SOC200 - The Elaboration Model (Chapter 15 + 16)

Question 1

The Elaboration Model

Answer 1

Elaboration Paradigm, The Interpretation Method, the Lazarsfeld Method; the Columbia School Method
logical approach used for understanding relationship betw two variables

Question 2

The Elaboration Model

Answer 2

observing impact on other variables when third variable (a “control/test” variable) is introduced.

Question 3

The Central Logic of the Elaboration Model

Answer 3

observed relationship betw 2 variables + hunch that one variable is causing other
Think of 3rd variable then divide sample into groups based on the categories in that third variable

Question 4

The Central Logic of the Elaboration Model

Answer 4

students and non-students

for each subgroup, recompute relationship betw 2 original variables

Question 5

The Central Logic of the Elaboration Model

Answer 5

Partial Table – partialing out relationship betw 2 variables via 3rd variable
compare relationship exhibited in partial (3-way) table with relationship in the zero-order relationship (2-way table)

Question 6

The Central Logic of the Elaboration Model

Answer 6

Partial Relationships: full-time/part time + student status
Compare relationship with relationship in zero order
Regardless of student status – larger % of part time still female

Question 7

The Central Logic of the Elaboration Model

Answer 7

Zero-order relationship: without added 3rd variable
student status – lot of students work part time
Zero order relationship for students are reduced
Student status is important as well
Relationship betw male + female for not a student about same as zero order

Question 8

The Central Logic of the Elaboration Model

Answer 8

However, student status is also important: Compared to the non-student group, % of PT workers is much higher in the student group, regardless of sex
diff betw sexes smaller in PT category (was 14% now 9%)

Question 9

An Elaboration Analysis is Guided by the Type of Test Variable: Intervening Test Variable (not prior in time to the IV and DV)

Answer 9

test variable affects way iv affects dv

Student Status

Question 10

An Elaboration Analysis is Guided by the Type of Test Variable: Antecedent Test Variable (prior in time to the IV and DV)

Answer 10

iv + dv not actually related appear to show relationship, affected by a test variable directly affecting both
Sex affects both IV + DV

Question 11

Types of relationships shown when partial table is compared against original table

Answer 11

Summary of potential outsomes in elaboration analysis
Antecedent:
Same relationship: replication
Smaller relationship: explanation

Question 12

Replication

Answer 12

Relationship betw sex + PT status substantially same for students and non-students.
zero-order relationship: 11.4% of M + 25.4% of F PT – diff of about 14%
Numbers might change, but diff doesn’t change
Replication because numbers don’t change

Question 13

Explanation

Answer 13

original relationship shrinks/made nonexistent in both partial relationships after introducing test variable
test variable logically precedes IV + DV (antecedent variable)
assumes relationship betw student & PT status is preceded by sex
Because relationship betw student status + part time status shrunk, we would call this an explanation

Question 14

Interpretation

Answer 14

Like explanation except test variable does not precede IV + DV
Relationship shrunk from zero-order relationship

Question 15

Interpretation

Answer 15

relationship betw sex + PT status genuine one, but substantially shrinks because student status (intervening variable) helps interpret mechanism through which sex “causes” PT status

Question 16

Specification

Answer 16

When partial relationships differ significantly from each other (one same as/stronger than original table + other is less than original table/reduced to zero

Question 17

Specification

Answer 17

Among non student no diff from original table
Among students shrunk to almost no diff
Non student doesn’t explain anything
Student status only explains relationship betw iv + dv

Question 18

Suppression

Answer 18

3rd variable hiding relationship betw bivariate relationship
No diff betw M + F working Δ = 1.4%
BUT expected difference appears after controlling for student status Δ = 31% for each partial

Question 19

Suppression

Answer 19

3rd variable embedded in 2 variables
shows up as no relationship betw iv + dv
3rd variable possibly suppressing depends on the theory

Question 20

Distortion (an Extreme Version of Suppression)

Answer 20

3rd variable causes reversal in direction of zero order relationship
Males show a higher incidence of working PT

Question 21

Distortion (an Extreme Version of Suppression)

Answer 21

expected diff (favoring females) appears after controlling for student status
Δ = 31% for each partial favouring females in PT
rare
have to think theoretically
should think of what variables to control for beforehand

Question 22

Social Statistics

Answer 22

Help Researchers Describe characteristics of interest in pop/sample
Help Researchers Identify/Explain relationships betw characteristics of interest

Question 23

Social Statistics

Answer 23

Help Researchers Infer relationships betw characteristics in a pop/sample that may not be directly observable
Summary value of a sample

Question 24

How do researchers do this?

Answer 24

through measures of association: analyses that enable researchers to summarize association betw variables

Question 25

measures of association

Answer 25

For nominal (categorical) variables: Is sex associated with PT/FT status? Is left-handedness associated with occupation? For ordinal (categorically ranked) variables: Is social class related to smoking? Is employer size associated with higher wages?

