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Y603 Lectures Online Lecture #4 1. F distribution Derivation of F ratio (the special case under Ho, the ratio of MSb/MSw) F-distribution (positively skewed, positive numbers, mean=df2/(df2-2)) F-curve (see Figure 3.1-2 on page 77 of Kirk) F-table (Table E.4 starting on page 800 plus the handout, Fupper, Flower, df1 and df2) Practice 1: Assuming , what is the F upper critical value? Practice 2: Assuming , what is the F upper critical value? Practice 3: Assuming , what is the F lower critical value?   F degrees of freedom (two numbers, be consistent) Hypothesis testing of the equality of two population variances with F-ratio (Example 2 on the back; be consistent with degrees of freedom, interval estimation) Assumptions: (a) Normally distributed populations of scores (b) Random selection of subjects from each population (c) the numerator and the denominator of the F ratio are independent.   Relationship of F to normal, t, and Chi-square   2. Assignments: (1) Read pages 76B - 80, 85B-86 in Kirk. (2) Do questions 7, 8, 9, 18, and 19 at the end of Chapter 3 in Kirk. (3) Identify critical values or p-level according to the F table: (a) (b) (c) (d) (e) (f) (A) (B) (C) (D) (E) (F)   (4) Study Sections 5.1 - 5.3, 3.3 (Fixed-Effects Model) and 3.5 in Kirk on your own.     Test of Equality in Variances (Two Samples)   Example 2: It is hypothesized that boys and girls exhibit different variability on a motor task. We tested 20 randomly selected boys and 25 girls. vs. (let alpha = .05) Test statistic and   Decision rule Reject if or if   Collected data (or given data)   Decision Reject ; Conclude.   Estimation of   or   Hence,   Assumptions: (a) Normally distributed populations of scores (b) Random selection of subjects from each population (c) The numerator and the denominator of the F ratio are independent. 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