1 / 27

Z-Scores

Z-Scores. Quantitative Methods in HPELS 440:210. Agenda. Introduction Location of a raw score Standardization of distributions Direct comparisons Statistical analysis. Introduction. Z-scores use the mean and SD to transform raw scores  standard scores What is a Z-score?

cayla
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 Quantitative Methods in HPELS 440:210

  2. Agenda • Introduction • Location of a raw score • Standardization of distributions • Direct comparisons • Statistical analysis

  3. Introduction • Z-scores use the mean and SD to transform raw scores  standard scores • What is a Z-score? • A signed value (+/- X) • Sign: Denotes if score is greater (+) or less (-) than the mean • Value (X): Denotes the relative distance between the raw score and the mean • Figure 5.2, p 141

  4. Introduction • Purpose of Z-scores: • Describe location of raw score • Standardize distributions • Make direct comparisons • Statistical analysis

  5. Agenda • Introduction • Location of a raw score • Standardization of distributions • Direct comparisons • Statistical analysis

  6. Z-Scores: Locating Raw Scores • Useful for comparing a raw score to entire distribution • Calculation of the Z-score: • Z = X - µ /  where • X = raw score • µ = population mean •  = population standard deviation

  7. Z-Scores: Locating Raw Scores • Example 5.3, 5.4 p 144

  8. Z-Scores: Locating Raw Scores • Can also determine raw score from a Z-score: • X = µ + Z

  9. Agenda • Introduction • Location of a raw score • Standardization of distributions • Direct comparisons • Statistical analysis

  10. Z-Scores: Standardizing Distributions • Useful for comparing dissimilar distributions • Standardized distribution: A distribution comprised of standard scores such that the mean and SD are predetermined values • Z-Scores: • Mean = 0 • SD = 1 • Process: • Calculate Z-scores from each raw score

  11. Z-Scores: Standardizing Distributions • Properties of Standardized Distributions: • Shape: Same as original distribution • Score position: Same as original distribution • Mean: 0 • SD: 1 • Figure 5.3, p 145

  12. Z-Scores: Standardizing Distributions • Example 5.5 and Figure 5.5, p 147

  13. µ = 3 •  = 2

  14. Agenda • Introduction • Location of a raw score • Standardization of distributions • Direct comparisons • Statistical analysis

  15. Z-Scores: Making Comparisons • Useful when comparing raw scores from two different distributions • Example (p 148): • Suppose Bob scored X=60 on a psychology exam and X=56 on a biology test. Which one should get the higher grade?

  16. Z-Score: Making Comparisons • Required information: • µ of each distribution of raw scores •  of each distribution of raw scores • Calculate Z-scores from each raw score

  17. Psychology Exam Distribution: µ = 50  = 10 Biology Exam Distribution: µ = 48  = 4 Z = X - µ /  Z = 60 – 50 / 10 Z = 1.0 Z = X - µ /  Z = 56 - 48 / 4 Z = 2.0 Based on the relative position (Z-score) of each raw score, it appears that the Biology score deserves the higher grade

  18. Agenda • Introduction • Location of a raw score • Standardization of distributions • Direct comparisons • Statistical analysis

  19. Z-Scores: Statistical Analysis • Appropriate usage of the Z-score as a statistic: • Descriptive • Parametric

  20. Z-Scores: Statistical Analysis • Review: Experimental Method • Process: Manipulate one variable (independent) and observe the effect on the other variable (dependent) • Independent variable: Treatment • Dependent variable: Test or measurement

  21. Z-Scores: Statistical Analysis • Figure 5.8, p 153

  22. Z-Score: StatisticalAnalysis • Value = 0  No treatment effect • Value > or < 0  Potential treatment effect • As value becomes increasingly greater or smaller than zero, the PROBABILITY of a treatment effect increases

  23. Problems: 1, 2, 9, 17, 23 Textbook Problem Assignment

More Related