[R] Fractional Factorial - Wrong values using lm-function

Staleno sn at bergen-plastics.no
Mon Jun 25 11:26:35 CEST 2012


Hello.

I'm a new user of R, and I have a question regarding the use of aov and
lm-functions. I'm doing a fractional factorial experiment at our production
site, and I need to familiarize myself with the analysis before I conduct
the experiment. I've been working my way through the examples provided at 
http://www.itl.nist.gov/div898/handbook/pri/section4/pri472.htm
http://www.itl.nist.gov/div898/handbook/pri/section4/pri472.htm , but I
can't get the results provided in the trial model calculations. Why is this.
Here is how I have tried to do it:

> data.catapult=read.table("Fractional.txt",header=T) #Read the data in the
> table provided in the example.

> data.catapult
   Distance    h  s b l  e
1     28.00 3.25  0 1 0 80
2     99.00 4.00 10 2 2 62
3    126.50 4.75 20 2 4 80
4    126.50 4.75  0 2 4 45
5     45.00 3.25 20 2 4 45
6     35.00 4.75  0 1 0 45
7     45.00 4.00 10 1 2 62
8     28.25 4.75 20 1 0 80
9     85.00 4.75  0 1 4 80
10     8.00 3.25 20 1 0 45
11    36.50 4.75 20 1 4 45
12    33.00 3.25  0 1 4 45
13    84.50 4.00 10 2 2 62
14    28.50 4.75 20 2 0 45
15    33.50 3.25  0 2 0 45
16    36.00 3.25 20 2 0 80
17    84.00 4.75  0 2 0 80
18    45.00 3.25 20 1 4 80
19    37.50 4.00 10 1 2 62
20   106.00 3.25  0 2 4 80

> aov.catapult =
> aov(Distance~h+s+b+l+e+h*s+h*b+h*l+h*e+s*b+s*l+s*e+b*l+b*e+l*e,data=data.catapult)
> summary(aov.catapult)
            Df Sum Sq Mean Sq F value  Pr(>F)   
h            1   2909    2909  15.854 0.01638 * 
s            1   1964    1964  10.701 0.03076 * 
b            1   7537    7537  41.072 0.00305 **
l            1   6490    6490  35.369 0.00401 **
e            1   2297    2297  12.518 0.02406 * 
h:s          1    122     122   0.667 0.45998   
h:b          1    345     345   1.878 0.24247   
h:l          1    354     354   1.929 0.23724   
h:e          1      0       0   0.001 0.97578   
s:b          1    161     161   0.877 0.40199   
s:l          1     20      20   0.107 0.75966   
s:e          1    114     114   0.622 0.47427   
b:l          1    926     926   5.049 0.08795 . 
b:e          1    124     124   0.677 0.45689   
l:e          1    158     158   0.860 0.40623   
Residuals    4    734     184                   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

This seems just about right to me. However, when I attempt to make the
linear model, based on main factors and two-factor interactions, I get a
completely different result:

> lm.catapult =
> lm(Distance~h+s+b+l+e+h*s+h*b+h*l+h*e+s*b+s*l+s*e+b*l+b*e+l*e,data=data.catapult)
> summary(lm.catapult)

Call:
lm(formula = Distance ~ h + s + b + l + e + h * s + h * b + h * 
    l + h * e + s * b + s * l + s * e + b * l + b * e + l * e, 
    data = data.catapult)

Residuals:
      1       2       3       4       5       6       7       8       9     
10 
-0.8100 22.3875 -3.6763 -3.8925 -3.8925 -0.8576  7.0852 -0.8100 -0.8100
-0.8576 
     11      12      13      14      15      16      17      18      19     
20 
-0.8576 -0.8576  7.8875 -3.8925 -3.8925 -3.6763 -3.6763 -0.8100 -0.4148
-3.6763 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)  
(Intercept)  25.031042 100.791955   0.248   0.8161  
h            -3.687500  22.466457  -0.164   0.8776  
s             0.475446   2.446791   0.194   0.8554  
b           -39.417973  44.906164  -0.878   0.4296  
l           -18.938988  12.233954  -1.548   0.1965  
e            -0.158449   1.230683  -0.129   0.9038  
h:s          -0.368750   0.451546  -0.817   0.4600  
h:b          12.375000   9.030925   1.370   0.2425  
h:l           3.135417   2.257731   1.389   0.2372  
h:e           0.008333   0.258026   0.032   0.9758  
s:b          -0.634375   0.677319  -0.937   0.4020  
s:l          -0.055469   0.169330  -0.328   0.7597  
s:e           0.015268   0.019352   0.789   0.4743  
b:l           7.609375   3.386597   2.247   0.0879 .
b:e           0.318397   0.387008   0.823   0.4569  
l:e           0.089732   0.096760   0.927   0.4062  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 13.55 on 4 degrees of freedom
Multiple R-squared: 0.9697,     Adjusted R-squared: 0.8563 
F-statistic: 8.545 on 15 and 4 DF,  p-value: 0.02559

This result is nothing like the results provided in the example. Why is
this? Any help is very much appreciated.

Regards, Ståle.

--
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