As Bob Hayden has already pointed out, you have interrupted time-series
data. However, you actually have three diferent such time series, and it
seems to me that differences between them may be your principal interest.
Schematically, you have (I think) the following, in temporal order:
1. Pretest weight (42 readings, averaged)
2. 10 weeks of Diet A (or Diet B, or Diet C, in the other two groups)_
3. Post-diet weight #1 (42 readings, averaged)
4. 10 weeks of uncontrolled non-diet
5. New non-diet baseline weight #2 (42 readings, averaged)
6. 10 weeks of Diet B (or Diet C, or Diet A, respectively)
7. Post-diet weight #2 (42 readings, averaged)
8. 10 weeks of uncontrolled non-diet
9. New non-diet baseline weight #3 (42 readings, averaged)
10. 10 weeks of Diet C (or Diet A, or Diet B, respectively)
11. Post-diet weight #3 (42 readings, averaged)
[I might have argued for a further 10 weeks of non-diet, with another
weighing at the end of it; but that would depend on whether your
interest be only in the weight loss attributable to a particular diet,
or to the persistence of that loss after one has stopped dieting.]
You have not said whether the panelists differed systematically on any
variables other than the assigned diet. In particular, one might suspect
that effects, if any, differ for males and females.
Suppose you are interested in differences in weight loss as a function of
the several diets. For each person, you have 3 weight-loss values,
being the difference between measurements at #1 and #3 above, between #5
and #7, and between #9 and #11. For conceptual simplicity, let's take
those as differences between the averaged values. (What _kind_ of
averages may also be up for grabs; the median of each set of 42 values
might be best, as being relatively uninfluenced by unexpected, and
perhaps unaccountable, extreme values for an individual.) These values
are in a Latin square structure that can be displayed thus:
Group Diet
A B C
ABC 1 2 3
BCA 3 1 2
CAB 2 3 1
where the numbers give the sequential position of that Diet in that Group
(1st, 2nd, 3rd). This leads to a summary table of this form:
source d.f.
Group 2
Respondents within Group 48
Diet 2
Sequence 2
GxDxS interactions 2
Diet x Resp. within Group 96
The Group main effect represents any systematic differences due to
whether the sequence of diets was (A,B,C) or (B,C,A) or (C,A,B).
The Diet main effect represents the effects presumably of interest, that
is, whether the three diets differed in amount of weight loss observed.
The Sequence effect shows whether being the 1st, 2nd, or 3rd diet in the
temporal sequence makes any difference. The remaining 2 d.f. for
assorted interactions is unlikely to be interesting, but if significant
might indicate something that might be worth pursuing. (The problem with
interactions in a Latin square is that GD interactions are confounded
with the S main effect, GS with D, and DS with G.) (The mean square
for Respondents within Group is the error term, or denominator mean
square, against which the mean square for Group is tested; the mean
square for Diet X Respondents within Group is the error mean square for
Diet, Sequence, and the remaining interaction mean square.)
So far we've considered weight loss as the simple difference between
average pre-diet weight and average post-diet weight. But you migh wish
also to consider relative weight loss: that difference as a proportion
of pre-diet weight. Same structure and analysis, possibly different
results. Or use pre-diet weight as a covariate for the simple weight
loss as a response variable. There may also be interesting comparisons
to be made between the several pre-diet average weights; one can imagine
that these might differ depending on which diet preceded them, or on
their position in the temporal sequence.
One flaw in the design is the several 10-week periods when panelists went
back to their previous (non-diet) eating habits. These appear not to
have been controlled much, and it is imaginable that some panelists may
have (without necessarily intending to do so) changed their diet, either
toward or away from the three diets (A, B, C) imposed by the
experimenter. Hard to see how one could observe that sort of thing, and
measure it so as to take account of it.
On 15 Jan 2000, ZCharlieS7 wrote:
>> I did a weight-loss trial with 51 people comparing 3 diets (alternate
use). Panelists weighed themselves 6 times a day for a week (42 readings
to get an accurate value of weight before new Diet). 17 people had Diet A
1st for 10 weeks. Similarly, 17 people each were started on Diets B or C.
>> During the 10th week, panelists weighed themselves 6 times a day (42
readings). All of the panelists were then given 10 weeks off to go back
to their original (non-trial) diet and weighed themselves as above before
starting a new diet. They were next given another different Diet for 10
weeks (i.e., A people now on B or C), etc.
>> As above, weights were taken in the 10th week. All of the panelists
were then given 10 weeks off to go back to their original (non-trial) diet
and weighed themselves as above before starting a new diet. In the final
10-week period, the panelists went on the Diet they had not tried before.
>> How do I analyze?
< snip, various suggestions >
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