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Rating Scale Analysis

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Rating Scale Analysis. Michael Glencross. Community Agency for Social Enquiry (CASE) ... Calculates the variance ( ) of the N ratings in the sample ... – PowerPoint PPT presentation

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Title: Rating Scale Analysis


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?
(1SD 2D 3U 4A 5SA)
7
Example 2Respondents Disagree/Undecided/Agree?
(1SD 2D 3U 4A 5SA)
8
Example 3Respondents Disagree/Undecided/Agree?
(1SD 2D 3U 4A 5SA)
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 gt 200, calculates Cooper z and displays
    appropriate message
  • Result is significant, plt0.01, i.e., there is
    strong evidence that the respondents agree with
    the statement
  • Result is significant, plt0.05, 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 lt 200, calculates Whitney t and displays
    appropriate message
  • Result is significant, plt0.01, i.e., there is
    strong evidence that the respondents disagree
    with the statement
  • Result is significant, plt0.05, 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 (plt0.01) heterogeneity (disagreement)
    of population ratings
  • The lack of significance is associated with
    significant (plt0.05) 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
  • N627
  • N gt 200 so use Cooper z
  • Mean_c 2.8070175
  • Cooper z -3.416934
  • Result is significant, plt0.01, i.e., there is
    strong evidence that respondents disagree with
    the statement

18
Example 2 Analysis
  • N468
  • N gt 200 so use Cooper z
  • Mean_c 3.1346154
  • Cooper z 2.0592194
  • Result is significant, plt0.05, i.e., there is
    evidence that the respondents agree with the
    statement

19
Example 3 Analysis
  • N542
  • N gt 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 (max1 numeric)
  • quietly summarize varlist'
  • gen Nr(N)
  • gen Sr(sum)

21
Stata code (2)
  • if Ngt200
  • display "N gt 200 so use Cooper z"
  • display " Mean_c " r(mean)
  • gen z(r(sum)-3N)/sqrt(2r(N))
  • display "Cooper z " z
  • if zgt2.58
  • display "Result is significant, plt0.01"
  • display "i.e., there is strong evidence that
    the respondents agree with the statement"
  • else if zgt1.96 zlt2.58 . . .

22
Stata code (3)
  • . . .
  • else
  • gen chisq01invchi2tail((r(N)-1),0.01)
  • gen critvar01(0.764chisq01)/(r(N)-1)
  • gen chisq05invchi2tail((r(N)-1),0.05)
  • gen critvar05(0.764chisq05)/(r(N)-1)
  • . . .

23
Stata code (4)
  • . . .
  • if abs(z)lt1.96 critvar01lt0.764
  • display "The lack of significance in Cooper z is
    associated with significant (plt0.01)
    heterogeneity (polarisation/disagreement) of
    population ratings"
  • else if abs(z)lt1.96 critvar01gt0.764
    critvar05lt0.764

24
Stata code (5)
  • else
  • display "N lt 200 so use Whitney t"
  • display " Mean_t " r(mean)
  • gen isq varlist'varlist'
  • quietly summarize isq
  • gen t(S-3N)/sqrt((Nr(sum)-S2)/(N-1))
  • display "Whitney t " t

25
Stata code (6)
  • gen Tttail((r(N)-1),t)
  • if tgt0 Tlt0.01
  • display "Result is significant,plt0.01"
  • display "i.e., there is strong evidence that
    the respondents agree with the statement"
  • else if tgt0 Tlt0.05 Tgt0.01 . . .

26
Stata code (7)
  • if Tgt0.05 critvar01lt0.764
  • display "Lack of significance in Whitney t is
    associated with significant (plt0.01)
    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 gt A gt U gt D gt 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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