By Ruthie Swibel, Research Consultant

If you have struggled to interpret your child’s standardized test scores, you are not alone. Even those who don’t put a lot of stock into test scores (because we all agree— our children are so much more than a data point!), might still be curious if their child is on track academically and look to standardized assessments for insight.  

Standardized measures can be very helpful in determining if students are on track with their academic progress, but grade and age level equivalents are not helpful in determining this. Why are age and grade-level equivalents so unhelpful?

Let’s say a second grader received a grade-level equivalency of 4.0 on a reading assessment. This does not mean that this child is capable of reading texts that students in 4th grade read or that the student is “reading on a 4th grade level.” It means that the student performed as well as the average 4th grade student would on 2nd grade work.

Here’s another example. It makes intuitive sense to think that if your child scores a grade-level equivalency of 4.5 (4th grade, 5th month) at the start of the year and a 5.5 grade-level equivalency at the end of the year your child has made the equivalent of one grade level year of growth. If only it were that easy! The test creators calculate grade-level equivalency scores by counting the number of correct answers (called a raw score) and then converting this number to a grade-level equivalency based on a system of averaging raw scores of thousands of students who were used to create the grade-level equivalency for the normed sample in the first place. This raw score provides nothing in the way of understanding growth over time. Confused? You’re not alone.

Time for another example. Let’s say 2nd grade students A and B both take a math assessment that includes one-digit addition, multi-digit addition, and multiplication. Child A might answer all of the one-digit addition problems correctly, and none of the more challenging multiplication or addition problems. Child B might answer all of the multiplication problems correctly and few of the more simple addition problems. Both children could receive the same number of correct answers (raw score) and therefore the same grade-level equivalency score. When we retest the students at the end of the year their raw scores might be higher, but that might be from simply answering more of the simple problems correctly! The new, higher raw score might look like growth, but skill levels are not looked at to calculate a grade-level equivalency equivalency score and therefore we can’t get much information from this grade-level equivalency.

To further complicate the matter, age and grade-equivalent scores are not a ratio or based on an interval scale of measurement. Here is the irony of using a standardized test and then reporting a grade equivalent—grade level equivalents aren’t standardized! Further, they assume equal growth between grades, when in reality, students in lower grades tend to make more rapid progress in the acquisition of skills such as vocabulary and reading than students in higher grades.  Older students (middle school and beyond) generally acquire skills at a slower pace than elementary-aged students. A grade-level equivalency that is 1 year “behind” for a younger student may represent a greater difference in raw score points than for an older student. The 1-year “delay” can be caused by 1 or 2 raw points at the higher grade levels and by a larger number of raw score points at the lower grade levels. It takes just a small change in raw scores at the older grade levels to cause a large bump up in grade-level equivalency. Because grade-level equivalency scores are not a ratio or an interval scale of measurement, they cannot be added, subtracted, or averaged for teachers and administrators to look at growth by a group over time.

The takeaway: Pay attention to the percentile score (if the report provides only standard scores, use this chart to easily convert standard scores to percentile scores) for assessments. The percentile scores are more accurate and informative as they are calculated based on the average at a given grade level and on the average distribution of scores. This score will give you information as to how your student is performing compared to other peers at that same grade level.

PSYCHOMETRIC MEASURES DEFINITIONS:

Standard Scores are raw scores that have been converted to have a mean and a standard deviation. This is done so that the scores can be compared at different grades or age groups by converting the scores to the same numerical scale. These scores reflect a student's rank compared to others

Percentiles are probably the most commonly used test score in education. A percentile is a score that indicates the rank of the student compared to others the same age or grade.

Scaled scores are standard scores that have a mean of 10 and a standard deviation of 3.

ETS stands for Educational Testing Service

A T-score (a.k.a. a t-value) is equivalent to the number of standard deviations away from the mean of the t-distribution. A t-score is the number used in a t-test to determine whether, and how significantly, the mean of a sample population differs from the mean of the larger population. The t-score is only valid for normally distributed data.

A Z-score measures the distance between a data point and the mean using standard deviations. Z-scores can be positive or negative. The sign tells you whether the observation is above or below the mean. For example, a z-score of +2 indicates that the data point falls two standard deviations above the mean, while a -2 signifies it is two standard deviations below the mean. A z-score of zero equals the mean. Statisticians also refer to z-scores as standard scores.

Do you have concerns about your student’s academic progress? Reach out to us at Redwood Literacy! We are here to help your student receive the support they need to unlock their fullest potential.