this places the child in the 99.9 percentile, or scoring in the top 10 of a population of 10,000 equivalent children.
I find it very useful to use this measure of rarity, as it clarifies in my mind how unusual my children might be in their school and in their teacher’s experience. I actually carry a printout of an Excel spreadsheet I made (below) to meetings to help me re-interpret the numbers on the spot. The school psychologists I’ve worked with, and most of the school administrators have appreciated this viewpoint. One school psychologist asked me for a copy. It’s been hit or miss if teachers and intervention specialists understand it.
Note The most commonly used IQ test, the WISC (now on version 5), is for use with children between ages 6 to 17. The WISC-IV is based on 2200 children, with about 220 kids representing each year of age. The population frequencies I give here are mathematically derived assuming a bell-curve distribution of population. The tails at both high and low performance levels are very poorly represented, and there’s evidence that the population is not purely normally distributed when looking a great distance from the mean. I don’t intend the data I give to be taken literally, but instead as a means to give you and school administrators a sense of how unusual the child is.
It takes some practice and understanding of statistics to understand most standardized test scores. This applies to almost any achievement or cognitive ability test your child takes, including a wide variety of other tests your child might encounter if you head out for a private evaluation.
Our school likes to spring a boat load of test results on parents during IEP and IEP-qualification meetings. This isn't useful as it takes time to understand and digest information. One solution is to understand the scores in general, and come prepared with the means to understand them quickly.
Scores come expressed in a variety of ways, scaled scores, (“standard scores” for subtest results), percentiles, stanines, t-scores, and grade-level equivalents. It's truly a dizzying array of numbers, and unnecessarily complicated.
Scaled scores, standard scores, t-scores and stanines all are numbers that are derived assuming that a population’s performance on the test follows a normal distribution, or, something that falls on a bell curve. For traits that fall on a bell curve, most of the population is near the average. How tightly or broadly grouped a population is about the average is quantified by the standard deviation. For a normal distribution, 2/3 of the population will be within one standard deviation in either way about the average.
Scaled scores, the scores used for IQ scores and a variety of psychometric tests are all scaled such that average is 100, and the standard deviation is about 15 (some are 14-16, and the standard deviation is often easily located online with google if it’s not part of the report). Therefore, 2/3 of the population is between 85-115. Therefore, someone with an IQ of 115 scores better than about 87% of the population, or is in the 87th percentile. When you see 87% on a test report, this number therefore has nothing to do with the number of right or wrong answers, but is a percentile rank. The percent of the population that the child performs above is the percentile.
t-scores tend to have an average of 50 and standard deviation of 10, and standard scores have an average of 10 and standard deviation of 3. Stanines are generally tied to percentiles divided by ten (so 90th percentile is generally 9th stanine).
The grade-level equivalent represents the grade level of the mythical average child that would have performed the same as your child. This piece of information is generally least useful for children significantly above or below the average for a given skill. Don’t get distracted by these scores as they tend to be wildly misleading.
Key pieces of information to understand when looking at test results:
*What is population assumed? (particularly important if your school's population isn't typical)
*Is it age mates or grade mates? (particularly important for kids old- or young- for grade)
*Is it relative to a national normalization (“national norm”) or is it normed to kids in your school district, state, or similar socio-economic level?
Two standard deviations from the mean is generally what is taken to indicate that a child’s needs are different for the norm. An IQ score of 130 is just about the 98th percentile. Such a child, therefore, would be expected to be found in a typical population at a rate of about 2 in 100.
Because 2 individuals isn’t enough to discuss trends, let’s expand the population size to 10,000 individuals. Generally for things normed in the style of IQ tests, that means that you are comparing this child to 10,000 other children within about 3 months of age as your child. If the child is in the 98th percentile, this means that the child is scoring in the top 200 of those 10,000. If, however, you look at a child three standard deviations from the mean, or 145, then this places the child in the 99.9 percentile, or scoring in the top 10 of a population of 10,000 equivalent children.
I find it very useful to use this measure of rarity, as it clarifies in my mind how unusual my children might be in their school and in their teacher’s experience. I actually carry a printout of an Excel spreadsheet I made (below) to meetings to help me re-interpret the numbers on the spot. The school psychologists I’ve worked with, and most of the school administrators have appreciated this viewpoint. One school psychologist asked me for a copy. It’s been hit or miss if teachers and intervention specialists understand it.
Note The most commonly used IQ test, the WISC (now on version 5), is for use with children between ages 6 to 17. The WISC-IV is based on 2200 children, with about 220 kids representing each year of age. The population frequencies I give here are mathematically derived assuming a bell-curve distribution of population. The tails at both high and low performance levels are very poorly represented, and there’s evidence that the population is not purely normally distributed when looking a great distance from the mean. I don’t intend the data I give to be taken literally, but instead as a means to give you and school administrators a sense of how unusual the child is.
percentile_standardscore.xlsx |