As we approach the end of the school year, I’ve started to receive an increasing number of questions from partner schools and districts about how to interpret the growth of students. More specifically, these questions often center on how best to apply the 2011 student norms and/or the 2012 school norms to the achievement and growth information of their students, and when it is appropriate to use the student norms instead of the school norms, and vice versa. So, I thought it might be helpful to take a moment to provide a quick overview of when these different norms should be applied, and why they might appear to tell different stories about the test performance of students.
First, the 2011 student norms were developed to provide context to the achievement and growth for individual students. At every term you can understand the percentile rank associated with a student’s RIT score (to see how this student compares to other students across the nation), and also understand how the gains made by a student between two terms compare to the gains of other similar students. So, if a 5th grade student had a RIT score of 200 in mathematics in the Fall and a RIT score of 215 in the Spring, we know that the student was at the 18th percentile in the Fall and the 34th percentile in the Spring, and that this student’s RIT gain of 15 points from Fall to Spring well exceeded the typical gain of 8 RIT points observed for students in the same grade, in the same subject, and with the same Fall RIT score. The student norms provide us with context to be able to interpret the test performance of this particular student, and indicate that he showed really strong improvement over the course of the year.
The 2012 school norms, by contrast, provide information about the achievement and growth of groups of students. With these norms, you can understand what it means if the average RIT score in mathematics for all of the 5th graders in your school was a 200 in the Fall and a 215 in the Spring—here, the group of 5th graders began the year at the 3rd percentile, ended the year at the 27th percentile, and showed an average gain of 15 RIT points, which was equivalent to growth at the 97th percentile (that is, these students showed growth greater than 97% of similar groups of 5th grade students).
“But wait, why do these norms tell two different stories about the performance of 5th grade students?” is the question that invariably follows this description of the two different sets of norms. The reason for this difference is—put simply—because the achievement and growth patterns of individual students looks much different than the patterns of groups of students.
The best way to think about this is to consider the achievement distribution of students within a typical 5th grade classroom. In most schools the distribution of students will be approximately normal, so the majority of students will be right around the 50th percentile (or what might be considered “grade level”), with fewer students at the extremes of the achievement distribution (say, less than the 10th percentile or greater than the 90th percentile). So, on average, a grade level with a normal distribution of students will have a median percentile rank of…? You guessed it – the 50th percentile.
If you then think about all of the different groups of 5th grade students in schools across the nation, and if we assume the majority of them have this same distribution of students, then most of the groups of 5th grade students in schools across the country will also have a median percentile rank of…? Again – the 50th percentile.
So, while all of the 5th grade students across the country are normally distributed, the distribution of groups of 5th grade students looks much different. There is much less variation in the performance of groups of 5th grade students than there is for individual 5th grade students. Because of this, if on average, your group of 5th grade students is very high or very low performing, their percentile rank will look much different than what you might expect based on the individual student norms.
In short, if you want to interpret the growth of an individual student, use the 2011 student norms. And, if you want to interpret the growth of a group of students within your school, then you should use the 2012 school norms. But make sure that you don’t simply apply the 2011 student norms to the average RIT score of a group of students, as this approach is incorrect and will not provide you with accurate information about the achievement and growth of your students.
If you need some more clarification about the differences in these two sets of norms, leave me a comment below, and I’ll make sure to get your question answered. Good luck to everyone as we enter the final stretch of the school year!