1 / 9

Chapter 3

Chapter 3. Z Scores & the Normal Distribution Part 1 Thurs. Aug. 29, 2013. Z Scores. Number of standard deviations a score is above or below the mean Formula to change a raw score to a Z score: Sign of z indicates whether score is above or below mean.

alfredthompson
Download Presentation

Chapter 3

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. Chapter 3 Z Scores & the Normal Distribution Part 1 Thurs. Aug. 29, 2013

  2. Z Scores • Number of standard deviations a score is above or below the mean • Formula to change a raw score to a Z score: Sign of z indicates whether score is above or below mean. Magnitude of z – how many SDs above/below Example in class:

  3. Z Scores • Formula to change a Z score to a raw score: • Example?

  4. Z scores • Distribution of Z scores • Mean = 0 • Standard deviation = 1 • It’s a standardized scale • z scores can be used to compare 2 scores from same or different distributions • Z= +3 represents score that is very deviant from the mean, no matter the distribution

  5. Z as common unit of comparison • Comparing SAT and ACT scores • Which is a higher score? Getting a 620 on the SAT-verbal or a 27 on the ACT-verbal? • Information about ACT and SAT M and SD: • Did this person do better on the SAT or ACT?

  6. The Normal Distribution • In a normal curve (normal distribution), there will always be a standard % of scores between the mean and 1 and 2 standard deviations from the mean: • 50% all scores fall above the mean, 50% below • 34% betw M and +1 SD, 34% betw M and –1SD • 14% betw +1 and +2 SD, 14% betw –1 and –2SD • 2% above +2 SD and below –2 SD

  7. The Normal Distribution • Can remember this as the ‘50-34-14 rule’ • Appendix A is the normal curve table with Z scores • Gives the precise % of scores between the mean (which has a Z score of 0) and any other Z score • What % of scores are betw M and z = .75? • Table lists only positive Z scores, but since ND is symmetrical, same % for neg z scores (just look up its corresponding pos z)

  8. Using the Z table: From z to % • Steps for figuring the % of scores above or below a particular raw or Z score: 1. Table uses z scores, so convert raw score to Z score (if necessary) 2. Draw normal curve, indicate where the Z score falls on it, shade in the area for which you are finding the % 3. Make rough estimate of shaded area’s percentage (using 50%-34%-14% rule): • what % does it look like the shaded area covers? (use your judgment – we’ll check on this later…)

  9. (cont.) 4. Find exact % using normal curve table • that is, look up the z score you calculated in step 1 and find the % associated with it. 5. If needed, add or subtract 50% from this • since table only gives % between M and Z, if you’re interested in % above Z, subtract from 50% (see example) 6. Check to determine if your answer makes sense given the graph you drew in Step 3

More Related