What formula is used to calculate Z scores?

The formula used to calculate Z scores is represented as Z = (raw score - mean) / standard deviation. This formula standardizes a raw score by measuring its distance from the mean of the data set in terms of standard deviations.

In this context, the 'raw score' refers to the individual data point being analyzed, the 'mean' is the average of all scores in the distribution, and the 'standard deviation' provides a measure of how spread out the scores are. By subtracting the mean from the raw score, you determine how far away the score is from the average. Dividing this difference by the standard deviation then allows you to express this distance in standardized units, allowing for comparison across different datasets or distributions.

This process is essential in statistics, particularly in psychology research, as it enables practitioners to assess where a particular score lies in relation to the overall data, facilitating interpretations around performance, deviations, and identifying outliers effectively.