Looks to me as though your text has typographical (at least) errors.
There's no way one could get a total SS of 70 thousand from those data;
unless perhaps the text is using the European style of decimal notation,
in which "70,880" would mean what in North America would be written
"70.880". In any case, your analysis appears to be correct; using
Minitab, I get the same results. FWIW, I have appended the Minitab
output file to this post.
On Fri, 20 Dec 2002, Ronny Richardson wrote in part:
> ... the 3rd edition of Elementary Statistics by Bluman ... have an
> example problem on two-way ANOVA that I'm stuck on. (page 567)
>
> This is a simple 2x2 two-way ANOVA problem with the following data:
>
> Two Wheel Four-Wheel
> Regular 27.6 28.6
> 25.2 29.3
> High 32.8 24.2
> 32.8 24.2
>
> It does not matter, but this is gas mileage for two and four wheel
> drive on regular and "high test". They show the following ANOVA
> table:
>
> Source SS df
> --------------------------------
> Gasoline, A 3,920 1
> Automobile, B 9,680 1
> Interaction (AxB) 54,080 1
> Within (error) 3,300 4
> --------------------------------
> Total 70,880 7
>
> Excel does not offer two-way ANOVA but it does offer two-factor
> ANOVA with replication. I as assuming that two-way = two-factor
That is correct.
> ... and that seems to match problems in other books I've looked at.
> With Excel, I get the following:
>
> Source SS df MS F P-value F crit
> Sample 1.361 1 1.361 1.742 0.257 7.709
> Columns 18.301 1 18.301 23.426 0.008 7.709
> Interaction 62.161 1 62.161 79.566 0.001 7.709
> Within 3.125 4 0.781
> Total 84.949 7
This matches my results with Minitab. See below for confirmation.
> I don't think the differences between Bluman and Excel are due to any
> problems with Excel since it gets the right results with problems I tried
> from other textbooks. Any ideas on what I, Bluman, or Excel is doing wrong
> or differently?
I'd guess that Bluman was analyzing a different two-way with the same
structure (2 x 2, with 2 replications per cell), possibly one that had
appeared in this place in the second edition. If your text has an
e-mail address for the author, send him a note (forward this one if you
like): he'll be glad of the information and the opportunity to correct
the error for the next printing.
> Ronny Richardson
The Minitab file appears below my .sig (74 lines): -- 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]
-----------------------------------------------------------------------
<Comments edited in, shown in angle brackets.>
MTB > exec 'ronny'
MTB > note Original data, for two-way ANOVA:
MTB > note Two Wheel Four-Wheel 2-wheel 4-wheel
MTB > note Regular 27.6 28.6 High-test 32.8 24.2
MTB > note 25.2 29.3 32.8 24.2
MTB >
MTB > name c1 'Gas' c2 'Drive' c3 'Mileage' <supply variable names>
MTB > note Gas: 1 = regular, 2 = high-test
MTB > note Drive: 1 = two-wheel, 2 = four-wheel
MTB > set c3
DATA> 27.6 28.6 32.8 24.2
DATA> 25.2 29.3 32.8 24.2
DATA> end of data
MTB > set c1 <c1 = column 1 of the worksheet, named "Gas">
DATA> 2(1 2)2 <and similarly for c2, c3>
DATA> end of data
MTB > set c2
DATA> 4(1 2)
DATA> end of data
MTB > print c1-c3 <to verify accuracy of copying and indexes>
ROW Gas Drive Mileage
1 1 1 27.6
2 1 2 28.6
3 2 1 32.8
4 2 2 24.2
5 1 1 25.2
6 1 2 29.3
7 2 1 32.8
8 2 2 24.2
MTB > anova c3 = c2!c1 <Factorial ANOVA program>
Factor Type Levels Values
Drive fixed 2 1 2
Gas fixed 2 1 2
Analysis of Variance for Mileage
Source DF SS MS F P
Drive 1 18.301 18.301 23.43 0.008
Gas 1 1.361 1.361 1.74 0.257
Drive*Gas 1 62.161 62.161 79.57 0.001
Error 4 3.125 0.781
Total 7 84.949
MTB > twoway c3 c2 c1
ANALYSIS OF VARIANCE Mileage <2-way ANOVA program>
SOURCE DF SS MS <same results, but without
Drive 1 18.301 18.301 F and p calculations>
Gas 1 1.361 1.361
INTERACTION 1 62.161 62.161
ERROR 4 3.125 0.781
TOTAL 7 84.949
MTB > table c1 c2; <Table of means, to compare with
SUBC> mean c3. raw data, for verification.>
ROWS: Gas COLUMNS: Drive
1 2 ALL
1 26.400 28.950 27.675
2 32.800 24.200 28.500
ALL 29.600 26.575 28.087
CELL CONTENTS --
Mileage:MEAN
.
.
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