On 3 Jun 2000, Bill Venables posted (to the S-Plus email list) a very nice
explanation of how to think about split-plot designs using Cochran and
Cox's chocolate cake data and the lme function. A copy of that posting is
here:
https://biostat-lists.wustl.edu/sympa/arc/s-news/2000-06/msg00023.html
In that posting, Bill mentioned that the experiment details were not quite
clear on a detail, so I went to the source document and transcribed a few
of the details. (See below). I'm posting them here for posterity and the
curiosity of anyone interested.
Kevin Wright
Source: Frances E Cook. 1938. Chocolate cake I. Optimum baking
temperature. Thesis. Iowa State College. Now held in the Special
Collections department of the Iowa State University library.
Transcribed by Kevin Wright.
4. The purpose of one part of the study was to determine whether cakes
having a higher ratio of sugar would require a higher baking temperature.
In addition, since many people add hot rather than warm chocolate to the
cake batter, this practice was also studied to determine its effect on the
volume, texture, tenderness, and velvetiness of the baked cake.
8. For this study a total of 270 small loaf cakes was made. Series A with
the regular formula had the melted chocolate added at 40C. The same
proportions were used for Series B with the chocolate added at 60C and the
last series, also a variation of Series A, had the sugar increased to 450
grams. Each mix was divided into six cakes each of which was baked at a
different temperature.
The cakes were baked over a period of seven weeks from April 18 to June 2.
Usually only six cakes were baked daily, although occasionally two sets
consisting of 12 cakes were made in one day. The cakes were always scored
and tested the day after they were baked. The series were alternated so
that all three groups were finished at approximately the same time. The
order in which they were baked was also randomized. In this way the
scoring for each series was more valid since the judges did not score any
one series long enough to acquire a distinct preference or dislike for it.
15. Breaking Angle
The tenderness of the cake was tested with the breaking angle apparatus...a
slice of cake one-half inch thick was cut with a cookie cutter measuring
1.5 x 2.5 inches.
As the movable holder of the breaking angle apparatus was very gradually
moved away from the operator, the pointer showed the number of degrees
required for the angle of breakage. The readings were recorded at the
point where the slice of cake just began to break. The readings ranged
from 8 degrees to 36 degrees.
Two slices of cake, one from the end and the other from the center, were
tested from each cake and the scores totalled. Great care had to be taken
in slicing the cake, so that the slice was the same thickness at the bottom
as it was at the top. A definite technique had to be developed in
revolving the movable portion slowly and steadily.
28. Breaking angle
The data as tabulated in Table 8 indicated that with increasing baking
temperature up to 215C there was a similar increase in the amount of
pressure necessary to break the cake. The cakes baked at a low
temperature, though gummy, were very crumbly so that they broke more easily
than those baked at higher temperatures. A comparison of the average
breaking angle, 27.98 for the cakes baked at 175C to 35.86, the mean for
those baked at 215C, would indicate this.
The cakes in Series C broke slightly easier than those in the second
series. Undoubtedly the increased sugar was responsible for the lower
breaking angle of Series C in comparison with Series A. In Series B the
breaking angle was probably less because the high temperature chocolate
gave a better volume; with the more compact cake from Series A more
pressure would be required to break the sample.
An analysis of variance indicated highly significant differences for the
breaking angle between the six baking temperatures, between the three cake
series, and between the fifteen mixes within a given series.
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