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CSD 5100 Introduction to Research Methods in CSD

CSD 5100 Introduction to Research Methods in CSD. Analysis of Variance The Statistical Procedure for Factorial Design. Factorial Design. Experimental procedure for testing the null hypothesis when two independent variables, or factors, are considered simultaneously in a research study

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CSD 5100 Introduction to Research Methods in CSD

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  1. CSD 5100Introduction to Research Methods in CSD Analysis of Variance The Statistical Procedure for Factorial Design

  2. Factorial Design Experimental procedure for testing the null hypothesis when two independent variables, or factors, are considered simultaneously in a research study The ANOVA is the statistical procedure for analyzing data from factorial designs

  3. Advantages of Factorial Design • Efficiency • Control • Allows the study of the interaction between two or more independent variables

  4. Data Tables

  5. The ANOVA partitions the total variation of scores into four components Within cell variance Variation among the row (age) means Variation among the column (gender) means Variation due to the interaction of age x gender How Does the ANOVA Work? Age Within cell gender Age x gender

  6. What is Within Cell Variance? This is calculated as the variability of all individual cells of the data table • Source of natural variability • Source of “error”

  7. Mean Squares: Estimation of Variance MS = SS / df

  8. F-Distribution The ANOVA uses the F-statistic, which is based on an F-distribution rather than the normal distribution

  9. The Three Null Hypotheses F age = MS age / MS within Age Main Effect F gender = MS gender / MS within Gender Main Effect F AxG = MS AxG / MS within Interaction

  10. How Are the ANOVA Results Reported? The ANOVA Summary Here is the summary for voiced stops last time

  11. Illustrating Significant Effects Here is an illustration of the main effect of age for the voiced phonemes

  12. How Are the ANOVA Results Reported? The ANOVA Summary Here is the summary for voiceless stops last time

  13. Illustrating Significant Effects Here is an illustration of the interaction of age x gender for the voiceless phonemes

  14. Post-Hoc Tests for the ANOVA Tests of the hypotheses in the two-way ANOVA are only the first steps in the analysis of a set of data Multiple comparisons procedures

  15. The Tukey Method Also known as the honestly significant difference test Designed to make all pair-wise comparisons of means while maintaining the experiment-wise error rate at the pre-established probability level The test statistic is Q

  16. Illustrating Significant Effects Here is an illustration of the main effect of age for the voiced phonemes

  17. Tukey Summary for the Significant Age Effect (Voiced) The pair-wise comparisons deemed significantly different by the Tukey test are in bold.

  18. Tukey Procedure for the Significant Age x Gender Interaction (Voiceless)

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