Question

A department store supervisor is concerned about customer service. To check if this is an issue, the supervisor randomly selected a sample of clerks from stores at three different locations (A, B, C). Then the supervisor records the number of returns associated with each clerk for a month. What can the supervisor conclude with an α of 0.05?

A	B	C
8 10 7 9	11 12 14 10	8 10 7 10

Conduct Tukey's Post Hoc Test for the following comparisons:

1 vs. 3: difference =

f) Conduct Scheffe's Post Hoc Test for the following comparisons:
1 vs. 2: test statistic =
1 vs. 3: test statistic =   

Answer 1

Solution:

Your input data on k=3 independent treatments:

Treatment →	A	B	C
Input Data →	8.0 10.0 7.0 9.0	11.0 12.0 14.0 10.0	8.0 10.0 7.0 10.0

Descriptive statistics of your k=3 independent treatments:

Treatment →	A	B	C	Pooled Total
observations N	4	4	4	12
sum ∑xi	34.0000	47.0000	35.0000	116.0000
mean ¯x	8.5000	11.7500	8.7500	9.6667
sum of squares ∑x2i	294.0000	561.0000	313.0000	1,168.0000
sample variance s2	1.6667	2.9167	2.2500	4.2424
sample std. dev. s	1.2910	1.7078	1.5000	2.0597
std. dev. of mean SE¯x	0.6455	0.8539	0.7500	0.5946

One-way ANOVA of your kk=3 independent treatments:

source	sum of squares SS	degrees of freedom νν	mean square MS	F statistic	p-value
treatment	26.1667	2	13.0833	5.7439	0.0247
error	20.5000	9	2.2778
total	46.6667	11

Tukey HSD Test:

The p-value corrresponing 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,

Tukey HSD results

treatments pair	Tukey HSD Q statistic	Tukey HSD p-value	Tukey HSD inferfence
A vs B	4.3068	0.0335492	* p<0.05
A vs C	0.3313	0.8999947	insignificant
B vs C	3.9755	0.0483533	* p<0.05

Scheffé results

treatments pair	Scheffé TT-statistic	Scheffé p-value	Scheffé inferfence
A vs B	3.0454	0.0412856	* p<0.05
A vs C	0.2343	0.9730151	insignificant
B vs C	2.8111	0.0586569	insignificant