Z-scores & Review No office hours Thursday 9-21

The Standard Normal Distribution Z-scores –A descriptive statistic that represents the distance between an observed score and the mean relative to the standard deviation

Standard Normal Distribution Z-scores –Converts distribution to: Have a mean = 0 Have standard deviation = 1 –However, if the parent distribution is not normal the calculated z-scores will not be normally distributed.

Why do we calculate z-scores? To compare two different measures –e.g., Math score to reading score, weight to height. –Area under the curve Can be used to calculate what proportion of scores are between different scores or to calculate what proportion of scores are greater than or less than a particular score.

Class practice How much do you weigh? _____ 132, 149, 144,143, 113 Calculate z-scores for 120 & 133 What percentage of scores are less than 120? What percentage are less than 133? What percentage are between 120 and 133?

Z-scores to raw scores If we want to know what the raw score of a score at a specific %tile is we calculate the raw using this formula. Using previous data –What are the weights of individuals at the 20%tile & the 33%tile?

Transformation scores We can transform scores to have a mean and standard deviation of our choice. Why might we want to do this? Let’s say we have a set of spelling scores with a mean of 15 and a standard deviation of 5. We want to transform them to have a mean of 50 and a standard deviation of 10. What would be the transformed scores for 12 and 18?

IQ scores We want: –Mean = 100 –s = 15 Transform: –Z scores of: