1 / 22

z - SCORES

z - SCORES. standard score: allows comparison of scores from different distributions z-score : standard score measuring in units of standard deviations. Comparing Scores from Different Distributions.

yair
Download Presentation

z - SCORES

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. z - SCORES • standard score: allows comparison of scores from different distributions • z-score: standard score measuring in units of standard deviations

  2. Comparing Scores from Different Distributions • Suppose you got a score of 70 in Dr. Difficult’s class, and you got an 85 in Dr. Easy’s class. • In relative terms, which score was better?

  3. Suppose the M in Dr. Difficult’s class was 60 and the SD was 5. • So your score of 70 was two standard deviations above the mean. • That’s good!

  4. In Dr. Easy’s class, the M was 90, with a SD of 10. • So your score of 85 was half of a standard deviation below the mean. • Not as good!

  5. Calculating z-scores • Your z-score in Dr. Difficult’s class was two standard deviations above the mean. That means z = +2.00. • Your z-score in Dr. Easy’s class was half a standard deviation below the mean. That means z = -.50.

  6. z - score formula

  7. Cool Things About z-scores • Any distribution, when converted to z-scores, has • a mean of zero • a standard deviation of one • the same shape as the raw score distribution

  8. Finding Percentile Ranks with z-Scores • This only works for a normal distribution! • You have to know the m and sx. • All it takes is a little calculus.... • But the answer is in the back of the book.

  9. A Really Easy Example Suppose your score is at the mean of a distribution, and the distribution is normal. What is your percentile rank? Answer: 50th percentile rank The mean = the median 50% of the scores are below the median.

  10. Another Example Sam got a score of 515 on a normally distributed aptitude test. The m of the test is 500, with a s of 30. What is Sam’s percentile rank?

  11. m 515 500

  12. STEP 1: Convert to a z-score. z = (515-500)/30 = .50 STEP 2: Look up the z-score in the Normal Curve Table. Find the area between mean and z. area between mean and z = .1915

  13. STEP 3: Add the area below the mean. total area below = .1915 + .5000 = .6915 STEP 4: Convert the proportion to a percentage. percentile rank = 69%

  14. A Tricky Example Sam got a score of 470 on a normally distributed aptitude test. The m of the test is 500, with a s of 30. What is Sam’s percentile rank?

  15. m 470 500

  16. STEP 1: Convert to a z-score. z = (470-500)/30 = -1.00 STEP 2: Look up the z-score in the Unit Normal Table. Find the area beyond z. area beyond z = .1587

  17. STEP 3: Convert to a percentage. .1587 = 16%

  18. Working Backwards The m of the test is 500, with a s of 30. What score is at the 90th percentile?

  19. m 90% or .9000 500 X=?

  20. STEP 1: Look up the z-score. proportion beyond z = .1000 z = +1.28 STEP 2: Convert the z-score into raw score units, using x = m + zs x = 500 + (1.28)(30) = 500 + 38.40 = 538.40

  21. Finding Other Proportions • What proportion is above a z of .25? area beyond z = .4013 • What proportion is above a z of -.25? area between mean and z = .0987 proportion above = .0987 + .5000 = .5987

  22. What proportion is between a z of -.25 and a z of +.25? area between mean and z = .0987 proportion between = .0987 + .0987 = .1974

More Related