1 / 21

Name that tune.

Name that tune.  Song title?  Performer(s)?. Scientific Method (continued). “Finding New Information” 4/11/2011. Objectives. I want you to understand z scores. “Standard scores.” (Note – not standard deviation!) Pencils down. I don’t want you to take notes – just get the concept.

rosiec
Download Presentation

Name that tune.

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. Name that tune.  Song title?  Performer(s)?

  2. Scientific Method (continued) “Finding New Information” 4/11/2011

  3. Objectives • I want you to understand z scores. “Standard scores.” • (Note – not standard deviation!) • Pencils down. I don’t want you to take notes – just get the concept. • Randolph – remember to take roll.

  4. Which when?

  5. So far . . . • . . . we’ve talked of summarizing ONE distribution of scores. • By ordering the scores. • By organizing them in graphs/tables/charts. • By calculating a measure of central tendency and a measure of dispersion. • What happens when we want to compare TWO distributions of scores?

  6. “Now, why would I want to do that”? • Is your child taller or heavier? • Is this month’s SAT test any easier or harder than last month’s? • Is my 91 in my History class better than my 95 in my Math class? • Is the new library lay-out better than the old one? • Can more employees sign up, more quickly, for benefits with our new intranet site than with our old one? • Did my class perform better on the TAKS test than they did on the TAAS test?

  7. Well? • COULD it be the case that your 91 in your History class is better than your 95 in your Math class? • How?

  8. What if . . . • The mean in History was 50, and the mean in Digital Libraries Math was 99? • (What, besides the fact that everyone else is trying to drop the History class!) • So:

  9. The Point • As I said last week, you need to know BOTH a measure of central tendency AND a measure of spread to understand a distribution. • BUT STILL, this can be convoluted . . . • “Well, daughter, how are you doing in school this semester”?

  10. “Well, Mom . . . • “. . . I had a 91 on my History test but the mean was 50 and the standard deviation was 12. But I got a 95 on Math test, whereas the mean on that test was 99 with a standard deviation of 1.” • Of course, your mom’s reaction will be, “Just call home more often, dear.”

  11. Wouldn’t it be nice . . . • . . . if there could be one score we could use for BOTH classes, for BOTH the TAKS test and the TAAS test, for BOTH your child’s height and weight? • There is – and it’s called the “standard score,” or “z score.”

  12. Standard Score • z = (X - µ)/σ • “Hunh”? • Each score can be expressed as the number of standard deviations it is from the mean of its own distribution. • “Hunh”? • (X - µ) – This is how far the score is from the mean. (Note: Could be negative! No squaring, this time.) • Then divide by the SD to figure out how many SDs you are from the mean.

  13. Z scores (cont’d.) • z = (X - µ)/σ • Notice, if your score (X) equals the mean, then z is, what? • If your score equals the mean PLUS one standard deviation, then z is, what? • If your score equals the mean MINUS one standard deviation, then z is, what?

  14. An example

  15. Let’s calculate σ – Test 1 – Mean = 61

  16. Let’s calculate σ – Test 2= Mean = 83

  17. So . . . z = (X - µ)/σ • Kris had a 76 on both tests. • Test 1 - µ = 61, σ = 9 • So her z score was (76-61)/9 or 15/9 or 1.67. So we say that Kris’s score was 1.67 standard deviations above the mean. Her z score was 1.67. • Test 2 - µ = 83, σ = 5.4 • So her z score was (76-83)/5.4 or -7/5.4 or –1.3. So we say that Kris’s score was 1.3 standard deviations BELOW the mean. Her z score was -1.3. • Given what I said earlier about two-thirds of the scores being within one standard deviation of the mean . . . . • Wouldn’t it be nice if we knew exactly how many . . . ?

  18. z = (X - µ)/σ • If I tell you that the average IQ score is 100, and that the SD of IQ scores is 16, and that Bob’s IQ score is 2 SD above the mean, what’s Bob’s IQ? • If I tell you that your 75 was 1.5 standard deviations below the mean of a test that had a mean score of 90, what was the SD of that test?

  19. z scores – table values • z = (X - µ)/σ • It is often the case that we want to know “What percentage of the scores are above (or below) a certain other score”? • Asked another way, “What is the area under the curve, beyond a certain point”? • THIS is why we calculate a z score, and the way we do it is with the z table.

  20. Z distribution

  21. Study Guide . . . • Later tonight, online.

More Related