[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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