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Comparison of the various grading methods in a normal distribution, including: standard deviations, cumulative percentages, percentile equivalents, z-scores, T-scores. In statistics, the standard score is the number of standard deviations by which the value of a raw score (i.e., an observed value or data point) is above or below the mean value of what is being observed or measured.
A scaled score is the result of some transformation(s) applied to the raw score, such as in relative grading. The purpose of scaled scores is to report scores for all examinees on a consistent scale. Suppose that a test has two forms, and one is more difficult than the other. It has been determined by equating that a score of 65% on form 1 is ...
The two columns to the right of the left-most column in this computerized table are raw data. Raw data, also known as primary data, are data (e.g., numbers, instrument readings, figures, etc.) collected from a source. In the context of examinations, the raw data might be described as a raw score (after test scores).
where z is the standard score or "z-score", i.e. z is how many standard deviations above the mean the raw score is (z is negative if the raw score is below the mean). The reason for the choice of the number 21.06 is to bring about the following result: If the scores are normally distributed (i.e. they follow the "bell-shaped curve") then
Percentile ranks are commonly used to clarify the interpretation of scores on standardized tests. For the test theory, the percentile rank of a raw score is interpreted as the percentage of examinees in the norm group who scored below the score of interest. [3] [4]
Like stanines, individual sten scores are demarcated by half standard deviations. Thus, a sten score of 5 includes all standard scores from -.5 to zero and is centered at -0.25 and a sten score of 4 includes all standard scores from -1.0 to -0.5 and is centered at -0.75. A sten score of 1 includes all standard scores below -2.0.
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Norms provided for the 1978 edition include standard scores with a mean of 100 and a standard deviation of 15, percentile scores, and grade levels. The standard scores are scaled based on the norm group; the grade levels are arbitrarily assigned and can be interpreted only as rough references to achievement level. Only standard scores should be ...