On 1 Feb 2001 01:03:40 -0800, [EMAIL PROTECTED] (Will Hopkins) wrote:
> I have an important (for me) question, but first a preamble and hopefully
> some useful info for people using Likert scales.
>
> A week or so ago I initiated a discussion about how non-normal the
> residuals have to be before you stop trusting analyses based on
> normality. Someone quite rightly pointed out that it depends on the sample
> size, because the sampling distribution of almost every statistic derived
> from a variable with almost any distribution is near enough to normal for a
> large enough sample, thanks to the central limit theorem. Therefore you
> get believable confidence limits from t statistics.
>
> But how non-normal, and how big a sample? I have been doing simulations to
> find out. I've limited the simulations to t tests for Likert scales with
> only a few levels, because these crop up often in research, and
> Likert-scale variables with responses stacked up at one end are not what
> you call normally distributed. Yes, I know you can and maybe should
> analyze these with logistic regression, but it's hard work for
[ ... snip, rest ]
Here is an echo of comments I have posted before. You can use t-tests
effectively on outcomes that are dichotomous variables, and you use
the pooled version (Student's t) despite any difference in variances.
That is the test that gives you the proper p-levels.
"Likert scales" are something that I tend to think of as "well
developed" so they would offer no question to t-testing.
But, anyway, items with 3 or 4 or 5 scale points are not prone to
having extreme outliers; and if your actual responses across 5 points
are bi-modal, you might want to rethink your response-meanings.
Generally, I generalize from the dichomous case, to conclude that the
t-test will be robust for items with a few points. Years ago, I read
an article or two that explicitly asserted that conclusion, based on
some Monte Carlo simulations.
Just a few weeks ago, I read another justification for scoring
categories as integers -- the Mantel paper that is the basis for what
Agresti presents in his "Introduction to Categorical Data Analysis." .
That "M^2" test (page 35) makes use of fixed variances for
proportions. M^2 is tested as chi squared, and its computation is
almost identical to t.
So I don't fret about using t on items with Likert-type responses,
even for small N.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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