Summarizing Assessment Results: Comparing Test Scores to a Larger Population Video

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Lesson Transcript
Instructor: Melissa Hurst
Assessment results can yield valuable information about the individual test-taker and the larger population of test-takers. This lesson will describe how to compare test scores to a larger population by explaining standard score, stanines, z-score, percentile rank and cumulative percentage.

Standard Score, Stanines and Z-Score

Okay, you explained how to use a normal distribution to understand test scores. Now I still need to compare individual test scores to a larger population. Can you help me understand how to do that?

A common method to transform raw scores (the score based solely on the number of correctly answered items on an assessment) in order to make them more comparable to a larger population is to use a standard score. A standard score is the score that indicates how far a student's performance is from the mean with respect to standard deviation units.

In another lesson, we learned that standard deviation measures the average deviation from the mean in standard units. Deviation is defined as the amount an assessment score differs from a fixed value. The standard score is calculated by subtracting the mean from the raw score and dividing by standard deviation.

Example of a standard deviation graph
Standard Deviation Graph

In education, we frequently use two types of standard scores: stanine and Z-score.

Stanines are used to represent standardized test results by ranking student performance based on an equal interval scale of 1-9. A ranking of 5 is average, 6 is slightly above average and 4 is slightly below average. Stanines have a mean of 5 and a standard deviation of 2.

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