# PY 211 Lecture Notes - Lecture 13: Analysis Of Variance, F-Distribution, Multiple Comparisons Problem

1. Chapter 12: Analysis of Variance

12.1 Increasing k: A Shift to Analyzing Variance

1) More than two groups

a) So far, one or two groups (or two sets of scores)

b) What about comparing three groups?

b.i) Control group

b.ii) Treatment 1

b.iii) Treatment 2

c) Would need three different t tests for one study

d) New procedure affords one test to detect any differences

2) Analysis of Variance (ANOVA)

a) Used to test differences among means (2+)

a.i) One independent variable (factor)

a.ii) 2+ levels (conditions, groups) (k = # levels0

b) No population information is available

c) Shift from emphasis on means to variance

c.i) Back door method of testing differences among means

3) Different types of ANOVAs

a) One-way between subjects

a.i) One factor is tested (k = 2+ levels)

a.ii) Different subjects in each level

(a.ii.1) Independent samples, independent measures

b) One way within subjects

b.i) One factor (with k = 2+ levels)

b.ii) Same subjects in each level

(b.ii.1) Related samples, repeated measures

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c) Two way between subjects (two factors)

12.2 An Introduction to Analysis of Variance

Selecting independent samples

oQuasi-experiment

oExperiment

Changes in Notation

on = number of participants per level (group)

n1, n2, n3, …

oN = number of total participants in a study

N = n1 + n2 + n3 + …

When n is the same in each level, N = k(n)

ok= number of levels (groups)

Clicker Questions

1) What is a factor?

a) Dependent variable

b) The group that a subject is in

c) Independent variable

d) Number of groups

2) What is a level?

a) Dependent variable

b) The group that a subject is in

c) Independent variable

d) Number of groups

12.3 Sources of Variation and the Test Statistic

Variation in the dependent variable

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