>> As you describe the study, you have an unspecified number of children
>> divided into four groups in a two-way design of Treatments (2 levels)
>> by Prior Performance (2 levels). This would naturally lend itself to
>> a two-way analysis of variance, or equivalently (pace Joe Ward) to a
>> multiple regression analysis with three predictors: Treatment,
>> Performance, and Treatment*Performance. If there are indeed effects
>> attributable to Treatment and Performance, this analysis will be more
>> sensitive to them than the two separate t-tests you propose. And if
>> there is an interaction between Treatment and Performance, as there may
>> well be, the sensitivity to possible effects increases.
Firstly, thank you for your comments. Am I right in saying that the two
(equivalent) options I have are:
1. ANOVA
Yijk = mew + Ai + Bj + ABij + Eijk
Ai: a fixed factor representing the treatments (2 levels)
Bj: a fixed factor representing prior perfromance (2 levels)
ABij: an interaction between Ai and Bj
Yijk: the score of the kth child who received treatment i and is from group j
Eijk: random error
I suspect that this model is inapporpriate, as the Eijk term will represent
between subjects (children) variation, which is not usually included in the
estimate of random error.
2. MLR
Y = Bo + B1*X1 + B2*X2 + B3*X3 + E
X1: prior performance (0 => weak, 1 => strong)
X2: treatment (0 => treament A, 1 => treatment B)
X3: treatment*prior performance
I appreciate that prior performance is probably better considered as a
continuum, rather than a dichotomy.
>> Whether this is the best analysis available is another question entirely.
>>
>> 1. If there are children of different sexes, you may be able to
>> consider a three-way design, although I suspect it would be unbalanced,
>> which (I also suspect!) may induce serious difficulties for you.
You mean that there would not be the same numbers in each group? I can't
see why this should cause problems, but then that's probably due to my
relative ignorance of linear models!
>> 2. Your Performance information you have chosen to dichotomize,
>> although it is presumably (quasi-)continuous to start with. You might
>> find out something useful by treating it as a continuous predictor
>> rather than as a dichotomy: in effect carrying out an analysis of
>> covariance with pre-treatment reading score as the covariate, whether you
>> used an "Analysis of Covariance" program or a "Multiple Regression"
>> program or a "General Linear Model" (GLM) program to do the arithmetic.
Presumably, this could achieved by simply using the pre-treatment score
itself (rather than 0 or 1) for the value of X1 in the suggested MLR model
above?
Thanks Again,
D�nal.
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