Re: when is data considered "continuous" for parametric testing?

On 11 Sep 2006 18:33:29 -0700, jeffrey.ellenbogen@xxxxxxxxx wrote:

Hi,
I'm new to statistics, so forgive the basic question:
What does it mean to be "continuous"? I mean, I have some data -- 2
groups of approx. 20 people -- each where any individual person's mean
score (outcome measure) is one of 4 levels: 0, .25, .5 and 1. Can I do
a t-test comparing these two groups, or is that not continous data. I
mean, I know that if it were binary (0 or 1) I would do a chi square,

For a 2x2 table, the contingency test is what people usually
want to see. But if you try out a few examples, you will see that
the t-test works almost the same.

but when is data considered "continuous"? 5 levels, 100, 10000? The
more I think about it, the more I think that, theoretically, no data is
truly continous. But for practical purposes, what is the lower limit

For people who are developing rating scales, 4 or 5 interval points
is usually considered enough to preserve almost all of the
available information. That is a "practical" purpose, but it is
not directly related to ANOVA.

that satisfies the assumptions necessary for parametric testing (e.g.
t-test, ANOVA)?

The "rank-transformation" is applied to continuous data and
then the typical ANOVA is performed, for large-sample rank tests.

The typical ANOVA works pretty well for small samples measured
by ranks, too.

One assumption for *non-parametric* testing based on ranks
is that the data are continuous. When there are a lot of ties,
you want to look closely at what the *scoring* effect is,
of taking the rank-transformation. Does ranking improve the apparent
equality of the "intervals"? Are *your* intervals improved by
taking the rank-transformation, using the mean-rank for each score?

When there are a lot of ties (such as, for scale data), the ANOVA
can work better than the textbook correction for ties. (See
Conover's textbook on non-parametric testing.)

Hope this helps.

--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.

Relevant Pages

  • Re: Likert Scale Analysis
    ... > stated that Likert scale data is fine for ANOVA and other ... If your "3-point scale" is not considered interval, ... continuous measures (no ties). ... taking the *ranks* for the sample in hand. ...
    (sci.stat.edu)
  • Re: ANOVA on ordinal data
    ... The short answer to your question is yes you can do a t-test and ANOVA ... The more purist camp will tell you that you CANNOT use ... it’s only permissible to use Interval or Ratio ...
    (sci.stat.math)
  • Re: ANOVA QUESTION - Terminology
    ... I know two groups is t-test and more than two is ANOVA. ... I thought it was abundantly clear from the context of jp's immediately preceding statement that I was talking about the F-ratio from a one-way ANOVA and the t-ratio from an independent groups t-test. ... To me, this sounds like a two-way design, but I am confused because it ...
    (sci.stat.consult)
  • Re: ANOVA QUESTION - Terminology
    ... I know two groups is t-test and more than two is ANOVA. ... It is a two-way design. ... and there are second order interactions to ...
    (sci.stat.consult)
  • Re: ANOVA QUESTION - Terminology
    ... I know two groups is t-test and more than two is ANOVA. ... Most examples of ANOVA are 3 groups of race ... and Test# could serve as two independent variables, ... a repeated-measures analysis with several ...
    (sci.stat.consult)