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Y603 Lectures Online Lecture #3   1. Chi-square distribution Chi-square derivations (2, one with known sigma squared, the second without known sigma squared) Chi-square distribution (positively skewed, positive scores only, mean=df, variance=2df, mode=df-2, if df>2)   Chi-square curves (see Figure 3.1-1 on page 73 of Kirk) Chi-square table (chi-square upper, chi-square lower, see also pages 3-4 of this outline) practice 1: Assuming for a two-tailed test, what are the critical values needed on a chi-square curve? practice 2: Let us assume that for a two-tailed test. What are the critical values needed on the chi-square curve? Chi-square formulae (i.e., the height of the curve) is determined by:   is a constant depending on only; e equals 2.718... an irrational number. degrees of freedom (N or N-1) Additive property (and Hogg-Craig theorem) Hypothesis testing with Chi-square (Example 1 on the back; which chi-square formula is used here?)   2. Assignments on Chi-squares: (1) Read pages 72-76, 78-79 in Kirk. (2) Do questions 3, 4, and 5 at the end of Chapter 3 in Kirk. (3) Identify critical values or p-level according to the Chi-square table: (a) (b) (c) (d) (e) (f)   (A) (B) (C) (D) (E) (F) (G)   (4) Identify all threats to internal/external validities from the attached article below.     Test of One Variance (One Sample)   Example 1: We wish to determine whether special training has an effect on the variability of IQ scores, as compared with the norm, for which . We tested 30 randomly sampled children.   vs. (let alpha = .05) Test statistic   Decision rule Reject if or if .   Collected data (or given data)   Decision Reject ; Conclude .   Estimation of or   Hence,   Assumptions: (a) Normally distributed population of scores (b) Random selection of subjects from the population LINKS... Home Syllabus Lectures Discussion Practice Resources Comments: peng@indiana.edu Dr. Peng's Home Page: Dr. Chao-Ying Joanne Peng Copyright 1998, The Trustees of Indiana University