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