The t-Test for Differences Between Groups. The t-Test Tests whether the means of two groups are...

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The t-Test for Differences The t-Test for Differences Between Groups Between Groups

Transcript of The t-Test for Differences Between Groups. The t-Test Tests whether the means of two groups are...

Page 1: The t-Test for Differences Between Groups. The t-Test Tests whether the means of two groups are statistically different from each other.

The t-Test for Differences Between The t-Test for Differences Between GroupsGroups

Page 2: The t-Test for Differences Between Groups. The t-Test Tests whether the means of two groups are statistically different from each other.

The t-TestThe t-Test

Tests whether the Tests whether the meansmeans of two groups of two groups are are statisticallystatistically differentdifferent from each other from each other

Page 3: The t-Test for Differences Between Groups. The t-Test Tests whether the means of two groups are statistically different from each other.

Statistical AnalysisStatistical Analysis

Page 4: The t-Test for Differences Between Groups. The t-Test Tests whether the means of two groups are statistically different from each other.

Statistical AnalysisStatistical Analysis

Controlgroupmean

Page 5: The t-Test for Differences Between Groups. The t-Test Tests whether the means of two groups are statistically different from each other.

Statistical AnalysisStatistical Analysis

Controlgroupmean

Treatmentgroupmean

Page 6: The t-Test for Differences Between Groups. The t-Test Tests whether the means of two groups are statistically different from each other.

Statistical AnalysisStatistical Analysis

Controlgroupmean

Treatmentgroupmean

Is there a difference?

Page 7: The t-Test for Differences Between Groups. The t-Test Tests whether the means of two groups are statistically different from each other.

What Does What Does DifferenceDifference Mean? Mean?

Page 8: The t-Test for Differences Between Groups. The t-Test Tests whether the means of two groups are statistically different from each other.

What Does What Does DifferenceDifference Mean? Mean?

Mediumvariability

Page 9: The t-Test for Differences Between Groups. The t-Test Tests whether the means of two groups are statistically different from each other.

What Does What Does DifferenceDifference Mean? Mean?

Mediumvariability

Highvariability

Page 10: The t-Test for Differences Between Groups. The t-Test Tests whether the means of two groups are statistically different from each other.

What Does What Does DifferenceDifference Mean? Mean?

Mediumvariability

Highvariability

Lowvariability

Page 11: The t-Test for Differences Between Groups. The t-Test Tests whether the means of two groups are statistically different from each other.

What Does What Does DifferenceDifference Mean? Mean?

Mediumvariability

Highvariability

Lowvariability

The mean differenceis the same for all

three cases.

Page 12: The t-Test for Differences Between Groups. The t-Test Tests whether the means of two groups are statistically different from each other.

What Does What Does DifferenceDifference Mean? Mean?

Mediumvariability

Highvariability

Lowvariability

Which one showsthe greatestdifference?

Page 13: The t-Test for Differences Between Groups. The t-Test Tests whether the means of two groups are statistically different from each other.

What Does What Does DifferenceDifference Mean? Mean? A statistical difference is a function of the A statistical difference is a function of the

difference between meansdifference between means relative to the relative to the variabilityvariability..

A small difference between means with large A small difference between means with large variability could be due to variability could be due to chancechance..

Like a Like a signal-to-noisesignal-to-noise ratio. ratio.

Lowvariability

Which one showsthe greatestdifference?

Page 14: The t-Test for Differences Between Groups. The t-Test Tests whether the means of two groups are statistically different from each other.

What Do We Estimate?What Do We Estimate?

Lowvariability

Page 15: The t-Test for Differences Between Groups. The t-Test Tests whether the means of two groups are statistically different from each other.

What Do We Estimate?What Do We Estimate?

Lowvariability

Signal

Noise

Page 16: The t-Test for Differences Between Groups. The t-Test Tests whether the means of two groups are statistically different from each other.

What Do We Estimate?What Do We Estimate?

Lowvariability

Signal

Noise

Difference between group means=

Page 17: The t-Test for Differences Between Groups. The t-Test Tests whether the means of two groups are statistically different from each other.

What Do We Estimate?What Do We Estimate?

Lowvariability

Signal

Noise

Difference between group means

Variability of groups=

Page 18: The t-Test for Differences Between Groups. The t-Test Tests whether the means of two groups are statistically different from each other.

What Do We Estimate?What Do We Estimate?

Lowvariability

Signal

Noise

Difference between group means

Variability of groups=

=XT - XC

SE(XT - XC)

_ _

_ _

Page 19: The t-Test for Differences Between Groups. The t-Test Tests whether the means of two groups are statistically different from each other.

What Do We Estimate?What Do We Estimate?

Lowvariability

Signal

Noise

Difference between group means

Variability of groups=

XT - XC

SE(XT - XC)=

= t-value

_ _

_ _

Page 20: The t-Test for Differences Between Groups. The t-Test Tests whether the means of two groups are statistically different from each other.

What Do We Estimate?What Do We Estimate?

The t-test, one-way Analysis of Variance The t-test, one-way Analysis of Variance (ANOVA) and a form of regression all test the (ANOVA) and a form of regression all test the same thing and can be considered equivalent same thing and can be considered equivalent alternative analyses.alternative analyses.

The regression model is emphasized here The regression model is emphasized here because it is the most general.because it is the most general.

Lowvariability


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