{"id":19477,"date":"2025-09-25T05:00:00","date_gmt":"2025-09-25T12:00:00","guid":{"rendered":"\/blog\/?p=5337"},"modified":"2025-09-24T08:38:41","modified_gmt":"2025-09-24T15:38:41","slug":"measuring-growth-and-understanding-negative-growth","status":"publish","type":"post","link":"https:\/\/www.nwea.org\/blog\/2025\/measuring-growth-and-understanding-negative-growth\/","title":{"rendered":"Measuring growth and understanding negative growth"},"content":{"rendered":"\n
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In my time as an NWEA researcher, I often answered questions about how to interpret changes in observed scores on MAP\u00ae Growth\u2122<\/a>. Measuring student growth with MAP Growth is a lot like measuring growth in height with a tape measure. A student gets measured once, then, after an appropriate amount of time, gets measured again. Any observed changes in the student\u2019s measured height may be interpreted as growth.<\/p>\n\n\n\n

What adds complexity to measuring growth on MAP Growth, however, is that the assessment score, called a RIT score<\/a>, is reported along with a standard error of measurement (SEM), which conveys the margin of error for the measured score. For example, if I produced a RIT score of 214 in the fall, and my SEM was 3.2, my \u201ctrue score\u201d might have been a bit lower than 214 (as low as 210.8) or a little bit higher (as high as 217.2). The odds are that it fell somewhere in the range of 214\u00b13.2, but I can\u2019t know exactly where. Imagine, further, that I produced a winter RIT score of 212 with an SEM of 3.1. Again, the \u201ctrue score\u201d can\u2019t be exactly known, but it probably falls within the range of 212\u00b13.1.<\/p>\n\n\n\n

So, then, did I grow? The easy answer is that I lost two RIT points because the difference between my measured scores in winter and fall was -2 points. But since there are margins of error on the observed scores, there must be a margin of error for my observed loss, too. NWEA refers to these as growth standard errors.<\/p>\n\n\n\n

Understanding growth standard errors<\/h2>\n\n\n\n

Growth standard errors are related to the individual score SEMs, with smaller SEMs leading to smaller growth standard errors. In the example above, my growth standard error would be 4.46. This means that my \u201ctrue growth\u201d most likely falls within -2\u00b14.46, or between the range of -6.46 and 2.46 RIT points.<\/p>\n\n\n\n

This can be represented visually with a bell curve, as in the figure below, in which the red shaded area represents the range of \u00b11 standard error around the observed change (the vertical line at -2):<\/p>\n\n\n\n

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The bell curve displays the possible range of outcomes for my \u201ctrue growth.\u201d The red shaded area constitutes 68% of the total area under the bell curve, which is another way of saying that we can be 68% certain that my \u201ctrue growth\u201d falls within that range (between -6.46 and 2.46). But what are the chances that even though my observed score decreased by two points that my \u201ctrue growth\u201d was positive? Visually, that might look like this:<\/p>\n\n\n\n

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\"A<\/p>\n\n\n\n

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Figure 2 is the same graph and shows the same distribution of growth scores as Figure 1. The only difference is that I am now highlighting growth scores that are above zero.\u00a0The red shaded area (about 32% of the total area under the curve) represents the possibility that my \u201ctrue growth\u201d was greater than zero, or positive. In other words, there is about a 32% chance that my \u201ctrue score\u201d actually increased, despite the fact that my observed scores dropped by two points. There is also about a 68% chance that my \u201ctrue growth\u201d was negative.<\/p>\n\n\n\n

The value of precision <\/h2>\n\n\n\n

This information is useful in multiple ways. First, it highlights the fact that MAP Growth contains an element of measurement error, which can be expressed in terms of probabilities. In the example above, we saw that my \u201ctrue\u201d growth score had about a 32% chance of being positive (or that I gained ground) and about a 68% chance of being negative (i.e., that my true score dropped). These kinds of statements are possible for all assessments, of course, but with MAP Growth, the magnitude of error for most students is relatively small compared to fixed-form or shorter-length adaptive tests. And the smaller the error, the more precisely we can measure small amounts of real student growth.<\/p>\n\n\n\n

Another reason this is helpful is because it helps us to correctly understand and interpret the magnitude of growth relative to measurement error. In my example, the observed change (-2 points) was small, relative to the growth standard error. This means that there was considerable uncertainty (about a 32% chance) that the observed loss was not real. In general, when observed changes are very large relative to their standard errors, we can be much more confident that they are real and not simply artifacts of measurement error. When changes are small relative to their standard errors, we are much less confident that they are real.<\/p>\n\n\n\n

Testing conditions matter<\/h2>\n\n\n\n

All of the examples given so far rely upon a basic assumption, which is that the testing conditions and environmental factors remain consistent across time. If we wanted to measure how much a student\u2019s height increased during a school year, we wouldn\u2019t measure them while barefoot in the fall and then again wearing three-inch platforms in the spring. If we did, we could not be confident that the observed changes in student height were due solely to physical growth. The same principle applies when measuring growth in achievement.<\/p>\n\n\n\n

This is a particularly important factor to consider when understanding and interpreting unusually large increases or decreases in student MAP Growth scores over time. In many cases, when a student shows an unexpected drop in score between two test events, the change can be attributed to other factors. Did the student spend too little time on the test? Was the student actively engaged, or were they responding randomly to the items? MAP Growth is designed to invalidate any test where the test duration is six minutes or less, but test durations of 10\u201315 minutes may be suspect as well. For a student to finish a 40-item MAP Growth test in that time, they would almost certainly need to rush through the test. This could lead to a higher SEM and a lower RIT score.<\/p>\n\n\n\n

How to get accurate assessment results<\/h2>\n\n\n\n

To ensure MAP Growth reliably measures a student\u2019s progress, there are several things you can do:<\/p>\n\n\n\n