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Rating Scale Analysis Michael Glencross Community Agency for Social Enquiry (CASE) UK Stata Users Group Meeting 10 September 2009
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Rationale Attitudes, beliefs, opinions are often measured by means of a set of Likert items A Likert item is a statement which the respondent is asked to evaluate according to some subjective or objective criteria Usually the level of agreement or disagreement is measured
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Rationale The format of a typical 5-point Likert item is: 1.Strongly disagree 2.Disagree 3.Neither agree nor disagree 4.Agree 5.Strongly agree
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Likert Item StatementStrongly DisagreeDisagreeUndecidedAgreeStrongly Agree Police officials at this station are helpful 12345 Rate your level of agreement with the following statement:
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Rationale It is desirable to have a measure of the amount of agreement or disagreement in the sample This is preferable to making an arbitrary decision
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Example 1 Respondents: Disagree/Undecided/Agree? (1=SD; 2=D; 3=U; 4=A; 5=SA)
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Example 2 Respondents: Disagree/Undecided/Agree? (1=SD; 2=D; 3=U; 4=A; 5=SA)
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Example 3 Respondents: Disagree/Undecided/Agree? (1=SD; 2=D; 3=U; 4=A; 5=SA)
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Cooper (1978) N respondents, r response categories, S total score Sampling distribution of z is approx standard normal (N large)
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Whitney (1978) N respondents, r response categories, S total score Sampling distribution of t is approx t N-1 (N small)
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Hsu (1979) Calculates the variance ( ) of the N ratings in the sample This is compared with the variance ( ) of the null distribution of ratings The ratio has a distribution that is approximately For approx normal dist of population ratings,
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Hsu significantly large → heterogeneity of ratings, i.e., disagreement
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Hsu significantly small → homogeneity of ratings, i.e., agreement
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Likert.do If N > 200, calculates Cooper z and displays appropriate message: Result is significant, p<0.01, i.e., there is strong evidence that the respondents agree with the statement Result is significant, p<0.05, i.e., there is evidence that the respondents disagree with the statement Result is not significant, i.e., there is evidence that respondents are undecided about the statement
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Likert.do If N <= 200, calculates Whitney t and displays appropriate message Result is significant, p<0.01, i.e., there is strong evidence that the respondents disagree with the statement Result is significant, p<0.05, i.e., there is evidence that the respondents agree with the statement Result is not significant, i.e., there is evidence that respondents are undecided about the statement
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Likert.do If z or t are not significant, calculates Hsu and displays appropriate message: The lack of significance is associated with significant (p<0.01) heterogeneity (disagreement) of population ratings The lack of significance is associated with significant (p<0.05) homogeneity (agreement) of population ratings The lack of significance is not associated with any significant heterogeneity (disagreement) or homogeneity (agreement) of population ratings
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Example 1: Analysis N=627 N > 200 so use Cooper z Mean_c = 2.8070175 Cooper z = -3.416934 Result is significant, p<0.01, i.e., there is strong evidence that respondents disagree with the statement
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Example 2: Analysis N=468 N > 200 so use Cooper z Mean_c = 3.1346154 Cooper z = 2.0592194 Result is significant, p<0.05, i.e., there is evidence that the respondents agree with the statement
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Example 3: Analysis N=542 N > 200 so use Cooper z Mean_c = 3.0369004 Cooper z =.60745674 Result is not significant, i.e., there is evidence that respondents are undecided about the statement The lack of significance in Cooper z is not associated with any significant heterogeneity (disagreement) or homogeneity (agreement) of population ratings
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Stata code (1) capture program drop likert *! likert v1.1 MJ Glencross 13 August 2009 program define likert, rclass version 9.2 syntax varlist (max=1 numeric) quietly summarize `varlist' gen N=r(N) gen S=r(sum)
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Stata code (2) if N>200 { display "N > 200 so use Cooper z" display " Mean_c = " r(mean) gen z=(r(sum)-3*N)/sqrt(2*r(N)) display "Cooper z = " z if z>2.58 { display "Result is significant, p<0.01" display "i.e., there is strong evidence that the respondents agree with the statement" } else if z>1.96 & z<2.58 {...
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Stata code (3)... else{ gen chisq01=invchi2tail((r(N)-1),0.01) gen critvar01=(0.764*chisq01)/(r(N)-1) gen chisq05=invchi2tail((r(N)-1),0.05) gen critvar05=(0.764*chisq05)/(r(N)-1)...
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Stata code (4)... if abs(z)<1.96 & critvar01<0.764 { display "The lack of significance in Cooper z is associated with significant (p<0.01) heterogeneity (polarisation/disagreement) of population ratings" } else if abs(z) 0.764 & critvar05<0.764 {
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Stata code (5) else { display "N <= 200 so use Whitney t" display " Mean_t = " r(mean) gen isq= `varlist'*`varlist' quietly summarize isq gen t=(S-3*N)/sqrt((N*r(sum)-S^2)/(N-1)) display "Whitney t = " t
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Stata code (6) gen T=ttail((r(N)-1),t) if t>0 & T<0.01{ display "Result is significant,p<0.01" display "i.e., there is strong evidence that the respondents agree with the statement" } else if t>0 & T 0.01 {...
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Stata code (7) if T>0.05 & critvar01<0.764 { display "Lack of significance in Whitney t is associated with significant (p<0.01) heterogeneity (polarisation/disagreement) of population ratings" }...... } end
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Other issues Assumptions about a Likert item –Interval level data? Use parametric analysis –Ordinal (ordered categorical) data? Use non- parametric analysis Likert scale is a summation of Likert items –Unidimensional scale is implied. How do you know? Principal component analysis? Correspondence analysis? Assumptions about Cooper z, Whitney t and Hsu chi sq
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Problems of Likert Scales Response set –tendency to give identical responses, regardless of item content Response style –tendency to favour a particular subset of responses (SA or D) Agreement bias –tendency to agree with statements regardless of content
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Problems of Likert Scales Social desirability bias –tendency to provide responses to please interviewer Assumed ordinality –assumption that SA > A > U > D > SD Meaning of middle category –“Undecided” might be a genuine neutral or just a ‘safe’ option
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Further Research Develop tests (z and t) for difference between two Likert items Develop test for differences between three or more items (ANOVA, Kruskal-Wallis) Rating scales and Item Response Theory models (1-, 2- and 3-parameter models)
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Further Research Use Likert scale data as a basis for obtaining interval level estimates on a continuum by applying the polytomous Rasch model Model allows testing of hypothesis that statements represent increasing levels of attitude Not all Likert scaled items can be used
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References Cooper, M. (1978) An exact probability test for use with Likert-type scales. Educational and Psychological Measurement, 36, 647-655. Hsu, L. (1979) Agreement or disagreement of a set of Likert-type ratings. Educational and Psychological Measurement, 39, 291-295. Whitney, D. R. (1978) An alternative test for use with Likert-type scales. Educational and Psychological Measurement, 38, 15-18.
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