Data Analysis of Coded Chats Study of correlation and regression between different dimension...

Data Analysis of Coded Chats Study of correlation and

regression between different dimension variables

Progress Report, VMT Meeting, Jan. 19th 2005Fatos Xhafa

VMT Project

January 19th, 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


The variables under study

Social Reference Pbm Solving Math Move

- Still at the first level of analysis - The same sample of six powwows


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


Test for Normal distributions (II)

Social reference dimension variable: Not a good approximation to

Normal distribution Could be indicating outlier/s

0.0 0.2 0.4 0.6 0.8 1.0

Observed Cum Prob

0.0

0.2

0.4

0.6

0.8

1.0

Exp

ecte

d C

um

Pro

b

Normal P-P Plot of Percentage Social reference postings


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

0.0 0.2 0.4 0.6 0.8 1.0

Observed Cum Prob

0.0

0.2

0.4

0.6

0.8

1.0

Exp

ecte

d C

um

Pro

b

Normal P-P Plot of Percentage Social reference postings


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 Movecan be studied for the whole sample


CorrelationsCorrelations

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 5 5 5

Percentage Pbm Solving postings

Pearson Correlation

-.970(**) 1.967(**)

Sig. (2-tailed).006 .

.007

N 5 5 5


Pearson Correlation

-.942(*) .967(**)1

Sig. (2-tailed).017 .007

.

N 5 5 5

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


Regression: Social reference vs. Pbm Solving The two variables are strongly and negatively

correlated (-.970) What type of correlation? How are they

correlated?


Regression: Social reference vs. Pbm Solving

Linear Regression

26.00 28.00 30.00 32.00 34.00


10.00

20.00

30.00

40.00P

erce

nta

ge

Pb

m S

olv

ing

po

stin

gs

pow1

pow2_1

pow2_2

pow9

pow10

Percentage Pbm Solving postings = 126.01 + -3.36 * PercSocRR-Square = 0.94


Analytically…Model Summary

Model RR

SquareAdjusted R

Square Std. Error of the Estimate

1 .970(a) .941 .921 3.17911

a Predictors: (Constant), Percentage Social reference postings

ANOVA(b)

Model Sum of

Squares dfMean

Square F Sig.

1 Regression480.208 1 480.208 47.514

.006(a)

Residual30.320 3 10.107

Total 510.528 4

a Predictors: (Constant), Percentage Social reference postingsb Dependent Variable: Percentage Pbm Solving postings


Analytically…

Coefficients(a)

Model Unstandardized

Coefficients

Standardized

Coefficients t Sig.

BStd. Error Beta

1 (Constant) 126.014

14.683

8.582 .003


-3.356 .487 -.970 -6.893 .006

a Dependent Variable: Percentage Pbm Solving postings


Regression: Social reference vs. Math Move The two variables are strongly and negatively

correlated (-.942) What type of correlation? How are they

correlated?


Regression: Social reference vs. Math Move

Linear Regression

26.00 28.00 30.00 32.00 34.00


5.00

10.00

15.00

20.00

25.00P

erce

nta

ge

Mat

h M

ove

po

stin

gs

pow1

pow2_1

pow2_2

pow9

pow10

Percentage Math Move postings = 89.50 + -2.44 * PercSocRR-Square = 0.89


Analytically…Model Summary

Model RR

SquareAdjusted R

Square

Std. Error of the

Estimate

1 .942(a) .887 .850 3.27875

a Predictors: (Constant), Percentage Social reference postings

ANOVA(b)

Model Sum of

Squares dfMean

Square F Sig.

1 Regression 254.157 1 254.157 23.642 .017(a)

Residual 32.251 3 10.750

Total 286.408 4

a Predictors: (Constant), Percentage Social reference postingsb Dependent Variable: Percentage Math Move postings


Analytically…

Coefficients(a)

Model Unstandardized

Coefficients

Standardized

Coefficients t Sig.

BStd. Error Beta

1 (Constant) 89.505 15.143 5.911 .010


-2.441 .502 -.942-

4.862.017

a Dependent Variable: Percentage Math Move postings


Regression: Pbm Solving vs. Math Move The two variables are strongly and positively

correlated (.967) What type of correlation? How are they

correlated?


