PLEASE SHOW ALL WORK IN DETAIL NO CALCULATOR. The data below are from an indepen

ID: 3316682 • Letter: P

Question

PLEASE SHOW ALL WORK IN DETAIL NO CALCULATOR.

The data below are from an independent-measures experiment comparing three different treatment conditions.

Treatment 1 Treatment 2 Treatment 3

0 1 6

1 4 5

0 1 8

3 2 5

––––––––––––––––––––––––––––––––––––

a. Use an analysis of variance with = .05 to determine whether these data indicate any significant mean differences among the treatments.

b. Compute 2 , the percentage of variance accounted for by the treatment.

c. Use the Tukey’s HSD test to determine which of the treatments are significantly different from each other. Use the .05 level of significance for all tests.

Explanation / Answer

Hypothesis,

The hypotheses of interest in an ANOVA are as follows:

for Groups,

enter data in excel and follows the path;,

data analysis >ANOVA:single factor > select data ,

output as follows,

SUMMARY

Groups

Count

Sum

Average

Variance

treat1

treat2

treat3

ANOVA

Source of Variation

P-value

F crit

Between Groups

0.001727

4.256495

Within Groups

Total

Conclusion: from the p-value which is less than the 0.05 , we can conclude that there is significant diffreance between the all treatmet

The p-value corresponding to the F-statistic of one-way ANOVA is lower than 0.05 which strongly suggests that
one or more pairs of treatments are significantly different. You have k=3 treatments, for which we shall apply
Tukey's HSD test to each of the 3 pairs to pinpoint which of them exhibits statistically significant difference.

We first establish the critical value of the Tukey-Kramer HSD QQ statistic based on the k=5 treatments
and =9 degrees of freedom for the error term, for significance level =0.05 (p-values) in
the Student zed Range distribution. We obtain these critical values for Q for of 0.05,
critical value of Q at Q =0.05,k=5,=18 Q= 5.42

so here is the , between the treatment A and C , there is significant diffreance.

and b and c , there is significant siffreance.

thanks