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. All F values are positive. Notice (from the first slide) t*= , and ( ) 2 =17.09

11.10 Page 344 n=30 observations c=5 groups j=6 observations in each group Fcrit=F 0.05,4,25 =2.76 There is evidence of a difference in the mean rating of the five advertisements. MSA MSW The single factor is the Ad influencing the Rating.

SSW, measure of variation within group SST, measure of TOTAL variation SSA, measure of variation in means among groups SSW mean group A mean group B mean group C mean group D mean group E SSA

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 df num =c and df denom =n-c. A,B0.333 A,C6.667* A,D9.000* A,E2.667 B,C6.333* B,D8.667* B,E2.333 C,D2.333 C,E4.000 D,E6.333*

MSW df = n-c c

One-Way ANOVA Summary SourcedfSSMSF Amongc-1SSAMSA F*=MSA/MSW Withinn-cSSWMSW Fcrit=F ,c-1,n-c Totaln-1SST Main Hypothesis F distribution test, df num =c-1, df denom =n-c T-K all pairs test Q distribution test, df num =c, df denom =n-c Test regarding the difference between population means of multiple groups. One factor of influence. Equal variance assumption.

Homework 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.