This is a brief (exploratory) discussion of how to run statistical analysis of responses to Likert items. The data used is from a study I ran on users of the PARC Wikipedia dashboard "WikiDashboard" looking at how the tool changed perceptions of credibility.

1. Analyzing Responses to Likert Items An Exploration of Data from a Credibility Study Involving WikiDashboard (http://wikidashboard.parc.com) by Sanjay Kairam

2. WikiDashboard Study The System The Study The Data

3. WikiDashboard “Social Dynamic Analysis Tool” for Wikipedia Michael Scott (The Office): “Wikipedia is the best thing ever. Anyone in the world can write anything they want about any subject, so you know you are getting the best possible information” What happens when we see who is doing the editing?

4. WikiDashboard (Close-Up)

5. WikiDashboard Study Study conducted on Amazon Mechanical Turk N = 288 subjects Subjects paid $0.08 / HIT “Please read and evaluate this Wikipedia Article.”

6. Experiment Conditions Participants each placed in 1 of 3 conditions (each N = 96): Wiki Only (WO) Wiki + History (WH) WikiDashboard (WD)

7. Articles Used Each subject read 1 (of 8 possible) Wikipedia articles. Article “Quality”: “Low-Quality” articles were those flagged as “B-Class” or “C-Class” by the Wikipedia community. “High-Quality” articles were those which had at one time been “Featured Articles”. Article “Controversiality”: “Controversial” articles were those on the extensive “List of Controversial Articles”.

8. Survey Self-Reported Expertise “How familiar are you with the topic discussed on this Wikipedia page?” Manipulation/Quality Checks “In 5-20 words, please describe what this Wikipedia page is about.” “Please describe one fact from the article that you found interesting.” (WO) “Please name at least one user (by username or IP address) who has made multiple edits to this page. (WH, WD)

9. Credibility Assessment Assessing agreement with these statements: “I believe that the information on this page is accurate.” (Accuracy) “I believe that the information on this page is objective.” (Objectivity) “I believe that the information on this page is current and up-to-date.” (Currency) “I believe that this page fully covers the relevant information on the topic.” (Coverage) “I trust the information on this page.” (Trust)

10. Likert Item Responses Participants answered using a 5-point scale: -2: “Strongly Disagree” -1: “Somewhat Disagree” 0: “Neither Agree nor Disagree” +1: “Somewhat Agree” +2: “Strongly Agree” Now, what do we do with this data?

11. Analyzing Likert Item Responses Very often, we see papers reporting Likert responses using means: What is the average of 1 “Somewhat Agree” and 3 “Somewhat Disagree”s? Hint: It’s not “Somewhat Disagree and a Half” In this case, what does a “mean” mean? In most cases, an ANOVA would definitely not work as well, though people still try!

12. Options for Analysis Non-Parametric Tests for Ordinal Data Conversion to an Interval Scale Aggregating Items

13. Mann-Whitney U Test Also called “Mann-Whitney-Wolcoxon”, “Wilcoxon Rank-Sum”, or “Wilcoxon-Mann-Whitney” test. Non-parametric test for assessing whether two independent samples of observations have equally large values. http://en.wikipedia.org/wiki/Mann-Whitney_U

14. Mann-Whitney U Test Assumptions: All observations from both groups are independent of each other. The responses are ordinal or continuous measurements. Null hypothesis includes symmetry between two populations considered Under alternative hypothesis, probability of an observation from pop. X exceeding an observation from pop. Y is not equal to 0.5 http://en.wikipedia.org/wiki/Mann-Whitney_U

15. Kruskal-Wallis ANOVA What if we want to test more than 2 groups? (as we do, given our 3 experimental conditions) Kruskal-Wallis ANOVA is an extension of Mann-Whitney U to 3 or more groups. Also non-parametric, though it does assume that both distributions have a similar underlying shape. http://en.wikipedia.org/wiki/Kruskal-Wallis_one-way_analysis_of_variance

16. Analysis Using Non-Parametric Tests Do participants actually notice differences in article quality? Mann-Whitney: Significant effects of article quality for ratings of Accuracy (p< 0.001), Coverage (p< 0.01), Currency (p< 0.001), and Trust (p< 0.001), with marginally significant effect on Objectivity (p< 0.096). Kruskal-Wallis: Significant effect on ratings of Accuracy (p< 0.001), Coverage (p< 0.012), Currency (p< 0.001), and Trust (p< 0.001), with no significant effect on Objectivity.

17. Sample Boxplots: Ratings by Article Quality Accuracy Coverage

18. Analysis Using Non-Parametric Tests Do participants notice differences in how “controversial” an article is? Mann-Whitney: Significant effect on ratings of Coverage (p < 0.039), Currency (p < 0.039), Objectivity (p < 0.021), and Trust (p < 0.021), with no effect on ratings of Accuracy. Kruskal-Wallis: Significant effect on ratings of Objectivity (p < 0.042), and marginally significant effect for Coverage (p < 0.077) and Currency (p < 0.083), but no significant effect on Accuracy or Trust.

19. Analysis Using Non-Parametric Tests What we really want to know, however, is whether using WikiDashboard or Wiki + History makes participants more sensitive to article quality or controversiality than participants using Wikipedia on its own. Both tests only allow us to compare populations separated on the basis of a single variable, however, so we can’t explore these interaction effects.

20. Conversion to Interval Scale If there were a way to map our Likert item responses on to an interval scale, we could use more familiar/powerful statistical tests. If we found that the mapped data was normal, for instance, we could use our usual parametric tests such as MANOVA, which would help us find these interaction effects.

21. Conversion to Interval Scale E.J. Snell (1964) describes a procedure for mapping ordered data, like Likert responses, to an assumed underlying continuous scale of measurement. At the end, he emphasizes that “the usefulness of the proposed method depends upon the assumption that the underlying scale of measurement can be transformed to produce a normal distribution.” Snell, E.J. A Scaling Procedure for Ordered Categorical Data, Biometrics 20(3), pp. 592-607 (1964). http://www.jstor.org/stable/2528498

22. Utilizing the Snell Conversion The conversion procedure was used to transform the data – essentially mapped each response (ranging from -2 to +2) to a new point which ranged from roughly -1.00 to +4.05 Essentially, it looks as if only the distances between the values has changed.

23. Histogram: Original Data

24. Histogram: Snell-Converted Data

25. Aggregating Likert Items If we consider the various Likert items to be different measurements of a certain underlying trait (Credibility), then can we sum them and run parametric statistical tests? Haven’t tried this yet – is this a valid approach?

26. Analyzing Responses to Likert Items by Sanjay Kairam Email: sanjay.kairam@gmail.com Twitter: @skairam