1 / 26

Reasoning in Psychology Using Statistics

This quiz covers tables, graphs, measures of center, and measures of variability. Transforming scores into z-scores, normal distribution, and using unit normal table. It lays the foundation for upcoming exams and extra credit opportunities. Ensure to grasp the concepts now to build upon them effectively.

lorettareynolds
Télécharger la présentation

Reasoning in Psychology Using Statistics

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. Reasoning in PsychologyUsing Statistics Psychology 138 2019

  2. Quiz 3 is posted, due Friday, Feb. 22 at 11:59 pm • Covers • Tables and graphs • Measures of center • Measures of variability • You may want to have a calculator handy • Exam 2 is two weeks from today (Wed. Mar. 6th) • Don’t forget about Extra-Credit through SONA Annoucement

  3. Transformations: z-scores • Normal Distribution • Using Unit Normal Table • Combines 2 topics Today • Statistical Snowball: • For the rest of the course, new concepts build upon old concepts • So if you feel like you don’t understand something now, ask now, don’t wait. X X X X Outline for next 2 classes

  4. CVA Rotunda • North (and 10o West) • Approx. 1625 ft. 1625ft. • Where is Bone student center? • Reference point • Direction • Distance Location

  5. Reference point • Direction • Distance μ • Where is a score within distribution? • Obvious choice is mean • Negative or positive sign ondeviation score Subtract mean from score (deviation score). • Value of deviation score Locating a score

  6. Reference point Direction μ X1 - 100= +62 X1 = 162 X2 = 57 X2 - 100= -43 Locating a score

  7. Below Above μ X1 - 100= +62 X1 = 162 Direction X2 = 57 X2 - 100= -43 Locating a score

  8. Distance Distance μ X1 - 100= +62 X1 = 162 X2 = 57 X2 - 100= -43 Locating a score

  9. Raw score Population mean Population standard deviation • Direction and Distance • Deviation score is valuable, • BUT measured in units of measurement of score • AND lacks information about average deviation • SO, convert raw score (X) to standard score (z). • This puts the deviation into a neutral unit of measurement: standard deviation units • Recall: standard deviation is the average distance scores deviate from the mean, so this puts things relative to that average deviation in the distribution Transforming a score

  10. z-score: standardized location of X value within distribution X1 - 100= +1.24 50 X2 - 100= -0.86 μ 50 If X1 = 162, z = • Direction. Sign of z-score (+ or -): whether score is above or below mean • Distance. Value of z-score: distance from mean in standard deviation units If X2 = 57, z = Transforming scores

  11. z-score: standardized location of X value within distribution X1 - 20= +1.2 5 X2 - 20= -0.8 μ 5 μ = 20 σ = 5 If X1 = 26, z = • Direction. Sign of z-score (+ or -): whether score is above or below mean • Distance. Value of z-score: distance from mean in standard deviation units If X2 = 16, z = Transforming scores

  12. Can transform all of scores in distribution • Called a standardized distribution • Has known properties (e.g., mean & stdev) • Used to make dissimilar distributions comparable • Comparing your height and weight • Combining GPA and GRE scores • This particular standardize distribution: z-distribution • One of most common standardized distributions • Can transform all observations to z-scores if we know distribution mean & standard deviation (can do the same thing for populations and samples) Transforming distributions (transforming all the scores)

  13. Shape: • Mean: • Standard Deviation: Properties of z-score distribution

  14. transformation 50 150 μZ μ • Shape: Same as original distribution of raw scores. Every score stays in same position relative to every other score. original z-score • Note: this is true for other shaped distributions too: • e.g., skewed, mulitmodal, etc. Properties of z-score distribution

  15. transformation 50 150 μZ μ Xmean = 100 • Shape: Same as original distribution of raw scores. Every score stays in same position relative to every other score • Mean • If X = μ, z = ? • Meanz always = 0 = 0 = 0 Properties of z-score distribution

  16. Shape: Same as original distribution of raw scores. Every score stays in same position relative to every other score • Mean: always = 0 • Standard Deviation: Properties of z-score distribution

  17. transformation +1 μ μ X+1std = 150 • Shape: Same as original distribution of raw scores. Every score stays in same position relative to every other score • Mean: always = 0 • Standard Deviation: For z, 50 150 = +1 z is in standard deviation units Properties of z-score distribution

  18. transformation -1 μ μ X-1std = 50 • Shape: Same as original distribution of raw scores. Every score stays in same position relative to every other score • Mean: always = 0 • Standard Deviation: For z, 50 150 +1 = +1 X+1std = 150 = -1 Properties of z-score distribution

  19. Shape: Same as original distribution of raw scores. Every score stays in same position relative to every other score • Mean: always = 0 • Standard Deviation: always = 1, so it defines units of z-score Properties of z-score distribution

  20. μ μ transformation 50 150 -1 +1  z = -0.60 • Can go both directions: If knownz-score,mean & standard deviation of original distribution, can find raw score (X) • have 3 values, solve for 1 unknown  (z)( σ) = (X - μ)  X = (z)( σ) + μ X = 70  X = (-0.60)( 50) + 100 = -30 +100 From z to raw score:

  21. Example 1 A student got 580 on the SAT. What is her z-score? Another student got 420. What is her z-score? • Population parameters of SAT: μ= 500, σ= 100 SAT examples

  22. Student said she got 1.5 SD above mean on SAT. What is her raw score? • Population parameters of SAT: μ= 500, σ= 100 Example 2 X = z σ + μ = 150 + 500 = 650 = (1.5)(100) + 500 • Standardized tests often convert scores to: μ = 500, σ = 100 (SAT, GRE) μ = 50, σ = 10 (Big 5 personality traits) SAT examples

  23. Example 3 Suppose you got 630 on SAT & 26 on ACT. Which score should you report on your application? • SAT: μ = 500, σ = 100 • ACT: μ = 21, σ = 3 z-score of 1.67 (ACT) is higher than z-score of 1.3 (SAT), so report your ACT score. SAT examples

  24. Example 4 On Aptitude test A, a student scores 58, which is .5 SD below the mean. What would his predicted score be on other aptitude tests (B & C) that are highly correlated with the first one? Test B: μ = 20, σ = 5 XB < or > 20? How much: 1? 2.5? 5? 10? Test C: μ = 100, σ = 20 XC < or > 100? How much: 20? 10? If XA = -.5 SD, then zA = -.5 XB = zBσ + μ XC = zCσ + μ = (-.5)(20) + 100 = -10 + 100 = 90 Find out later that this is true only if perfectly correlated; if less so, then XB and XC closer to mean. = (-.5)(5) + 20 = -2.5 + 20 = 17.5 Example with other tests

  25. X X X X Formula Summary

  26. In lab • Using SPSS to convert raw scores into z-scores; copy formulae with absolute reference • Questions? • Brandon Foltz: Understanding z-scores (~22 mins) • StatisticsFun (~4 mins) • Chris Thomas. How to use a z-table (~7 mins) • Dr. Grande. Z-scores in SPSS (~7 mins) Wrap up

More Related