The t-Test for Differences Between Groups

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Presentation transcript:

The t-Test for Differences Between Groups

The t-Test 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 Is there a difference? 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? The mean difference is the same for all three cases. Medium variability High variability Low variability

What Does Difference Mean? Medium variability High variability Which one shows the greatest difference? Low variability

What Does Difference Mean? 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. Which one shows the greatest difference? Low variability

What Do We Estimate? Low variability

What Do We Estimate? Signal Noise Low variability

Difference between group means What Do We Estimate? Signal Difference between group means = Noise Low variability

Difference between group means What Do We Estimate? Signal Difference between group means = Noise Variability of groups Low variability

Difference between group means What Do We Estimate? Signal Difference between group means = Noise Variability of groups _ _ XT - XC = _ _ SE(XT - XC) Low variability

Difference between group means What Do We Estimate? Signal Difference between group means = Noise Variability of groups _ _ XT - XC = _ _ SE(XT - XC) = t-value Low variability

What Do We Estimate? 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