On Mon, 19 Jun 2000, Donal wrote:
> I'm currently analysing data resulting from a study of children's
> reading ability.
I shall resist the temptation to quibble over your inability to observe
reading ability (as distinct from some indeterminate lower bound on that
ability) ...
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.
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.
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.
3. In addition to sex, there may be other lurking variables in your data
that could be used as predictors. Whether it is sensible to consider
including them in a hypothetical model depends partly on how many
children you have all together, and partly on the distribution of any
such candidate variable among _these_ children.
> The study involves two treatments and each child's reading ability was
> measured before and after the application of one of the treatments.
> Thus, each child received one or the other (but not both) of two
> possible treatments. The children are divided into two groups:
Well, that's not quite true. You chose to categorize them into two
groups, but they could equally well have been divided into three, or
four, or six (depending on the number of children available and one's
degree of interest in fine-tuning the "Weak/Strong" dimension).
And if you have both boys and girls, you have two sexes as well, and
it would not be surprising if they differed in their responses to the
two treatments. And how about the ages of the children?
> Weak readers: those whose pre-treatment reading score was less than
> the mean pre-treatment reading score
> Strong readers: those whose pre-treatment reading score was greater
> than the mean pre-treatment reading score
It is more usual, in situations like this, to divide at the median
rather than the mean. (For one thing, you're more likely to end up
with groups of at least approximately equal size.) Did you have a
reason for using the mean? Where did you put persons whose score
was equal to the mean?
> Anyhow, I would like to test (for each treatment) whether or not the
> change in reading score (Post-treatment score - Pre-treatment score)
> is the same for weak readers and strong readers. I have attempted to
> test this by:
> 1. Creating a new variable, "Change"
> Change = Post-treatment score - Pre-treatment score
>
> 2. Using a two-sample t-test to determine whether or not the mean
> value of "Change" measured over the weak readers is significantly
> different from the mean value of "Change" measured over the strong
> readers.
> Similarly, I'd like to test whether or not the change in the reading
> score is the same for each treatment. I have attempted to test this by:
>
> 1. Creating a new variable, "Change" [as above]
>
> 2. Using a two-sample t-test to determine whether or not the mean value
> of "Change" measured over treatment A is significantly different from
> the mean value of "Change" measured over treatment B
>
> However, I am not certain that this is the best way to test my
> hypothesis, if anyone can suggest a better way, I'd be very grateful
> for their assistance.
Do these in fact represent your hypotheses, or were they just the
closest you thought you could get to what you really wanted to find out?
E.g., are you REALLY only interested in the change scores, or are you
(perhaps ALSO) interested in the level of proficiency attained, as
measured (however imperfectly) by your post-test reading scores?
-- DFB.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
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