Question

Consider the data in the table collected from four independent populations. The conclusion of a​ one-way ANOVA test using alphaαequals=0.05 is that the population means are not all the same. Determine which means are different using alphaαequals=0.05		Sample 1	Sample 2	Sample 3	Sample 4
		6	13	23	9
		7	16	13	8
		8	19	19	10
		9		22

Click here to view the ANOVA summary table.

Find the​ Tukey-Kramer critical range CR for each of these differences.

CR​1,2	equals=	?	CR​2,3	equals=	?
CR​1,3	equals=	?	CR​2,4	equals=	?
CR​1,4	equals=	?	CR​3,4	equals=	?

​(Round to two decimal places as​ needed.)

Answer 1

Applying One way ANOVA from excel: data-data analysis: ANOVA(one factor):

Source of Variation	SS	df	MS	F
Between Groups	352.25	3	117.4167	13.69291
Within Groups	85.75	10	8.575
Total	438	13

from above:

MSE=			8.575
df(error)=			10
number of treatments =			4
pooled standard deviation=Sp =√MSE=			2.928

critical q with 0.05 level and k=4, N-k=10 df=			4.33
Tukey's (HSD) =(q/√2)*(sp*√(1/ni+1/nj)         =

CR_1-2 =(4.33/sqrt(2))*(2.928)*sqrt(1/4+1/3)=6.85

CR_1-3 =6.34

CR_1-4 =6.85

CR_2-3 =6.85

CR_2-4 =7.32

CR_3-4 =6.85