Three final candidates (Alex, Bo, and Chris) for a position happen to take different versions of the aptitude test. You are supposed to choose the one who performed best out of these three final candidates and the test results are as follows:
Alex received 88 from the test version A
Bo received 424 from the test version B
Chris received 1095 from the test version C
1.1 Excel Data file: Data 1. has test scores from the test version A, B, and C. Check the file. When comparing three candidates’ scores, would it be okay to compare their scores directly? If not, why?
It would be okay to compare the Z scores, but not the raw scores, from each test. In order to do that, you would have to know the mean and standard deviation of each test, assuming they were all normally distributed.
When comparing the scores of the three candidates (Alex, Bo, and Chris) who took different versions of the aptitude test, it is not okay to compare their scores directly. The reason is that the scores are from different test versions, which means they are measured on different scales or criteria.
To determine who performed best among the three candidates, you need to standardize or normalize the scores. This can be done by converting the scores to a common scale or by calculating the z-scores for each candidate's score.
Here is how you can compare the scores using z-scores:
1. Calculate the mean and standard deviation for each test version separately.
2. Convert each candidate's score to a z-score using the formula:
z-score = (candidate's score - mean) / standard deviation
This will represent how far above or below the mean the candidate's score is, in terms of standard deviations.
3. Compare the z-scores of the three candidates. The candidate with the highest z-score performed the best.
By following these steps, you can compare the scores of the three candidates efficiently and fairly despite the difference in test versions.