Thought you might be interested in a graphical display of the four cell
means, available from Minitab by treating the data as a one-way ANOVA
with four groups:
MTB > note use oneway for graphical output.
MTB > name c4 'Group'
MTB > let c4 = 2*'Drive' + 'Gas' - 2
MTB > note 1 = Regular, 2-wheel; 2 = High-test, 2-wheel;
MTB > note 3 = Regular, 4-wheel; 4 = High-test, 4-wheel.
MTB > table c1 c2;
SUBC> mean c4. # To verify coding.
ROWS: Gas COLUMNS: Drive <Gas: 1 = regular, 2 = high-test;
Drive: 1 = 2-wheel, 2 = 4-wheel>
1 2 ALL
1 1.0000 3.0000 2.0000
2 2.0000 4.0000 3.0000
ALL 1.5000 3.5000 2.5000
CELL CONTENTS --
Group:MEAN
MTB > oneway c3 c4
ANALYSIS OF VARIANCE ON Mileage
SOURCE DF SS MS F p
Group 3 81.824 27.275 34.91 0.003
ERROR 4 3.125 0.781
TOTAL 7 84.949
INDIVIDUAL 95 PCT CI'S FOR MEAN
BASED ON POOLED STDEV
LEVEL N MEAN STDEV ------+---------+---------+---------+
1 2 26.400 1.697 (----*----)
2 2 32.800 0.000 (----*----)
3 2 28.950 0.495 (----*----)
4 2 24.200 0.000 (----*----)
------+---------+---------+---------+
POOLED STDEV = 0.884 24.5 28.0 31.5 35.0
>From the diagram, one can see that group 2 (high-test, 2-wheel) gets
higher mileage than any of the other groups; and that group 3 (regular,
4-wheel) gets higher mileage than group 4 (high-test, 4-wheel). This
pattern, while reflected in the 2-way output, is not so easily derived
from that output, which showed a significant interaction and a main
effect of the kind of drive, but no main effect due to type of fuel.
Formally, the main effect of fuel type is the comparison between the
average of groups 1 and 3, and the average of groups 2 and 4; the main
effect of type of drive is the comparison between the average of groups
1 and 2, and the average of groups 3 and 4; and the interaction is the
comparison of the average of groups 1 and 4, and the average of groups 2
and 3. Examining the means plotted above, you can see how these
comparisons lead to the two-way results, and how taking those results at
face value might mislead one as to what is "really" (so to speak) going
on; or at least, those results do not lead very obviously to the
description in the previous paragraph ("From the diagram, ...").
-- DFB.
-----------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
56 Sebbins Pond Drive, Bedford, NH 03110 (603) 626-0816
[was: 184 Nashua Road, Bedford, NH 03110 (603) 471-7128]
.
.
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