Regression: Pbm Solving vs. Math Move

Linear Regression

20.00 30.00 40.00


10.00

15.00

20.00

25.00

Per

cen

tag

e M

ath

Mo

ve p

ost

ing

s

pow1

pow2_1

pow2_2

pow9

pow10

pow18

Percentage Math Move postings = -2.63 + 0.73 * PercPbmSR-Square = 0.91


Regression: Math Move vs. Pbm Solving

Linear Regression

10.00 15.00 20.00 25.00


20.00

30.00

40.00P

erce

nta

ge

Pb

m S

olv

ing

po

stin

gs

pow1

pow2_1

pow2_2

pow9

pow10

pow18

Percentage Pbm Solving postings = 5.50 + 1.26 * PerMathMR-Square = 0.91


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


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)


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


Individual vs. group references in Pbm Solving

Group Ref.Individual Ref.Identify otherRisk-taking

social

Pies show percents

40.00%

20.00%

20.00%

20.00%

Check Orientation Perform

Result Restate Reflect

Strategy Tactic

100.00% 100.00%

100.00%

20.00%

60.00%

20.00%

57.14%

42.86%

100.00% 100.00%

POWWOW2-1 POWWOW2-2

100.00%

Check Orientation Perform

Result Restate Reflect

Strategy Tactic

100.00% 100.00%

83.33%

16.67%

100.00%

25.00%

50.00%

25.00%

100.00%

33.33%

66.67%

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.


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


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?


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 Cg P Geo

AVR do you follow me? Cg

PIN hey its 124.708 Ch Nc

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 Cg Ch Nc

SUP then einstein over here was confusing me Io

PIN or no?

AVR yes we do Cg Ch

Powwow2-1


Discussion: from CA perspective (II)Handle Posting Soc. Ref. Pbm Solv. Math Move

REA I got 15 R

MCP I'm getting 15 also

Ch Nc

REA I'll explain

Ci

AH3 Yep, that's right– I got 15 also

Ci Ch Nc

REA now

AH3 For the extra, let

REA first i got the area to both triangles

Ci T Geo

REA With the first one with edgelengths of 9

REA I used the 30-60-90 fourmla

Ci P Geo

Powwow2-2


Discussion: from CA perspective (III)Handle Posting Soc. Ref

Pbm Solving

Math Move

AVR so now we add the two areas Cg T

SUP just a little

PIN its 194.852 R Nc

AVR exactly Ch

AVR or 194.85 as I got it :-) Ci Re

AVR multiply it by two P Nc

AVR and you get 389.704 = bh Ci P Geo

PIN we should get the exact measure

ment Cg Ch Nc

Powwow2-1


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


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.


Annex


LLR Smoother (for the whole sample)

LLR Smoother

15.00 20.00 25.00 30.00 35.00


20.00

30.00

40.00

Per

cen

tag

e P

bm

So

lvin

g p

ost

ing

s

pow1

pow2_1

pow2_2

pow9

pow10

pow18

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.


Correlation Pbm Solving vs. Math Move (without removing pow18)

Correlations


Percentage Math

Move postings


Pearson Correlation

1.956(**)

Sig. (2-tailed).

.003

N 6 6


Pearson Correlation

.956(**)1

Sig. (2-tailed).003

.

N 6 6

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


Individual vs. group action references in Social Activity (count; for percents look at slide 23)

CheckOrientation

PerformResult

RestateReflect

StrategyTactic

0

1

2

3

4

5

6

7

Co

un

t

Social Ref.

Collaboration group

Collaboration individual

Identify other

Risk-taking

Composition of Pbm Solving in terms of Social Ref.

POWWOW2-1 POWWOW2-2

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.

CheckOrientation

PerformResult

RestateReflect

StrategyTactic

0

1

2

3

4

5

6 Social Ref.

Collaboration group

Collaboration individualIdentify self

Resource

Composition of Pbm Solving in terms of Social Reference

Data Analysis of Coded Chats Study of correlation and regression between different dimension...

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