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10.12 Page 344. Two Sample t-test regarding (2) population means. 10.12 Page 344. ANOVA Method. 10.12 Page 344. ANOVA Method. Think of the F distribution as the t distribution squared. All F-tests are one-tail tests. For a 2-tailed t-test, the area in the two-tails are combined.

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10.12 Page 344

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10 12 page 344

10.12

Page 344

Two Sample t-test regarding (2) population means


10 12 page 344

10.12

Page 344

ANOVA Method


10 12 page 344

10.12

Page 344

ANOVA Method


10 12 page 344

Think of the F distribution as the t distribution squared.

All F-tests are one-tail tests.

For a 2-tailed t-test, the area in the two-tails are combined.

All F values are positive.

Notice (from the first slide) t*=-4.1343, and (-4.1343)2=17.09


10 12 page 344

11.10

Page 344

The single factor is the Ad influencing the Rating.

Fcrit=F0.05,4,25=2.76

There is evidence of a difference in the mean rating of the five advertisements.

n=30 observations

c=5 groups

j=6 observations in each group

MSA

MSW


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mean group A

mean group B

SSW

mean group C

SSA

mean group D

mean group E

SSA, measure of variation in means among groups

SSW, measure of variation within group

SST, measure of TOTAL variation


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Tukey-Kramer Procedure for Comparing all Pairs

If the absolute value of the mean difference in a pair is greater than the Critical Range (CR) value, the difference is significant.

The CR is obtained from the Q, Studentized Range distribution, with dfnum=c and dfdenom=n-c.


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MSW df = n-c

c


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One-Way ANOVA Summary

Main Hypothesis

F distribution test, dfnum=c-1, dfdenom=n-c

  • Test regarding the difference between

  • population means of multiple groups.

  • One factor of influence.

  • Equal variance assumption.

T-K all pairs test

Q distribution test, dfnum=c, dfdenom=n-c


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Homework 11.13 a and b

Perform the T-K procedure manually and in NCSS.

If you have time, try to obtain SSA, SSW, and SST manually with the use of Excel. Be able to

Compute MSA and MSW from SSA and SSW.

Compute F* and Fcrit and interpret.

Obtain Q Critical Range value and perform the T-K procedure to compare means of pairs.


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