1. 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

2. January 19 th, 2005. VMT Meeting 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. January 19 th, 2005. VMT Meeting The variables under study Social Reference Pbm Solving Math Move - Still at the first level of analysis - The same sample of six powwows

4. January 19 th, 2005. VMT Meeting 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. January 19 th, 2005. VMT Meeting Test for Normal distributions (II) Social reference dimension variable:  Not a good approximation to Normal distribution  Could be indicating outlier/s

6. January 19 th, 2005. VMT Meeting 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. January 19 th, 2005. VMT Meeting 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. January 19 th, 2005. VMT Meeting Correlations Percentage Social reference postings Percentage Pbm Solving postings Percentage Math Move postings Percentage Social reference postings Pearson Correlation 1-.970(**) -.942(*) Sig. (2-tailed)..006.017 N 555 Percentage Pbm Solving postings Pearson Correlation -.970(**)1.967(**) Sig. (2-tailed).006..007 N 555 Percentage Math Move postings Pearson Correlation -.942(*).967(**) 1 Sig. (2-tailed).017.007. N 555 ** Correlation is significant at the 0.01 level (2-tailed). * Correlation is significant at the 0.05 level (2-tailed).

9. January 19 th, 2005. VMT Meeting Regression: Social reference vs. Pbm Solving The two variables are strongly and negatively correlated (-.970) What type of correlation? How are they correlated?

10. January 19 th, 2005. VMT Meeting Regression: Social reference vs. Pbm Solving

11. January 19 th, 2005. VMT Meeting Analytically… Model Summary ModelR R Square Adjusted R SquareStd. Error of the Estimate 1.970(a).941.9213.17911 a Predictors: (Constant), Percentage Social reference postings ANOVA(b) Model Sum of Squaresdf Mean SquareFSig. 1Regression 480.2081 47.514.006(a) Residual 30.320310.107 Total510.5284 a Predictors: (Constant), Percentage Social reference postings b Dependent Variable: Percentage Pbm Solving postings

12. January 19 th, 2005. VMT Meeting Analytically… Coefficients(a) Model Unstandardized Coefficients Standard ized Coefficie ntstSig. B Std. ErrorBeta 1(Constant) 126.01 4 14.68 3 8.582.003 Percentage Social reference postings -3.356.487-.970-6.893.006 a Dependent Variable: Percentage Pbm Solving postings

13. January 19 th, 2005. VMT Meeting Regression: Social reference vs. Math Move The two variables are strongly and negatively correlated (-.942) What type of correlation? How are they correlated?

14. January 19 th, 2005. VMT Meeting Regression: Social reference vs. Math Move

15. January 19 th, 2005. VMT Meeting Analytically… Model Summary ModelR R Square Adjusted R Square Std. Error of the Estimate 1.942(a).887.8503.27875 a Predictors: (Constant), Percentage Social reference postings ANOVA(b) Model Sum of Squaresdf Mean SquareFSig. 1Regression254.1571 23.642.017(a) Residual32.251310.750 Total286.4084 a Predictors: (Constant), Percentage Social reference postings b Dependent Variable: Percentage Math Move postings

16. January 19 th, 2005. VMT Meeting Analytically… Coefficients(a) Model Unstandardized Coefficients Standardize d CoefficientstSig. B Std. ErrorBeta 1(Constant) 89.50515.143 5.911.010 Percentage Social reference postings -2.441.502-.942 - 4.862.017 a Dependent Variable: Percentage Math Move postings

17. January 19 th, 2005. VMT Meeting Regression: Pbm Solving vs. Math Move The two variables are strongly and positively correlated (.967) What type of correlation? How are they correlated?

18. January 19 th, 2005. VMT Meeting Regression: Pbm Solving vs. Math Move

19. January 19 th, 2005. VMT Meeting Regression: Math Move vs. Pbm Solving

20. January 19 th, 2005. VMT Meeting 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. January 19 th, 2005. VMT Meeting 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. January 19 th, 2005. VMT Meeting 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 at pow2-1 vs. pow2-2

23. January 19 th, 2005. VMT Meeting Individual vs. group references in Pbm Solving POWWOW2-1POWWOW2-2 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.

24. January 19 th, 2005. VMT Meeting 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. January 19 th, 2005. VMT Meeting 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. January 19 th, 2005. VMT Meeting Discussion: from CA perspective (I) Handle Posting Soc. Ref Pbm Solving Math Move AVR it's okay PIN hahaa Ss SUP my internet explorer wouldnt open PIN ena you gotta hurtet! Ci PIN haha jk Ss PIN hurry* AVR so now for the new triangle we have: 194.79 = 1/2bh CgPGeo AVR do you follow me? Cg PIN hey its 124.708 ChNc PIN cuz look AVR http://www.math.com/students/calculators/source/scientific.htm Rs AVR and do the calculation PIN we agree it is 10.392 CgChNc SUP then einstein over here was confusing me Io PIN or no? AVR yes we do CgCh Powwow2-1

27. January 19 th, 2005. VMT Meeting Discussion: from CA perspective (II) Handle Posting Soc. Ref.Pbm Solv.Math Move REA I got 15 R MCP I'm getting 15 also ChNc REA I'll explain Ci AH3 Yep, that's right– I got 15 also CiChNc REA now AH3 For the extra, let REA first i got the area to both triangles CiTGeo REA With the first one with edgelengths of 9 REA I used the 30-60-90 fourmla CiPGeo Powwow2-2

28. January 19 th, 2005. VMT Meeting Discussion: from CA perspective (III) HandlePosting Soc. Ref Pbm Solving Math Move AVR so now we add the two areas CgT SUP just a little PIN its 194.852 RNc AVR exactly Ch AVR or 194.85 as I got it :-) CiRe AVR multiply it by two PNc AVR and you get 389.704 = bh CiPGeo PIN we should get the exact measure ment CgChNc Powwow2-1

29. January 19 th, 2005. VMT Meeting Discussion: from CA perspective (IV) Handle Posting Soc. Ref Pbm Sol Math Move OFF hey... Gr SUP what do we fdomwith the area Ss AVR off spring do SO not rule! OFF lol Ss AVR especially if you are a woman! AVR no jk jk Ss OFF lol Ss OFF im no woman PIN lol Ss AVR well I am SUP hey hey SUP women are great Ss GER why don't the three old timers explain what you have figured out OFF oh AVR women are great... Ss SUP ok AVR but pain-enduring SUP they wont explain it to me Cg AVR okay, let's explain Cg Powwow2-1

30. January 19 th, 2005. VMT Meeting 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. January 19 th, 2005. VMT Meeting Annex

32. January 19 th, 2005. VMT Meeting 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. January 19 th, 2005. VMT Meeting Correlation Pbm Solving vs. Math Move (without removing pow18) Correlations Percenta ge Pbm Solving postings Percenta ge Math Move postings Percentage Pbm Solving postings Pearson Correlation 1.956(**) Sig. (2-tailed)..003 N 66 Percentage Math Move postings Pearson Correlation.956(**) 1 Sig. (2-tailed).003. N 66 ** Correlation is significant at the 0.01 level (2-tailed).

34. January 19 th, 2005. VMT Meeting Individual vs. group action references in Social Activity (count; for percents look at slide 23) POWWOW2-1POWWOW2-2 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. Check Orientation Perform Result Restate Reflect Strategy Tactic 0 1 2 3 4 5 6 Count Social Ref. Collaboration group Collaboration individual Identify self Resource Composition of Pbm Solving in terms of Social Reference