Zscores Zscore or standard score A statistical techniques

Z-scores

Z-score or standard score ¢A statistical techniques that uses the mean and the standard deviation to transform each score (X) into a zscore ¢ Why z-scores are useful?

Z-scores and location in a distribution ¢ The sign of the z-score (+ or –) ¢ The numerical value corresponds to the number of standard deviations between X and the mean

The relationship between z-scores and locations in a distribution

Transforming back and forth between X and z ¢ The basic z-score definition is usually sufficient to complete most z-score transformations. However, the definition can be written in mathematical notation to create a formula for computing the z-score for any value of X. X– μ Deviation score z = ──── Standard deviation σ

What if we want to find out what someone’s raw score was, when we know their z-score? Example: ¢ Distribution of exam scores has a mean of 70, and a standard deviation of 12. ¢

Transforming back and forth between X and z (cont. ) ¢ So, the terms in the formula can be regrouped to create an equation for computing the value of X corresponding to any specific z-score. X = μ + zσ

Distribution of z-scores ¢ shape will be the same as the original distribution ¢ z-score mean will always equal 0 ¢ standard deviation will always be 1

Using z-scores to make comparisons Example: ¢ You got a grade of 70 in Geography and 64 in Chemistry. In which class did you do better? ¢

z-Scores and Samples ¢ It is also possible to calculate z-scores for samples.

z-Scores and Samples Thus, for a score from a sample, X–M z = ───── s ¢ Using z-scores to standardize a sample also has the same effect as standardizing a population. ¢