Statistics for the Social Sciences LECTURE OUTLINE: CHAPTER 5: Z SCORES REVISITED, T SCORES AND OTHER NORMAL CURVE TRANSFORMATIONS. 

10

WHERE ARE WE? Previously we learned how to locate any given point in a standard distribution (normal curve) in this chapter we will learn other transformations of the normal curve beyond the z score and how these transformations are related to each other.



LEARNING GOALS: (1) Learn how to manipulate z scores and find percentiles, raw scores, means, and the standard deviation. (2) Be able to explain the differences and different applications of the other normal curve transformation presented in this chapter.



BACKGROUND: This chapter will lay the foundation for understanding probability (ch. #6) and sampling distributions (Ch. #7). Additionally, the math will not get harder than this throughout the rest of the text!



KEY TERMINOLOGY: Grade-equivalent scores (GES); NCE (normal curve equivalent score; percentile; Stanine; T score; z score; z test



LECTURE OUTLINE: I. Activity "Curing the Algebra phobic" II. Other application of the z score: A. From z score to Raw score "X":  X= z(SD)+M B. The percentile table A (p. 601) C. From percentile to z score: table B (p. 602). D. From percentiles to Raw scores  X= z(SD)+M E. From z score to standard deviation: 

SD

X

M z

F. Finding the range: "The range is roughly six times the standard deviation"  R=(6) (SD) STEPS: STEP 1: Take the SD and times it by "6" STEP 2: Divide the value by two STEP 3: add the values from step two to the mean. STEP 4: Subtract the value from step two from the mean.

G. From z score to the mean:  M= X-z(SD) III: T scores and the T distribution: *"A T score is a converted z score, with the mean set at 50 and the standard deviation equal to ten."

 T = z(10)+50 Review: Figure 5.1 T scores and SD units (p 110). Applications of T scores: "remember, the T like the Z still provides a standard by which performance on separate tests can be compared."

From T to raw scores:

 Z = X-M/SD = T-50/10 IV. Other types of standard scores:  ACTIVTY: (Applying table 5.2 will increase your understanding of these concepts! Pp. 112-113) 1. NCE's = Normal Curve Equivalents: M= 50 and SD = 21 2. STANINES: M=5 SD= approximately 3. 3. Grade equivalent scores (GEs): M= 6.45R=0-12.9 *Two cautions for using GE's 

CONCEPT REVIEW & APPLICATION QUESTIONS: 1. 2. 3. 4. 5.

A z score of +3.00, means that… All z scores falling to the LEFT of the mean… The Range of the T score distribution always equals approximately… A T score of 60 is equal to a z score of… The distribution of T scores is assumed to be… A. Gaussian; b. normal; c. mesokurtic; d. all of these.

6. SPSS TIP For Finding Percentiles: To Specify Statistics for Explore From the menus choose: Analyze Descriptive Statistics Explore... In the Explore dialog box, select Statistics in the Display group to enable the Statistics pushbutton. Click on the Statistics button Check the box for Percentiles. *Hint check out the Frequencies option under Descriptive Statistics as well. NEXT CLASS: Know how to find and interpret percentiles, kurtosis, and skewness. Chapter 6: Probability. Learn what most Gamblers' don't know! (The Gamblers' Fallacy) 