1 / 17

Chapter 5: z -Scores

Chapter 5: z -Scores. 5.1 Purpose of z -Scores. Identify and describe location of every score in the distribution Take different distributions and make them equivalent and comparable. Figure 5.1 Two Exam Score Distributions. 5.2 z -Scores and Location in a Distribution.

raine
Download Presentation

Chapter 5: 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. Chapter 5:z-Scores

  2. 5.1 Purpose of z-Scores • Identify and describe location of every score in the distribution • Take different distributions and make them equivalent and comparable

  3. Figure 5.1Two Exam Score Distributions

  4. 5.2 z-Scores and Location in a Distribution • Exact location is described by z-score • Sign tells… • Number tells…

  5. Figure 5.2 Relationship Betweenz-Scores and Locations

  6. Learning Check • A z-score of z = +1.00 indicates a position in a distribution ____

  7. Learning Check • Decide if each of the following statements is True or False.

  8. Equation (5.1) for z-Score • Numerator is a… • Denominator expresses…

  9. Determining a Raw Score From a z-Score • so • Algebraically solve for X to reveal that… • Raw score is simply the population mean plus (or minus if z is below the mean) z multiplied by population the standard deviation

  10. Learning Check • For a population with μ = 50 and σ = 10, what is the X value corresponding to z = 0.4?

  11. Learning Check • Decide if each of the following statements is True or False.

  12. 5.3 Standardizing a Distribution • Every X value can be transformed to a z-score • Characteristics of z-score transformation • Same shape as original distribution • Mean of z-score distribution is always 0. • Standard deviation is always 1.00 • A z-score distribution is called a standardized distribution

  13. Figure 5.4 Visual Presentation of Question in Example 5.6

  14. z-Scores Used for Comparisons • All z-scores are comparable to each other • Scores from different distributions can be converted to z-scores • z-scores (standardized scores) allow the direct comparison of scores from two different distributions because they have been converted to the same scale

  15. 5.5 Computing z-Scoresfor a Sample • Populations are most common context for computing z-scores • It is possible to compute z-scores for samples • Indicates relative position of score in sample • Indicates distance from sample mean • Sample distribution can be transformed into z-scores • Same shape as original distribution • Same location for mean M and standard deviation s

  16. Figure 5.10 Distribution of Weights of Adult Rats

  17. Learning Check • Last week Andi had exams in Chemistry and in Spanish. On the chemistry exam, the mean was µ = 30 with σ = 5, and Andi had a score of X = 45. On the Spanish exam, the mean was µ = 60 with σ = 6 and Andi had a score of X = 65. For which class should Andi expect the better grade?

More Related