1 / 12

Outline

Outline. I. What are z-scores? II. Locating scores in a distribution A. Computing a z-score from a raw score B. Computing a raw score from a z-score C. Using z-scores to standardize distributions III. Comparing scores from different distributions. You scored 76 How well did you perform?

azize
Download Presentation

Outline

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Outline I. What are z-scores? II. Locating scores in a distribution A. Computing a z-score from a raw score B. Computing a raw score from a z-score C. Using z-scores to standardize distributions III. Comparing scores from different distributions

  2. You scored 76 How well did you perform?  serves as reference point: Are you above or below average?  serves as yardstick: How much are you above or below? Convert raw score to a z-score z-score describes a score relative to  &  Two useful purposes: Tell exact location of score in a distribution Compare scores across different distributions I. What are z scores?

  3. II. Locating Scores in a distribution Deviation from  in SD units Relative status, location, of a raw score (X) z-score has 2 parts: • Sign tells you above (+) or below (-)  • Value tells magnitude of distance in SD units

  4. A. Converting a raw score (X) to a z-score: Example: Spelling bee:  = 8  = 2 Garth X=6  z = Peggy X=11  z =

  5. Example • Let’s say someone has an IQ of 145 and is 52 inches tall • IQ in a population has a mean of 100 and a standard deviation of 15 • Height in a population has a mean of 64” with a standard deviation of 4 • How many standard deviations is this person away from the average IQ? • How many standard deviations is this person away from the average height?

  6. B. Converting a z-score to a raw score: Example: Spelling bee:  = 8  = 2 Hellen z = .5  X = Andy z = 0  X = raw score = mean + deviation

  7. C. Using z-scores to Standardize a Distribution Convert each raw score to a z-score What is the shape of the new dist’n? Same as it was before! Does NOT alter shape of dist’n! Re-labeling values, but order stays the same! What is the mean?  = 0 Convenient reference point! What is the standard deviation?  = 1 z always tells you # of SD units from !

  8. An entire population of scores is transformed into z-scores. The transformation does not change the shape of the population but the mean is transformed into a value of 0 and the standard deviation is transformed to a value of 1.

  9. Example: So, a distribution of z-scores always has:  = 0  = 1 A standardized distribution helps us compare scores from different distributions

  10. III. Comparing Scores From Different Dist’s Example: Jim in class A scored 18 Mary in class B scored 75 Who performed better? Need a “common metric” Express each score relative to it’s own &  Transform raw scores to z-scores Standardize the distributions  they will now have same  & 

  11. Example: Class A: Jim scored 18  = 10  = 5 Class B: Mary scored 75  = 50  = 25 Who performed better? Jim! Two z-scores can always be compared

  12. Homework • Chapter 5 • 7, 8, 9, 10, 11

More Related