Z-scores & Review

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

2. 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

3. 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.

4. 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.

5. 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?

6. 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?

7. 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?

8. IQ scores • We want: • Mean = 100 • s = 15 • Transform: • Z scores of: • -1.23 • 1.56 • 1.32