Question 26

Measures of Association using the Proportionate Reduction of Error (PRE) Model

Answer 26

Not all measures of association are PRE measures | PRE measures are useful for introducing measures of association because they have standard interpretation

Question 27

Measures of Association using the Proportionate Reduction of Error (PRE) Model

Answer 27

Principle - all PRE measures based on comparing errors made in predicting DV while ignoring independent variable vs errors made when making predictions that use info about IV Reduce error by simply choosing everyone here worked full time: Still have 18 errors

Question 28

PRE measure with nominal variables

Answer 28

measure of lambda (λ) which people in a sample of 100 worked full-time 82 of 100 worked full- time, fewer errors by always guessing full-time: would still have 18 errors out of 100 predictions (100 – 82 = 18)

Question 29

PRE measure with nominal variables

Answer 29

``` told each person’s gender before, even fewer errors by guessing FT for every man + PT for every woman 8 errors (3 for the PT men + 5 for FT women ```

Question 30

PRE measure with nominal variables

Answer 30

knowing sex, 10 fewer errors than without this info lambda (λ) = .55 (10/18) error in predicting FT status reduced by 55%

Question 31

PRE measure with ordinal variables

Answer 31

Gamma (γ) similar rules but guess: For any given pair of cases (any 2 people), does ordinal ranking on 1 variable correspond to ordinal ranking on another? compare every pair of cases opposite pair: contradictory to theory excluded 3 pairs because they have same income +/or same support

Question 32

Measure of Association with Ordinal Variables - Gamma

Answer 32

In a positive association: if John ranked above Julie on income, he would tend to rank above her on political support. In a negative association: if John ranked above Julie on income, he would tend to rank below her on political support.

Question 33

Principles behind Gamma

Answer 33

test the direction of relationship betw income + political support by comparing every pair of cases + ignoring all pairs where people have same income and/or support classify 6 pairs that differ in both income & support into “same pairs” + “different pairs”:

Question 34

Computing Gamma

Answer 34

1) # of pairs in “same” category + subtract from # of pairs in “opposite” category: Same Pairs – Opposite Pairs: 2 – 1 = 1

Question 35

Computing Gamma

Answer 35

2) Add total number of pairs compared Same Pairs + Opposite Pairs: 2 + 1 = 3 3) divide 1) by2): (2–1)/(2+1)= .33

Question 36

Interpreting Gamma

Answer 36

33 percent more of pairs compared had “same” ranking, rather than opposite ranking as income level increases, support for Rob Ford seems stronger

Question 37

Interpreting Gamma

Answer 37

more ppl in sample higher income = higher support Than opposite if negative number, 33% more that show higher income, lower support

Question 38

Interpreting Gamma

Answer 38

33 percent more of the pairs that had the “opposite” ranking than the same ranking: as income level increases, political support for Ford seems weaker

Question 39

Gamma: The Reality

Answer 39

In reality, way more cases + more than 2 ordinally ranked categories Resulting in 100s or 1000s of pairs to compare Makes calculation by hand difficult long way, but pg 442, of your Textbook illustrates a shortcut which can be used by hand or is used by computer programs.

Question 40

Measures of Association with Interval/Ratio Level Variables

Answer 40

Lambda: reducing error by guessing most frequently occurring category (mode) Gamma: reducing error in guessing relationship betw 2 variables with ordinally ranked categories

Question 41

Measures of Association with Interval/Ratio Level Variables

Answer 41

Pearson’s r: focuses on reducing error in guessing exact value of 1 variable by knowing exact value of other

Question 42

Measures of Association with Interval/Ratio Level Variables

Answer 42

errors in guessing how well value of Y corresponds with X always minimized by guessing how far actual values of X + Y deviate from mean values of X + Y

Question 43

DEMONSTRATING WHY THE ERRORS ARE MADE SMALLER USING GUESSES FROM THE MEAN

Answer 43

Sum of squared deviations from mean divided by number of cases: X:98/7 = 14; Y: 21320.87/7= 3045

Question 44

DEMONSTRATING WHY THE ERRORS ARE MADE SMALLER USING GUESSES FROM THE MEAN

Answer 44

variance in error from guessing from mean smaller than variance in error from guessing from median (so the mean is always our best guess)

Question 45

Pearson’s r

Answer 45

Pearson’s r correlation: testing strength + direction of association betw 2 interval/ratio level (count) variables Strength: size of # indicates how strongly 2 variables associated Effect size is capped at 1, with values closer to 0 indicating weaker correlation

Question 46

Pearson’s r

Answer 46

Direction: correlation +/–, depending in whether values of 1 variable move in same direction as the other/opposite direction measures the linearity, (more variable/less variable) doesn’t = slope

Question 47

VISUAL EXAMPLES OF Pearson r CORRELATION STRENGTH AND DIRECTION

Answer 47

Positive Correlation: Values increase together Negative Correlation: One value increases while other decreases size of the value shows how good the correlation is + if positive/negative