Meaning of Scaled Score in CAT



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On popular demand to help you all understand Scaled score in CAT, we bring to you in this article the meaning of scaled score in CAT.

Meaning of Scaled Score in CAT

Scoring :
Psychometrically-sound approach is used for the scoring process for all CAT candidates. 

Raw Score is “Equated”
Equating is a statistical process used to adjust scores on two or more alternate forms of an assessment so that the scores may be used interchangeably. Industry standard processes are used for equating.

Equated Raw Score is “Scaled”
In order to ensure appropriate interpretation of an equated raw score, the scores must be placed on a common scale or metric. A linear transformation is used for this scaling process, which is an industry standard practice.

This method used for the test forms vary in difficulty terms and allows score to scale. To consider this method mathematically, we take two different test forms X and Y. The linear conversion is mathematically defined by

Where

X = Raw score of a student in test form X

Y = Raw score of a student in test form Y

mean(X) and mean(Y) are the mean of all raw scores of test form X and Y respectively

SD(X) and SD(Y) are the standard deviation of all raw scores of test form X and Y respectively.

Solving above equation for the score in test form Y will give us a formula for adjusting any given raw score X on the test form Y.

The adjusted scores of the form X will have the same mean and standard deviation as the raw scores on the form Y.

Scaling the Adjusted Score:

To obtain scale scores again linear conversion is used.

Where

sc(Y) = scale score of raw score Y in test form Y.

mean(sc) and SD(sc) are mean and standard deviation of scale scores. The testing agency chooses constant value for these. For example, IBPS used mean(sc) = 25 and SD(sc) = 5 for CWE-POs/MTs-II.

Let us consider above method through an example:

Assume two test forms X and Y of maximum score 50.

On calculating mean and standard deviation for form X and Y, we have

Mean(X) = 22, SD(X) = 3.29

Mean(Y) = 24, SD(Y) = 2

Using equation 1, we have adjusted raw score X on the test Y as below:

Now using equation 2, convert above equated scores to scale scores.

Use mean(sc) = 25, SD(sc) = 5

Please note that ‘0 to 50 scale’ is used in this example. Generally testing agencies use different scale from maximum marks to avoid confusion. 

The IIM scaling model is as follows:
Section Scores = 0 to 150
Total Exam Score = 0 to 450
 
Four scaled scores are presented for each candidate: an overall scaled score and three separate scaled scores for each section. Kindly note that overall scaled score is not the direct addition of sectional scaled scores. Overall scaled score is based on raw overall score and is independent of sectional scaled score.

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