5.2.2: Nested Model in Minitab

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In Minitab, for the following (Nested Example Data):

Stat > ANOVA > General Linear Model > Fit General Linear Model

Enter the factors 'Region' and 'City' in the Factors box, then click on Random/Nest...Here is where we specify the nested effect of City in Region.

Minitab General Linear Model pop-up window, with 'Ex_hours' in the Responses window and "Region" and "City" in the Factors window. — Figure \(\PageIndex{1}\): General Linear Model pop-up window.

General Linear Model: Random Nest pop-up window, with "Region" entered in the City window and the Fixed factor type selected for both Region and City. — Figure \(\PageIndex{2}\): Random Nest pop-up window.

The output is shown below.

Factor Information

General Linear Model: response versus School, Instructor

Factor	Type	Levels	Values
Region	Fixed	2	1,2
City(Region)	Fixed	6	Atlanta(1), Chicago(1), SanFran(1), Atlanta(2), Chicago(2), SanFran(2)

Analysis of Variance

Source	DF	Adj SS	Adj MS	F	P
Region	1	108.00	108.000	15.43	0.008
City(Region)	4	616.00	154.000	22.00	0.001
Error	6	42.00	7.000
Total	11	766.00

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
2.64575	94.52%	89.95%	78.07%

Following the ANOVA run, you can generate the mean comparisons by

Stat > ANOVA > General Linear Model > Comparisons

Then specify "Region" and "City(Region)" for the comparisons by checking the boxes.

Comparisons pop-up window with "Ex_hours" selected in the Response dropdown, "Pairwise" selected in the Type of comparison dropdown, "Tukey" selected for the Method and "Region" and "City(Region)" selected in the "choose terms for comparisons" section. — Figure \(\PageIndex{3}\): Comparisons pop-up window.

Then choose Graphs to get the following dialog box, where "Interval plot for difference of means" should be checked.

Checking the box for "Interval plot for differences of means" in the Comparisons: Graphs pop-up window. — Figure \(\PageIndex{4}\): Comparisons: Graphs pop-up window.

The outputs are as follows.

Comparison for Ex_hours

Tukey Pairwise Comparisons: Region

Grouping Information Using Tukey Method and 95% Confidence

Region	N	Mean	Grouping
1	6	18	A
2	6	12	B

Means that do not share a letter are significantly different.

Minitab Tukey Simultaneous 95% CIs Differences of Means for Ex_Hours graph — Figure \(\PageIndex{5}\): Tukey simultaneous 95% CIs differences of means graph for Ex_hours, by Region.

Tukey Pairwise Comparisons: (City)Region

Grouping Information Using Tukey Method and 95% Confidence

City(Region)	N	Mean	Grouping
Atlanta (1)	2	27.0	A
Chicago(2)	2	20.0	A	B
SanFran(1)	2	18.5	A	B	C
Atlanta(2)	2	12.5		B	C	D
Chicago(1)	2	8.5			C	D
SanFran(2)	2	3.5				D

Means that do not share a letter are significantly different.