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Rating Scale Analysis

Learn about the importance of Likert scales in measuring attitudes, beliefs, and opinions, with detailed examples and analysis using Stata software.

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Rating Scale Analysis

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  1. Rating Scale Analysis Michael Glencross Community Agency for Social Enquiry (CASE) UK Stata Users Group Meeting 10 September 2009

  2. 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

  3. Rationale • The format of a typical 5-point Likert item is: • Strongly disagree • Disagree • Neither agree nor disagree • Agree • Strongly agree

  4. Likert Item Rate your level of agreement with the following statement:

  5. 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

  6. Example 1Respondents: Disagree/Undecided/Agree?(1=SD; 2=D; 3=U; 4=A; 5=SA)

  7. Example 2Respondents: Disagree/Undecided/Agree? (1=SD; 2=D; 3=U; 4=A; 5=SA)

  8. Example 3Respondents: Disagree/Undecided/Agree? (1=SD; 2=D; 3=U; 4=A; 5=SA)

  9. Cooper (1978) • N respondents, r response categories, S total score • Sampling distribution of z is approx standard normal (N large)

  10. Whitney (1978) • N respondents, r response categories, S total score • Sampling distribution of t is approx tN-1 (N small)

  11. 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,

  12. Hsu • significantly large → heterogeneity of ratings, i.e., disagreement

  13. Hsu • significantly small → homogeneity of ratings, i.e., agreement

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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)

  21. 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 { . . .

  22. 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) . . .

  23. 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)<1.96 & critvar01>0.764 & critvar05<0.764 {

  24. 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

  25. 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<0.05 & T>0.01 {. . .

  26. 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

  27. 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

  28. 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

  29. 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

  30. 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)

  31. 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

  32. 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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