# PY 211 Lecture Notes - Lecture 27: Analysis Of Variance, Repeated Measures Design, Test Statistic

Chapter 12: Analysis of Variance (ANOVA)

One-way Between-Subjects Design 4/10/2017 4:56:00 PM

Increasing k: a shift to analyzing variance

ā¢ More than two groups so far, one or two groups (or two sets of

scores)

ā¢ What about comparing three groups?

o Control group

o Treatment 1

o Treatment 2

ā¢ Would need three different t tests for one study

o Ad bc more tests you do, more likely you are going to come

up with wrong answer

ā¢ New procedure affords one test to detect any difference

Analysis of Variance (ANOVA)

ā¢ Used to test differences among means (2+)

o One independent variable (factor)

o 2+ levels (conditions, groups) (k= # levels)

o one dependent variable

ā¢ no population information is available

ā¢ shift from emphasis on means to variances

o back-door method of testing differences among means

Different Types of ANOVAS

ā¢ One-way between-subjects

o One factor is tested (with k= 2+ levels)

o Different subjects in each level

āŖ Independent samples, independent measures

ā¢ One-way within-subjects

o One factor (with k= 2+ kevels)

o Same subjects in each level

āŖ Related samples, repeated measures

ā¢ Two-way between-subjects (two factors)

An introduction to analysis of variance

ā¢ Selecting independent samples

o Quasi-Experiment

find more resources at oneclass.com

find more resources at oneclass.com

o Experiment

Changes in Notation

ā¢ n= number of participants per level (group

ā¢ N=number of total participants in a study

o When n is the same in each level, N= k * n

ā¢ k= number of levels (groups)

Sources of Variation and the Test Statistic

ā¢ Variation in the Dependent Variable

o Scores from DV vary from subject to subject, and level to

level (group to group)

o Calculate the variance of all the scores from the study

āŖ Regardless of group

āŖ This is called ātotal varianceā

o Parse how much of the total variance is from

āŖ Difference between levels

āŖ Differences within levels

Sources of Variation and the Test Statistic

ā¢ Sources of variation

o Between groups variation- differences between means

o Within groups (error) variation- differences within group

ā¢ Calculation of difference between groups

o Inherently has difference within groups

o Cannot separate them mathematically

o Can do this:

āŖ Weighted average of variance in each group

āŖ Variance attributed to chance

What to do now?

ā¢ Mathematically, inappropriate to subtract

o Group/within variation- within variation

ā¢ Instead, calculate ratio- F ratio

o Note: this is not the calculation formula

āŖ Fobt= variance attributed to group differences

ļŗ Variance attributed to chance

find more resources at oneclass.com

find more resources at oneclass.com