Which of the following is the primary reason for transforming a set of raw scores into a set of $z$-scores?

• A. To eliminate all outliers from the data set
• B. To change the shape of the distribution to a uniform distribution
• C. To increase the mean of the distribution
• D. To standardize scores so they can be compared across different distributions

Answer: (D)

Verified step by step guidance

1. Understand what a z-score represents: a z-score indicates how many standard deviations a raw score is from the mean of its distribution.
2. Recall the formula for calculating a z-score: \(z = \frac{X - \mu}{\sigma}\), where \(X\) is the raw score, \(\mu\) is the mean of the distribution, and \(\sigma\) is the standard deviation.
3. Recognize that transforming raw scores into z-scores standardizes the data by centering it around a mean of 0 and scaling it to have a standard deviation of 1.
4. Understand that this standardization allows scores from different distributions (with different means and standard deviations) to be compared directly on the same scale.
5. Note that z-score transformation does not eliminate outliers, change the shape of the distribution to uniform, or increase the mean; its primary purpose is standardization for comparison.