The tTest for Differences Between Groups The tTests
The t-Test for Differences Between Groups
The t-Tests whether the means of two groups are statistically different from each other
Statistical Analysis
Statistical Analysis Control group mean
Statistical Analysis Control group mean Treatment group mean
Statistical Analysis Control group mean Treatment group mean Is there a difference?
What Does Difference Mean?
What Does Difference Mean? Medium variability
What Does Difference Mean? Medium variability High variability
What Does Difference Mean? Medium variability High variability Low variability
What Does Difference Mean? Medium variability The mean difference is the same for all three cases. High variability Low variability
What Does Difference Mean? Medium variability High variability Low variability Which one shows the greatest difference?
What Does Difference Mean? l l l A statistical difference is a function of the difference between means relative to the variability. A small difference between means with large variability could be due to chance. Like a signal-to-noise ratio. Low variability Which one shows the greatest difference?
What Do We Estimate? Low variability
What Do We Estimate? Signal Noise Low variability
What Do We Estimate? Signal Noise = Low variability Difference between group means
What Do We Estimate? Signal Noise = Low variability Difference between group means Variability of groups
What Do We Estimate? Signal Noise = = Low variability Difference between group means Variability of groups _ _ XT - X C _ _ SE(XT - XC)
What Do We Estimate? Signal Noise = = = Low variability Difference between group means Variability of groups _ _ XT - X C _ _ SE(XT - XC) t-value
What Do We Estimate? l l The t-test, one-way Analysis of Variance (ANOVA) and a form of regression all test the same thing and can be considered equivalent alternative analyses. The regression model is emphasized here because it is the most general. Low variability
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