# Re: ANOVA on ordinal data

**From:** Jeff Sauro (*jeff_sauro_at_despammed.com*)

**Date:** 11/23/04

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Date: Tue, 23 Nov 2004 20:21:02 +0000 (UTC)

The short answer to your question is yes you can do a t-test and ANOVA

on ordinal data. The major caveat comes from interpreting your

results. If you find a significant difference, you should only report

that one group mean is higher or lower than another group mean—an

ordinal statement. You get into trouble if you start making interval

statements such as “group one is twice as much as the other group.”

The major difference between ordinal and interval data is that the

latter has equal differences between each number, whereas with ordinal

data, you cannot say much more that the order (x is greater than y).

With interval data you can say (x is twice as likely as y).

You should know however, that there are two camps when it comes to

this issue. The more purist camp will tell you that you CANNOT use

those parametric tests with ordinal data. The other camp (most social

scientists and practitioners) will tell you it's fine.

The purist camp will cite the work of SS Stevens. He’s the guy who

came up with the whole hierarchy of data (Nominal, Ordinal, Interval

and Ratio) in his 1946 work “On the Theory of Scale Measurement”.

According to Stevens, it’s only permissible to use Interval or Ratio

data to use parametric tests (t-test, ANOVA etc). In fact, even

computing the mean and standard deviation aren’t permissible unless

you have at least interval data.

The “practitioner” camp (for lack of better word) argues that such a

rigid structure, although meaningful for classifying data should not

dictate the tests one performs. They say that “the numbers don’t know

where they come from.” One of the best works is “On the Statistical

Treatment of Football Numbers” by F. M. Lord. Lord shows how football

numbers (Nominal Data) can be averaged and manipulated to settle an

argument about whether Freshman have lower numbers than upper

classmen.

For a good discussion of both sides (with a bias toward the

practitioner camp) you should read a publicly available paper:

“Nominal, Ordinal, Interval, and Ratio Typologies are Misleading”

http://www.spss.com/research/wilkinson/Publications/Stevens.pdf

In fact, the vast majority of scales and measurements used in modern

psychology are ordinal scales! With this in mind, I’d proceed to see

what conclusions you would draw with the t-test and ANOVA and just be

careful about equal-interval statements.

Good Luck

Jeff

On 23 Nov 04 12:05:14 -0500 (EST), Kelly wrote:

*>Can you reasonably do t-tests or anovas on ordinal data.
*

Additionally,

*>would this be considered ordinal data: a ratio of two concentrations
*

*>of two reagents and the ratio of this product can only be between 0
*

*>and 1.
*

*>Thanks for any help
*

**Next message:**Bill Tan: "Software effectiveness"**Previous message:**Jeff Sauro: "Re: t-test question posting again"**In reply to:**Kelly: "ANOVA on ordinal data"**Next in thread:**Richard Ulrich: "Re: ANOVA on ordinal data"**Reply:**Richard Ulrich: "Re: ANOVA on ordinal data"**Messages sorted by:**[ date ] [ thread ]