Quantitative Data Analysis

1
Chapter 14

• Quantitative Data Analysis
• Supplementary Materials

2
Descriptive, bivariate techniques

• Bivariate analysis - the analysis of two
  variables simultaneously for the purpose of
  determining the relationship between them
• Bivariate crosstabulation table - a table
  displaying the joint distribution of two
  variables.
• By convention, column independent variable row
  dependent variable.

3
Descriptive, bivariate techniques

• Open SPSS
• Main menu - Edit... Options... 
• (On General tab) Variable Lists - Choose Display
  Names and Alphabetical
• Open the GSS data set
• Main menu - File... Open... Data
• Browse and find on the L drive in our class
  directory and Data files subdirectory GSSJH.SAV

4
Bivariate crosstabulation in SPSS

• (Main menu - Analyze... Descriptive Statistics...
  Crosstabs)
• DEGREE2 in Column box COUNREC in Row box
• Cells Percentages, Column
• Continue OK

5
A bivariate measure of association - Gamma

• Gamma Summary measure of the strength and
  direction of the relationship
• Strength 0no relationship, 1perfect
  relationship
• Direction Positive/direct relationship or
  Negative/indirect relationship (See next 2
  slides)
• Choose gamma for your bivariate table if BOTH
  variables are either dichotomous (two values, any
  level) or ordinal level

6
Positive/Direct IV?DV? and IV?DV?
Income (DV)
High
Low
Low
High
Number of Years of Formal Education (IV)
7
Negative/Indirect IV?DV? and IV?DV?
Income (DV)
High
Low
Low
High
Number of Years of Formal Education (IV)
8
Obtaining Gamma in SPSS

• In the Crosstabs dialog box, click Statistics and
  select Gamma (under Ordinal).
• The gamma results will be displayed in a table
  labeled Symmetric Measures.
• Look at the first row (Ordinal by Ordinal-
  Gamma) and note the value of gamma (under
  Value).
• Be sure to note both the sign ( or -) and exact
  value of gamma

9

• Compare gammas for
• COUNREC by DEGREE2
• COUNREC by INCOME4
• COUNREC by SEX
• DEGREE2 by SEX
• DEGREE2 by AGEREC
• HAPMAR by DEGREE2
• HAPMAR by SEX

10
But what if one or both variables is nominal
level, but not dichotomous?

• Many choices available.
• My favorite is Goodman and Kruskals tau.
• Interpret strength in the same manner as gamma.
• Strength 0no relationship, 1perfect
  relationship
• DO NOT attempt to interpret direction of
  association for tau.
• Nominal variable attributes are not rank-ordered.
  Therefore, they cannot be said to have a
  direction.

11
Obtaining GK Tau in SPSS

• In the Crosstabs dialog box, click Statistics and
  select Lambda (under Nominal).
• The tau results will be displayed in a table
  labeled Directional Measures.
• Look at row labeled Goodman and Kruskal tau.
• Choose the row showing the label of your
  dependent variable and note the value of tau
  (under Value).

12

• Compare GK taus for
• POSTLIFE by MARITAL
• HAPPY by MARITAL
• PRES92 by PARTYID

13
Beyond description - An inferential technique for
crosstabulations

• Inferential statistics - statistical computations
  conducted for the purpose of making inferences
  based on sample observations to a larger
  population
• Legitimately used only with probability samples
• Chi-square test of independence - how likely is
  it that a relationship would look this strong
  when, in fact, these two variables are unrelated
  in the population from which the sample is drawn?
• Can be used with both nominal and ordinal levels

14
Obtaining chi-square in SPSS

• In the Crosstabs dialog box, click Statistics and
  select Chi-square.
• The chi-square results will be displayed in a
  table labeled Chi-Square Tests.
• Look at the first row (Pearson Chi-Square) and
  note the significance level (under Asymp. Sig.
  (2-sided)).

15
Interpretation of chi-square results

• If the significance level for the chi-square is
  less than or equal to .05, the results are
  statistically significant.
• This means that we CAN REJECT the possibility
  that there is really NO RELATIONSHIP between
  these two variables in the population from which
  the sample was drawn. These two variables
  probably ARE RELATED in this population.
• GSS - Roughly speaking, this would be the
  American adult population.

16

• If the significance level for the chi-square is
  greater than .05, the results are NOT
  statistically significant.
• This means that we CANNOT reject the possibility
  that there is really NO RELATIONSHIP between
  these two variables in the population from which
  the sample was drawn. These two variables
  probably ARE NOT RELATED in this population.

17

• The .05 significance level is commonly used in
  the social sciences, but there are others.
• More stringently, we could decide not to consider
  our results statistically significant unless
  there is less than a 1/100 (.01) or 1/1000 (.001)
  chance that there is no relationship between our
  variables in the population.

18
Cautions in using inferential statistics

• Inferential statistics should be used only on
  scientifically drawn samples (probability samples
  - Ch. 7).
• A result can be statistically significant
  (plt.05, chi-square) and still be a weak
  relationship (gamma/tau).
• Statistical significance should not be
  misinterpreted as substantive significance or
  importance of results.