T Test

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A conceptual understanding of the T Test. . . some of these ideas are modified from Trochim, W. . . http://www. socialresearchmethod s. net/research/reshome. htm Check out his web site. . .

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The t-Test for Differences Between Groups : 

The t-Test for Differences Between Groups

The t-Test : 

The t-Test Tests whether the means of two groups are statistically different from each other

Statistical Analysis : 

Statistical Analysis

Statistical Analysis : 

Statistical Analysis Control group mean

Statistical Analysis : 

Statistical Analysis Control group mean Treatment group mean

Statistical Analysis : 

Statistical Analysis Control group mean Treatment group mean Is there a difference?

What Does Difference Mean? : 

What Does Difference Mean?

What Does Difference Mean? : 

What Does Difference Mean? Medium variability

What Does Difference Mean? : 

What Does Difference Mean? Medium variability High variability

What Does Difference Mean? : 

What Does Difference Mean? Medium variability High variability Low variability

What Does Difference Mean? : 

What Does Difference Mean? Medium variability High variability Low variability The mean difference is the same for all three cases.

What Does Difference Mean? : 

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

What Does Difference Mean? : 

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. Low variability Which one shows the greatest difference?

What Do We Estimate? : 

What Do We Estimate? Low variability

What Do We Estimate? : 

What Do We Estimate? Low variability Signal Noise

What Do We Estimate? : 

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

What Do We Estimate? : 

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

What Do We Estimate? : 

What Do We Estimate? Low variability Signal Noise Difference between group means Variability of groups = = M1 – M2 s(M1 – M2)

What Do We Estimate? : 

What Do We Estimate? Low variability Signal Noise Difference between group means Variability of groups = M1 – M2 s(M1 – M2) = = t-value

What Do We Estimate? : 

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

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