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.

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Click here to view a table of critical values for the studentized range.

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Let

x overbarx1​,

x overbarx2​,

x overbarx3​,

and

x overbarx4

be the means for samples​ 1, 2,​ 3, and​ 4, respectively. Find the absolute values of the differences between the means.

StartAbsoluteValue x overbar 1 minus x overbar 2 EndAbsoluteValuex1−x2	equals=	nothing	StartAbsoluteValue x overbar 2 minus x overbar 3 EndAbsoluteValuex2−x3	equals=	nothing
StartAbsoluteValue x overbar 1 minus x overbar 3 EndAbsoluteValuex1−x3	equals=	nothing	StartAbsoluteValue x overbar 2 minus x overbar 4 EndAbsoluteValuex2−x4	equals=	nothing
StartAbsoluteValue x overbar 1 minus x overbar 4 EndAbsoluteValuex1−x4	equals=	nothing	StartAbsoluteValue x overbar 3 minus x overbar 4 EndAbsoluteValuex3−x4	equals=	nothing

​(Type integers or decimals. Do not​ round.)

Source	Sum of Squares	Degrees of Freedom	Mean Sum of Squares	F
Between	352.25	3	117.417	13.693
Within	85.75	10	8.575
Total	438	13

Answer 1

The output of single anova factor is