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Fatos Xhafa VMT Project

Data Analysis of Coded Chats Study of correlation and regression between different dimension variables Progress Report , VMT Meeting, Jan. 19 th 2005. Fatos Xhafa VMT Project. Outline. The variables under study Test for Normal distribution of variables

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Fatos Xhafa VMT Project

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  1. Data Analysis of Coded ChatsStudy of correlation and regression between different dimension variablesProgress Report, VMT Meeting, Jan. 19th 2005 Fatos Xhafa VMT Project

  2. Outline • The variables under study • Test for Normal distribution of variables • Correlation between different variables • Regression between different variables • Discussion • From statistical perspective • From interaction based / CA perspective

  3. The variables under study • Social Reference • Pbm Solving • Math Move • Still at the first level of analysis • The same sample of six powwows

  4. Test for Normal distributions (I) • In correlation and regression variables under study are assumed to approximate a Normal distribution • We tested the normality distribution of the dimension variables: • Social reference • Problem Solving • Math Move

  5. Test for Normal distributions (II) • Social reference dimension variable: • Not a good approximation to Normal distribution • Could be indicating outlier/s

  6. Test for Normal distributions (III) • Social reference dimension variable: • Pow18 shows to be an outlier • After removing it from the sample a “perfect” approximation to Normal distribution is obtained

  7. Test for Normal distributions (IV) • The Pbm Solving and Math Move show good approximations to Normal distribution • Correlation and regression between: • Social reference and Pbm Solving • Social Reference and Math Move can be studied (pow18 excluded) • Correlation and regression between: • Pbm Solving and Math Move can be studied for the whole sample

  8. Correlations Correlations ** Correlation is significant at the 0.01 level (2-tailed). * Correlation is significant at the 0.05 level (2-tailed).

  9. Regression: Social reference vs. Pbm Solving • The two variables are strongly and negatively correlated (-.970) • What type of correlation? How are they correlated?

  10. Regression: Social reference vs. Pbm Solving

  11. Analytically… Model Summary a Predictors: (Constant), Percentage Social reference postings ANOVA(b) a Predictors: (Constant), Percentage Social reference postings b Dependent Variable: Percentage Pbm Solving postings

  12. Analytically… Coefficients(a) a Dependent Variable: Percentage Pbm Solving postings

  13. Regression: Social reference vs. Math Move • The two variables are strongly and negatively correlated (-.942) • What type of correlation? How are they correlated?

  14. Regression: Social reference vs. Math Move

  15. Analytically… Model Summary a Predictors: (Constant), Percentage Social reference postings ANOVA(b) a Predictors: (Constant), Percentage Social reference postings b Dependent Variable: Percentage Math Move postings

  16. Analytically… Coefficients(a) a Dependent Variable: Percentage Math Move postings

  17. Regression: Pbm Solving vs. Math Move • The two variables are strongly and positively correlated (.967) • What type of correlation? How are they correlated?

  18. Regression: Pbm Solving vs. Math Move

  19. Regression: Math Move vs. Pbm Solving

  20. Discussion: correlations (I) • The Social reference is strongly and negatively correlated to Pbm Solving (-.970) and Math Move (-.942) • The degree of the correlation may vary by enlarging the sample size • The strong correlation indicates that such a tendency is expected: • by enlarging the sample size (the sample was ‘randomly’ chosen) • even if coders might have influenced the strong correlation • Pow18 shows to be an outlier and requires a careful examination

  21. Discussion: correlations (II) • Question1: Why the “production” of Social reference influences negatively the “production” of Pbm Solving and Math Move? • A first interpretation • The math pbm solving activity takes place during a fixed amount of time (roughly an hour). • The more effort in “production” of Social Reference, less “production” of Math • Question2: Does this have anything to do with “exploratory” vs. “expository” mode? • e.g. pow2-1 vs. pow2-2 • we see that there is a considerable “distance” between the two (cf. regression)

  22. Discussion: correlations (III) • Study at the second level (subcategories) • Two codes from Social Ref. dimension seem particularly interesting: • References to individual actions vs. group actions seem to be a key point! • Code: Individual reference = Any utterance with a reference to the self or another member. This refers to the collaboration in a broader sense (an activity that has been done or will be done by the self or another group member) • Code: Group reference = Any utterance with a reference to the group. This refers to the collaboration in a broader sense (an activity that has been done or is assumed to be done or will be done by the group) • Let’s look atpow2-1 vs. pow2-2

  23. Individual vs. group references in Pbm Solving I thought of factoring (n + 2)^2 and n(n + 5)  Pbm Solving (Tactic) & Individual Ref. we could find a range  Pbm Solving (Tactic) & Group Ref. POWWOW2-1 POWWOW2-2

  24. This leads to… • Hypothesis: • in “expository” powwows there is more Individual ref. than Group Ref. and, • in “exploratory” powwows there is more Group Ref. than Individual ref. that we will study from • Statistical approach (second level of analysis) • distribution of freqs of individual vs. group refs • distribution of freqs of other subcategories • Thread analysis • computing and visualizing individual-like threads and group-like threads and combinations of them • CA approach

  25. Discussion: from CA perspective • How does the “social activity” unfolds sequentially during the pbm solving? • And, specifically, how does the individual vs. group reference unfolds?

  26. Discussion: from CA perspective (I) Powwow2-1

  27. Discussion: from CA perspective (II) Powwow2-2

  28. Discussion: from CA perspective (III) Powwow2-1

  29. Discussion: from CA perspective (IV) Powwow2-1

  30. Discussion: regression • Significant linear regressions between: • Social reference and Pbm Solving • Social reference and Math Move • Pbm Solving and Math Move • Coefficients in each equation show the estimation for each case.

  31. Annex

  32. LLR Smoother (for the whole sample) A smoother is a trend line that shows how the two variables (X and Y) are related to one another. It is not a statistical test !!! of the relationship of X and Y, although in most cases it is possible to infer the practical significance of the relationship.

  33. Correlation Pbm Solving vs. Math Move (without removing pow18) Correlations ** Correlation is significant at the 0.01 level (2-tailed).

  34. Composition of Pbm Solving in terms of Social Reference Social Ref. 6 Collaboration group 5 Collaboration individual Identify self 4 Resource 3 Count 2 1 0 Check Perform Restate Strategy Orientation Result Reflect Tactic Individual vs. group action references in Social Activity (count; for percents look at slide 23) I thought of factoring (n + 2)^2 and n(n + 5)  Pbm Solving (Tactic) & Individual Ref. we could find a range  Pbm Solving (Tactic) & Group Ref. POWWOW2-1 POWWOW2-2

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