elaboration elaboration extends our knowledge about an association to see if it continues or changes...

Elaboration

Elaboration extends our knowledge about an association to see if it continues or changes under different situations, that is, when you introduce an additional variable. This is sometimes referred to as a control variable because you are seeing if the original relationship changes or continues when you control for (hold the effects of) a new variable.

When you introduce one control variable the process is sometimes called first-order partialling. You can continue to add multiple variables, called second-order, third-order, and so on, for more elaborate models, but interpretation can get complex at that point especially if each of those variables has numerous values or categories. The original bivariate association is the zero-order relationship.

Voting in Election * Race of Respondent Crosstabulation

893 101 38 1032

71.2% 62.0% 50.7% 69.2%

337 56 27 420

26.9% 34.4% 36.0% 28.2%

19 5 10 34

1.5% 3.1% 13.3% 2.3%

5 1 6

.4% .6% .4%

1254 163 75 1492

100.0% 100.0% 100.0% 100.0%

Count

% within Race ofRespondent

Count


Count


Count


Count


voted

did not vote

not eligible

refused

Voting inElection

Total

white black other

Race of Respondent

Total

Chi-Square Tests

54.646a 6 .000

33.994 6 .000

27.663 1 .000

1492

Pearson Chi-Square

Likelihood Ratio

Linear-by-LinearAssociation

N of Valid Cases

Value dfAsymp. Sig.

(2-sided)

4 cells (33.3%) have expected count less than 5. Theminimum expected count is .30.

a.

Voting in Election * Race of Respondent * Married ? Crosstabulation

531 39 17 587

76.6% 67.2% 42.5% 74.2%

151 17 15 183

21.8% 29.3% 37.5% 23.1%

7 2 8 17

1.0% 3.4% 20.0% 2.1%

4 4

.6% .5%

693 58 40 791

100.0% 100.0% 100.0% 100.0%

362 61 21 444

64.5% 58.7% 60.0% 63.4%

186 39 12 237

33.2% 37.5% 34.3% 33.9%

12 3 2 17

2.1% 2.9% 5.7% 2.4%

1 1 2

.2% 1.0% .3%

561 104 35 700

100.0% 100.0% 100.0% 100.0%

Count


Count


Count


Count


Count


Count


Count


Count


Count


Count


voted

did not vote

not eligible

refused

Voting inElection

Total

voted

did not vote

not eligible

refused

Voting inElection

Total

Married ?yes

no

white black other

Race of Respondent

Total

Chi-Square Tests

75.921a 6 .000

39.848 6 .000

34.205 1 .000

791

4.865b 6 .561

3.926 6 .687

2.027 1 .155

700

Pearson Chi-Square

Likelihood Ratio


N of Valid Cases

Pearson Chi-Square

Likelihood Ratio


N of Valid Cases

Married ?yes

no

Value dfAsymp. Sig.

(2-sided)

5 cells (41.7%) have expected count less than 5. The minimumexpected count is .20.

a.

5 cells (41.7%) have expected count less than 5. The minimumexpected count is .10.

b.

multiple correlation (R) is based on the Pearson r correlation coefficient and essentially looks at the combined effects of two or more independent variables on the dependent variable. These variables should be interval/ratio measures, dichotomies, or ordinal measures with equal appearing intervals, and assume a linear relationship between the independent and dependent variable.

Similar to r, R is a PRE when squared. However, unlike bivariate r, multiple R cannot be negative since it represents the combined impact of two or more independent variables, so direction is not given by the coefficient.

Multiple R2 tell us the proportion of the variation in the dependent variable that can be explained by the combined effect of the independent variables

Multiple Correlation

Uncovering which of the independent variables are contributing more or less to the explanations and predictions of the dependent variable is accomplished by a widely used technique called linear regression. It is based on the idea of a straight line which has the formula

Y= a + bX

Y is the value of the predicted dependent variable, sometimes called the criterion and in some formulas represented as Y' to indicate Y-predicted;X is the value of the independent variable or predictor; a is the constant or the value of Y when X is unknown, that is, zero; it is the point on the Y axis where the line crosses when X is zero; and b is the slope or angle of the line and, since not all the independent variables are contributing equally to explaining the dependent variable, b represents the unstandardized weight by which you adjust the value of X. For each unit of X, Y is predicted to go up or down by the amount of b.

Regression

the regression line which predicts the values of Y, the outcome variable, when you know the values of X, the independent variables. What linear regression analysis does, is calculate the constant (a), the coefficient weights for each independent variable (b), and the overall multiple correlation (R). Preferably, low intercorrelations exist among the independent variables in order to find out the unique impact of each of the predictors. This is the formula for a multiple regression line:

Y' = a + bX1 + bX2 + bX3 + bX4 …. + bXn

The information provided in the regression analysis includes the b coefficients for each of the independent variables and the overall multiple R correlation and its corresponding R2. Assuming the variables are measured using different units as they typically are (such as pounds of weight, inches of height, or scores on a test), then the b weights are transformed into standardized units for comparison purposes. These are called Beta () coefficients or weights and essentially are interpreted like correlation coefficients: Those furthest away from zero are the strongest and the plus or minus sign indicates direction.

Model Summary

.294a .086 .080 4.754Model1

R R SquareAdjustedR Square

Std. Error ofthe Estimate

Predictors: (Constant), Size of Place in 1000s, HoursPer Day Watching TV, Respondent's Sex, Highest Yearof School Completed

a.

ANOVAb

1299.940 4 324.985 14.381 .000a

13740.066 608 22.599

15040.007 612

Regression

Residual

Total

Model1

Sum ofSquares df Mean Square F Sig.

Predictors: (Constant), Size of Place in 1000s, Hours Per Day Watching TV,Respondent's Sex, Highest Year of School Completed

a.

Dependent Variable: Age When First Marriedb.

Coefficientsa

22.204 1.094 20.290 .000

.307 .062 .202 4.978 .000

2.360E-02 .088 .011 .267 .790

-2.112 .392 -.210 -5.384 .000

5.474E-05 .000 .011 .283 .777

(Constant)

Highest Year ofSchool Completed

Hours Per DayWatching TV

Respondent's Sex

Size of Place in 1000s

Model1

B Std. Error

UnstandardizedCoefficients

Beta

Standardized

Coefficients

t Sig.

Dependent Variable: Age When First Marrieda.

SNSex: 1=Male, 2=Female

In Words: Respondents who marry at younger ages tend to have less education and are female. Those who marry later tend to have more education and are male.

elaboration elaboration extends our knowledge about an association to see if it continues or changes...

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