Download How to perform a one-way ANOVA using Minitab

Instructions for carrying out
statistical procedures and tests
using Minitab
These instructions are closely linked to the author’s book:
Essential Statistics for the Pharmaceutical Sciences
John Wiley & Sons Ltd http://eu.wiley.com
For all references to chapters or tables, see the above book.
Using Minitab to perform a
one-way analysis of variance
Using Minitab to perform a one-way analysis of variance
Example: Table 14.1 Effect of catalyst on yield (Percentage of
theoretical maximum) Use the XL file ‘Data for Table 14.1 (Minitab version)’
from the web site.
Label one column to hold the yields (‘Yield’) and another (‘Catalyst’) to hold
the labels that will indicate which group each yield belongs to.
Enter all the percentage yields into the relevant column and put suitable labels
into the other column. The worksheet should then look like this:
Follow the menus Stat / ANOVA / One-way…
In the top box, select ‘Response data are in one column for all factor levels’.
In the box labelled ‘Response:’, enter the name of the column containing the
data to be analysed (‘Yield’). In the box labelled ‘Factor:’, enter the name of
the column containing the labels for the groups (‘Catalyst’). OK.
The output will be as on next page:
One-way ANOVA: Yield versus Catalyst
Method
Null hypothesis
Alternative hypothesis
Significance level
All means are equal
At least one mean is different
α = 0.05
Equal variances were assumed for the analysis.
Factor Information
Factor
Catalyst
Levels
5
Values
Ir, Pd, Pd/Ir, Pt, Rh
Analysis of Variance
Source
Catalyst
Error
Total
DF
4
20
24
Adj SS
148.06
19.30
167.36
Adj MS
37.0156
0.9648
F-Value
38.37
P-Value
0.000
Model Summary
S
0.982242
R-sq
88.47%
R-sq(adj)
86.16%
R-sq(pred)
81.98%
Means
Catalyst
Ir
Pd
Pd/Ir
Pt
Rh
N
5
5
5
5
5
Mean
11.920
17.420
13.700
10.740
11.180
StDev
0.978
1.335
0.430
0.688
1.195
95%
(11.004,
(16.504,
(12.784,
( 9.824,
(10.264,
CI
12.836)
18.336)
14.616)
11.656)
12.096)
Pooled StDev = 0.982242
Minitab will also produce this Figure:
Interval Plot of Yield vs Catalyst
95% CI for the Mean
19
18
17
Yield
16
15
14
13
12
11
10
Ir
Pd
Pd/Ir
Catalyst
The pooled standard deviation was used to calculate the intervals.
Pt
Rh
The P value is reported as 0.000 (Which should be reported as ‘<0.001’) and
is clearly significant. This means that at least one of the catalysts differs from
one of the others. The problem is deciding which differs from which.
The figure, gives a visual impression, but can never be definitive. Palladium
is pretty clearly superior to all others but among the remainder, the situation is
unclear. For a definitive analysis, you will need to add on either a Tukey’s or
a Dunnett’s test.
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