[tips] Re: AW: Likert scale and ANOVA

[Rick Froman]

I believe that Lord’s example doesn’t, in any way, negate the relevance of determining scales of measurement in parametric analysis. It simply attacks the use of simple examples to describe scales of measurement (possibly a straw man). In fact, as soon as the players complained that their numbers were lower, they were not treating the numbers as nominal anymore. They were treating them as ratio. Therefore, means and t-tests could be calculated under that assumption. So Lord’s example doesn’t show that numbers with nominal qualities can be profitably used in a t-test, it just shows that there are some limited conditions under which football jersey numbers could be treated as more than nominal. It is a great caveat against making quick judgments about scales of measurement without knowing how the data is being used but it is not a useful argument against the relevance of scales of measurement to parametric tests. I would be tempted to give a student extra credit if I asked them the scale of measurement of football jersey numbers and they said ratio and gave me Lord’s scenario. It shows a level of complexity in thinking that I believe is commendable. It also does not invalidate the concept of scales of measurement. The numbers may not know or care where they came from (thus the acronym GIGO) but the person who collected the data should know and it should make a difference to them. Say that I code categorical data 1 for yellow, 2 for red, 3 for blue and 4 for orange. Could SPSS calculate a mean of that nominal data? Of course, SPSS doesn’t care where the numbers came from. Would the result make any sense? No, because I do care where the numbers came from and what information they contain (nominal, ordinal, interval or ratio). Those of us in the measurement business are concerned about making the round trip from concept to operationalization and back to concept again. To do that, you have to be aware of the information the numbers contain and don’t contain.   I also have a question for those who believe in the infinite robustness of parametric statistics to the violation of all assumptions. Do you see any need at all for nonparametric statistics?   Rick Dr. Rick Froman Professor of Psychology John Brown University 2000 W. University Siloam Springs, AR  72761 [EMAIL PROTECTED] (479) 524-7295 http://www.jbu.edu/academics/sbs/faculty/rfroman.asp From: Christopher D. Green [mailto:[EMAIL PROTECTED] Sent: Friday, April 28, 2006 9:06 AM To: Teaching in the Psychological Sciences (TIPS) Subject: [tips] Re: AW: Likert scale and ANOVA   Well, this is the answer that one defender of scales fo measurement gave. I don't think that makes it in any way definitive. Lord would respond, I think, that the coherence of the answer depends on the distinction made between "numbers" and "football numbers" and that this simply prejudges the case and makes the argument entirely circular. Regards, -- Christopher D. Green Department of Psychology York University Toronto, ON M3J 1P3 Canada 416-736-5115 ex. 66164 [EMAIL PROTECTED] http://www.yorku.ca/christo ============================= Scheuchenpflug wrote: From: "Stuart McKelvie" <[EMAIL PROTECTED]> Date: Thu, 27 Apr 2006 08:15:56 -0400 I would love to know what Rainer's exam question was!       Stuart (and any others who might be interested): The exam question was obviously in German; here is a rough translation, so please ignore awkward wording   1.      „On the statistical treatment of football numbers” In a classic article about the question of permissible statistical computations on different levels of measurement Lord (1953) presents the argument that for statistical analysis the level of measurement is irrelevant: "The numbers don't know where they come from". In his argument he uses the example of so-called football-numbers, the numbers on jerseys of a football team. (For people unfamiliar with football: The jersey-numbers help to distinguish different players from a distance; they are not associated with player position, time in the team or playing ability etc.) In the example in the article a junior footballteam complains that they received jerseys with smaller numbers than the senior team. To test this complaint a football-statistician computes mean and variance of the jersey numbers of both teams and concludes (on the basis of the t-Test, which you will learn next semester), that indeed the junior team received smaller numbers. Admonished by a professor of Psychology, that these were only football-numbers and he wasn't allowed to compute means, the statistician shrugs and says: "The numbers don't know where they come from"; the only important things would be fulfillment of distributional assumptions and independence in order to compute the t-Test. The professor who had averaged his ratings and questionnaire items in the seclusion of his office only is convinced and walks away and does it now openly. (As written in Lord, F. (1953). On the statistical treatment of football numbers. AmPsych, 8, 750-751.) 1.1. (1) On what kind of scale are football-numbers? 1.2. (2) Is the statistician allowed to compute means/standard deviations in the situation described? 1.3. (3) Do you find the argument convincing/conclusive? Please discuss.     Intended answers were: 1.1. Nominal 1.2. yes, he can do that, because the complaint is about the numbers themselves, not the attribute they represent (identity of player). 1.3. The argumentation is quite misleading; digits found on football jerseys are treated as numbers, not as "football numbers". (Numbers are on an absolute scale; "football numbers" are measurements of identity-or-difference). Since the absolute value of a number found on football jerseys is irrelevant for the purpose it serves (=nominal scale), manipulations of these values in order to compare their size are also meaningless. So if you take the "football number" property seriously, the complaint of the junior team is nonsense to begin with, not to talk about all what follows. If you take the numbers as numbers, they are no "football numbers" any more, so it is no example of "statistical treatment of football numbers".   As I said, this was a difficult one for my students (Intro to Statistics).   Dr. Rainer Scheuchenpflug Lehrstuhl für Psychologie III Röntgenring 11 97070 Würzburg Tel:   0931-312185 Fax:   0931-312616 Mail:  [EMAIL PROTECTED]         --- To make changes to your subscription go to: http://acsun.frostburg.edu/cgi-bin/lyris.pl?enter=tips&text_mode=0&lang=english         --- To make changes to your subscription go to: http://acsun.frostburg.edu/cgi-bin/lyris.pl?enter=tips&text_mode=0&lang=english --- To make changes to your subscription go to: http://acsun.frostburg.edu/cgi-bin/lyris.pl?enter=tips&text_mode=0&lang=english