Content Preview

Lorem ipsum dolor sit amet, consectetur adipisicing elit. Odit molestiae mollitia laudantium assumenda nam eaque, excepturi, soluta, perspiciatis cupiditate sapiente, adipisci quaerat odio voluptates consectetur nulla eveniet iure vitae quibusdam? Excepturi aliquam in iure, repellat, fugiat illum voluptate repellendus blanditiis veritatis ducimus ad ipsa quisquam, commodi vel necessitatibus, harum quos a dignissimos.

Close Save changes

Keyboard Shortcuts

Help F1 or ? Previous Page ← + CTRL (Windows) ← + ⌘ (Mac) Next Page → + CTRL (Windows) → + ⌘ (Mac) Search Site CTRL + SHIFT + F (Windows) ⌘ + ⇧ + F (Mac) Close Message ESC

10.4 - Minitab: One-Way ANOVA

In one research study, 20 young pigs are assigned at random among 4 experimental groups. Each group is fed a different diet. (This design is a completely randomized design.) The data are the pigs' weights in kg after being raised on these diets for 10 months. We wish to determine if there are any differences in mean pig weights for the 4 diets.

\(H_0: \mu_1 = \mu_2 = \mu_3 = \mu_4\)
\(H_a:\) Not all \(\mu\) are equal

Pig Weight Data

Feed_1	Feed_2	Feed_3	Feed_4
60.8	68.3	102.6	87.9
57.1	67.7	102.2	84.7
65.0	74.0	100.5	83.2
58.7	66.3	97.5	85.8
61.8	69.9	98.9	90.3

Contained in the Minitab file: ANOVA_ex.mpx

Note that in this file the data were entered so that each group is in its own column. In other words, the responses are in a separate column for each factor level. In later examples, you will see that Minitab will also conduct a one-way ANOVA if the responses are all in one column with the factor codes in another column.

Minitab 18

Minitab ® – One-Way ANOVA

To perform an Analysis of Variance (ANOVA) test in Minitab:

Open the Minitab file: ANOVA_ex.mpx
From the menu bar, select Stat > ANOVA > One-Way.
Click the drop-down menu and select 'Responses are in a separate column for each factor level'.
Enter the variables Feed_1, Feed_2, Feed_3, and Feed_4 to insert them into the Responses box.
Choose the Comparisons button and check the box next to Tukey. Under Results also select Tests.
OK and OK

The result should be the following output:

Method

Null hypothesis	All means are equal
Alternative hypothesis	At least one mean is different
Significance level	\(\alpha=0.05\)

Equal variances were assumed for the analysis

Factor Information

Factor	Levels	Values
Factor	4	Feed_1, Feed_2, Feed_3, Feed_4

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Factor	3	4703.2	1567.73	206.72	0.000
Error	16	121.3	7.58
Total	19	4824.5

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
2.75386	97.48%	97.01%	96.07%

Means

Factor	N	Mean	StDev	95% CI
Feed_1	5	60.68	3.03	(58.07, 63.29)
Feed_2	5	69.24	2.96	(66.63, 71.85)
Feed_3	5	100.340	2.164	(97.729, 102.951)
Feed_4	5	86.38	2.78	(83.77, 88.99)

Pooled StDev = 2.75386

Grouping Information Using the Tukey Method and 95% Confidence

Factor	N	Mean	Grouping
Feed_3	5	100.34	A
Feed_4	5	86.38	B
Feed_2	5	69.24	C
Feed_1	5	60.68	D

Means that do not share a letter are significantly different.

Difference of Levels	Difference of Means	SE of Difference	95% CI	T-Value	Adjusted P-Value
Feed_2 - Feed_1	8.56	1.74	(3.57, 13.55)	4.91	0.001
Feed_3 - Feed_1	39.66	1.74	(34.67, 44.65)	22.77	0.000
Feed_4 - Feed_1	25.70	1.74	(20.71, 30.69)	14.76	0.000
Feed_3 - Feed_2	31.10	1.74	(26.11, 36.09)	17.86	0.000
Feed_4 - Feed_2	17.14	1.74	(12.15, 22.13)	9.84	0.000
Feed_4 - Feed_3	-13.96	1.74	(-18.95, -8.97)	-8.02	0.000

Tukey Simultaneous Tests for Differences of Means

Individual confidence level = 98.87%