CSD 5100 Introduction to Research Methods in CSD
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Transcript of CSD 5100 Introduction to Research Methods in CSD
CSD 5100CSD 5100Introduction to Research Introduction to Research
Methods in CSDMethods in CSD
Analysis of VarianceAnalysis of Variance
The Statistical Procedure for The Statistical Procedure for Factorial DesignFactorial Design
Factorial DesignFactorial Design
Experimental procedure for testing the Experimental procedure for testing the null hypothesis when two independent null hypothesis when two independent variables, or factors, are considered variables, or factors, are considered simultaneously in a research studysimultaneously in a research study
The ANOVA is the statistical procedure for The ANOVA is the statistical procedure for analyzing data from factorial designsanalyzing data from factorial designs
Advantages of Factorial Advantages of Factorial DesignDesign
• EfficiencyEfficiency
• ControlControl
• Allows the study of the interaction Allows the study of the interaction between two or more independent between two or more independent variablesvariables
Data TablesData Tables
How Does the ANOVA Work?How Does the ANOVA Work?
The ANOVA partitions the The ANOVA partitions the total variation of scores total variation of scores into four componentsinto four components
• Within cell varianceWithin cell variance• Variation among the Variation among the
row (age) meansrow (age) means• Variation among the Variation among the
column (gender) meanscolumn (gender) means• Variation due to the Variation due to the
interaction of age x interaction of age x gendergender
Within cell
Age
Age x gender
gender
What is Within Cell What is Within Cell Variance?Variance?
This is calculated as the variability of This is calculated as the variability of all individual cells of the data tableall individual cells of the data table
• Source of natural variabilitySource of natural variability
• Source of “error”Source of “error”
Mean Squares: Estimation of Mean Squares: Estimation of VarianceVariance
MS = SS / dfMS = SS / df
F-DistributionF-Distribution
The ANOVA uses the The ANOVA uses the F-statistic, which is F-statistic, which is based on an F-based on an F-distribution rather distribution rather than the normal than the normal distributiondistribution
The Three Null HypothesesThe Three Null Hypotheses
F F age age = MS = MS age age / MS / MS within within Age Main Effect Age Main Effect
F F gender gender = MS = MS gender gender / MS / MS within within Gender Main Gender Main
EffectEffect
F F AxG AxG = MS = MS AxG AxG / MS / MS within within Interaction Interaction
How Are the ANOVA Results How Are the ANOVA Results Reported?Reported?
The ANOVA The ANOVA SummarySummary
Here is the summary Here is the summary for voiced stops for voiced stops last timelast time
Illustrating Significant Illustrating Significant EffectsEffects
Here is an illustration Here is an illustration of the main effect of the main effect of age for the of age for the voiced phonemesvoiced phonemes
How Are the ANOVA Results How Are the ANOVA Results Reported?Reported?
The ANOVA The ANOVA SummarySummary
Here is the summary Here is the summary for voiceless stops for voiceless stops last timelast time
Illustrating Significant Illustrating Significant EffectsEffects
Here is an illustration Here is an illustration of the interaction of the interaction of age x gender for of age x gender for the voiceless the voiceless phonemesphonemes
Post-Hoc Tests for the Post-Hoc Tests for the ANOVAANOVA
Tests of the hypotheses in the two-way Tests of the hypotheses in the two-way ANOVA are only the first steps in the ANOVA are only the first steps in the analysis of a set of dataanalysis of a set of data
Multiple comparisons proceduresMultiple comparisons procedures
The Tukey MethodThe Tukey Method
Also known as the honestly significant Also known as the honestly significant difference testdifference test
Designed to make all pair-wise Designed to make all pair-wise comparisons of means while comparisons of means while maintaining the experiment-wise error maintaining the experiment-wise error rate at the pre-established probability rate at the pre-established probability levellevel
The test statistic is QThe test statistic is Q
Illustrating Significant Illustrating Significant EffectsEffects
Here is an illustration Here is an illustration of the main effect of the main effect of age for the of age for the voiced phonemesvoiced phonemes
Tukey Summary for the Tukey Summary for the Significant Age Effect (Voiced)Significant Age Effect (Voiced)
The pair-wise The pair-wise comparisons comparisons deemed deemed significantly significantly different by the different by the Tukey test are Tukey test are in bold.in bold.
Tukey Procedure for the Tukey Procedure for the Significant Age x Gender Significant Age x Gender Interaction (Voiceless)Interaction (Voiceless)