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From |
Nick Cox <njcoxstata@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: RE: Mean test in a Likert Scale |

Date |
Fri, 31 Aug 2012 08:46:01 +0100 |

Thanks for the extra detail, but I don't think it lets me add much to my own advice, except that with a sample size of 20000 very small differences are likely to seem significant by any particular significance test. Nick On Fri, Aug 31, 2012 at 5:08 AM, Leonor Saravia <lmisaravia@gmail.com> wrote: > Dear Nick and David, > > I really appreciate your reply, thank you. > > I read carefully your answers to my questions and as Nick says, my > first question pointed to the fact that there could be the sence in > which computing the mean score of a Likert scale is allowed. I have > seen practical studies were the mean of this kind of scales are > calculated and interpreted. However, there is also literature that > indicates that, as the Likert scales are an ordinal-level measure, you > should not calculate the mean of it. So, I am confused because I do > not understand whether calculating and interpreting the mean of a > Likert scale is correct or not. > > The data I have is desagregated by individual (20000 observations) of > a treatment and a control group, and has the answer for each of the 26 > questions, a number between 1 and 5, which are the values of a 5 point > Likert scale from Disagree (1) to Agree (5). > > For instance, the first question (Q1) is: "Chilean people find > entrepreneurial activities socialy valuable" and the possible answers > are: > > 1 - Strongly disagree > 2 - Disagree > 3 - Nor agree nor disagree > 4 - Agree > 5 - Strongly agree > > So, the database has this structure: > > Observation Group Q1 Q2 ..... Q25 Q26 > 1 Treatment 1 5 ...... 3 1 > 2 Control 3 1 ....... 2 5 > . > . > 19999 Control 5 2 ........ 4 3 > 20000 Treatment 3 2 ......... 5 4 > > > From this, one could calculate the mean of Q1 for the treatment and > control group, but I do not know if the number obtained can be > interpreted and even more, if one can test mean differences between > both groups. > > Thank you very much for your help and advice. > > Best regards, > > Leonor > >>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). > >>Nick > > On Fri, Aug 31, 2012 at 12:13 AM, David Radwin <dradwin@mprinc.com> 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 >> >> www.mprinc.com >> >> >>> -----Original Message----- >>> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner- >>> statalist@hsphsun2.harvard.edu] On Behalf Of Leonor Saravia >>> Sent: Thursday, August 30, 2012 3:23 PM >>> To: statalist@hsphsun2.harvard.edu >>> 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? > * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**RE: st: RE: Mean test in a Likert Scale***From:*"David Radwin" <dradwin@mprinc.com>

**Re: st: RE: Mean test in a Likert Scale***From:*Nick Cox <njcoxstata@gmail.com>

**References**:**Re: st: RE: Mean test in a Likert Scale***From:*Leonor Saravia <lmisaravia@gmail.com>

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