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Thank you very much for your help and advice.

Best regards,


>I mostly disagree with David here. In particular, his proposal to
>collapse the Likert scales just throws away information in an
>arbitrary manner.

>I don't think his advice is even consistent. If it's OK to treat means
>of Bernoulli distributions as valid arguments for a t test, why is not
>OK to treat means of Likert scales as if they were?

>It's true that the reference case for a t test is two paired normal
>distributions, and Likert scales can not be normal if only because
>they are _not_ continuous, but there is always a judgment call on
>whether summaries of the data will in practice work similarly.

>A fair question is what exactly kind of advice is Leonor seeking? The
>question presumably isn't really whether it is possible -- clearly it
>is possible -- but perhaps somewhere between "Is it correct?" and "Is
>it a good idea?"

>Leonor's question appears to have the flavour of "I gather that this
>is wrong. but is there a sense in which this is allowed?" The long
>answer has to be that Leonor should tell us much more about the data
>and the problem in hand if a good answer is to be given. If means make
>sense as summary statistics, then comparing means with a t test is
>likely to work well, but watch out.

>David is clearly right in alluding to a purist literature in which you
>are told as a matter of doctrine that ordinal data shouldn't be
>summarised by means and so mean-based tests are also invalid. When
>acting as academics, the same people work with grade-point averages
>just like anybody else, at least in my experience.

>There is also a pragmatist literature which points out that despite
>all that, the sinful practice usually works well. Compare the t-test
>with e.g. a Mann-Whitney-Wilcoxon test and it's very likely that the
>P-values and z- or t-statistics will point to the same substantive
>conclusion and indicate just about the same quantitative effect. It's
>also likely that doing both tests will be needed because some reviewer
>has been indoctrinated against t-tests here, and especially if anyone
>is working with a rigid threshold (e.g. a 5% significance level).

>Also, the behaviour of t-tests in cases like this can always be
>examined by simulation, so no-one need be limited by textbook dogma
>(or wickedness).


On Fri, Aug 31, 2012 at 12:13 AM, David Radwin <> wrote:
> Leonor,
>No, you can't correctly calculate the mean of an ordinal-level measure
>like the Likert scale you describe, although plenty of people do it
> anyway.
> But you can use -ttest- with these data if you first collapse each
> variable to a dichotomous (dummy) variable, because the mean of a
> dichotomous variable is identical to the proportion where the value is 1.
> As a guess, you might set the highest two values to 1, the lowest two
> values to 0, and the middle value to missing to calculate the proportion
> agreeing or somewhat agreeing.
> David
> --
> David Radwin
> Senior Research Associate
> MPR Associates, Inc.
> 2150 Shattuck Ave., Suite 800
> Berkeley, CA 94704
> Phone:             510-849-4942
> Fax: 510-849-0794
>> -----Original Message-----
>> From: [mailto:owner-
>>] On Behalf Of Leonor Saravia
>> Sent: Thursday, August 30, 2012 3:23 PM
>> To:
>> Subject: st: Mean test in a Likert Scale
>> Hello,
>> I'm working with a survey that presents 26 questions and each of them
>> has as possible answer a 5 point Likert scale from Desagree (1) to
>> Agree (5). This survey was applyed for a treatment and a control
>> group.
>> As far as I know, it is possible to analyze the information given only
>> by the proportions of each answer; for instance, 25% agrees, 50%
>> desagree, or so.
>> I have two questions that maybe one of you have had before:
>> a) Is it possible to calculate the mean score of a sample (treatment
>> or control group) - adding the individual answers - when one is
>> working with a Likert scale?
>> b) If it is possible to calculate a mean score of a sample when using
>> a Likert scale, to compare the answers of the treatment versus the
>> control group, is it well done if I use the 'ttest' command?

>>Thank you in advance.
>>Best regards,
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