PLEASE NOTE THE DUE DATE:  IT IS FRIDAY  NOVEMBER 12 BY 3 PM!
 

OF COURSE YOU'LL DO COMPUTER RUNS IMMEDIATELY!
Strange things can happen...
 

In this assignment, you'll use the SDA system and the General Social Survey to see how a control variable may (or may not) alter the original correlation between two variables.

• Your independent variable will be year, 1972 or 2002.

• Your dependent variable will be degree (five levels) or the respondent's highest degree.

• Your control variable will be sex (gender, male or female)

Here are the first two basic questions we ask about a relationship between two variables:
 
 

This question typically examines what is called the "statistical significance" of the association.
 
 

Question 2 requires you to:

• Select the BEST or MOST APPROPRIATE correlation coefficient for your data from among the many that are available.
• Assess the strength of that correlation coefficient.
• At the same time, of course, you will assess direction and linearity or monotonicity.

If the correlation coefficient is statistically significant and at least weak (at least |.11| in magnitude, but ideally moderate or more), continue to question 3.
 
 

#3. If the bivariate relationship is probably nonzero and nontrivial in magnitude, what is the apparent causal structure of the bivariate relationship in non-experimental data? Question 3 requires you to add at least one "control variable."

REVIEW

Below are the six possible outcomes to the bivariate correlation when you add a third or control variable:

First, you must decide whether ANY CHANGES have occurred in the original bivariate relationship when you examine it across the separate values of the control variable.

• If no changes have occurred, decide whether the relationship is (1) joint or whether it is (2) extraneous.

If changes do occur, decide which ONE of the following patterns you have:

• (3) Interaction (moderated) effects

THEN STOP!!

If you do not have extraneous, joint, or interaction effects, study the pattern of your results for one of the following:

• (4) Intervening (mediated) effects
• (5) Spurious effects
• (6) Suppressor effects

BE SURE TO KEEP THE DIFFERENCE STRAIGHT BETWEEN:

(1) THE PROBABILITY LEVEL USED TO TEST WHETHER THE RELATIONSHIP IS ZERO AND
(2) THE CORRELATION COEFFICIENT USED TO ESTIMATE THE STRENGTH OF THE ASSOCIATION.
 

This total assignment is worth 20 points.

Correctly following all programming information for running frequency distributions on the two variables, the crosstabulation, and the difference of means test, and turning in all output = 2 points.

Although your actual output does not count very heavily, I MUST receive your output in order for you to receive credit on this assignment.

QUESTIONS YOU WILL NEED TO ANSWER, BASED ON YOUR OUTPUT DATA
 

Which correlation coefficient should you use to measure any association between degree and sex? BRIEFLY, WHY should you use that particular correlation coefficient? [If you use phi, examine the table size to see if you should use Cramer's V instead.]

Was there any association between degree and sex in your table for the total sample? (Was the association real or accidental?)

What was that significance level for the association between degree and sex?
(Remember:  a row of .00s here really means p < .01.)

Was this relationship curvilinear (non-linear), monotonic, approximately linear, or couldn't you tell? How did you know?

What was the numeric value of this correlation? Describe the strength [and direction if applicable] of this association in words.

Was there any association between year and degree in your table for the total sample? (Was the association real or accidental?)

What was that significance level for the association between year and degree?
(Remember:  a row of  two .00s here really means p < .01.)

Was this relationship curvilinear (non-linear), monotonic, approximately linear, or couldn't you tell? How did you know?

What was the numeric value of this correlation? Describe the strength [and direction if applicable] of this association in words.

Use the same kind of correlation coefficient that you chose for the relationship between year and degree IN THE TOTAL SAMPLE. What were the numeric values of the correlations between year and degree for:

• (A) Men and
• (B) Women separately?

What are your causal conclusions about the type of relationship considering all three variables together?

Do you have an extraneous relationship, a joint relationship, an interaction effect, an intervening (indirect or mediated) relationship, a spurious relationship, or a suppressed relationship?

Remember, you can make ONLY ONE CHOICE from among the SIX outcomes immediately above. (If your correlations for Men and Women differ by at least |.10| , you have an interaction effect and that is what you call it.)

In a sentence or so, discuss the reasoning behind your decision.

Lots of questions here, but take everything step by step and you should be able to answer them all.

OVERALL

FIRST, access SDA and the General Social Survey.

SECOND, run frequencies on all variables for this computer session (year, degree, sex). It is always a good idea to click the percents box to get a idea of the relative distributions.

THIRD, you will run your assigned crosstabulations.You will select the most appropriate statistics for your data and then decide what kind of causal relationship you have.

SPECIFICALLY

1. You will run univariate FREQUENCIES on the three variables for this exercise. You will watch for out of order codes, missing data, "wild punches," and other anomalies so that you can recode these if needed or restrict the range of valid codes.

You will run frequencies on:

sex (male or female)

degree (respondent's highest degree level, in five degrees)

year (year of study--we will only use 1972 and 2002)
 

2.   You will then conduct a crosstabulation of degree by sex for the total sample. In your program, you will request statistics and column percentages.

3.   Based on your crosstabulation, you will select the BEST or MOST APPROPRIATE correlation coefficient for your data. You will decide whether any apparent association between degree and the respondent's gender is ACCIDENTAL or REAL. You will report the level of "statistical significance" of this association.

4.  You will report the magnitude of the correlation coefficient, its direction (if appropriate), its form (IF APPROPRIATE), and how strong the correlation coefficient is in words.

5.  Next, you will conduct a crosstabulation of degree  by year for the total sample. In your program, you will request statistics and column percentages. (NOTE: this will be part of your control variable run. It comes out as the very last table in your output when you run the three way contingency table.)

6.  Based on your crosstabulation, you will select the BEST or MOST APPROPRIATE correlation coefficient for your data. You will decide whether any apparent association between year and the respondent's degree level is ACCIDENTAL or REAL. You will report the level of "statistical significance" of this association.

7.  You will report the magnitude of the correlation coefficient, its direction (if appropriate), its form (if appropriate), and how strong the correlation coefficient is in words.

8.  At the same time you conduct the crosstabulation for  degree by year for the total sample, you will request:

• a bivariate frequency table between degree by year for Men only and
• a bivariate frequency table between degree by year for Women only.

You will assess the statistical significance of the correlation separately for each sex, its magnitude, direction (if appropriate), its form (if appropriate), and its strength in words.

At step 8, you have conducted a multivariate crosstabulation (sometimes called a "three-way crosstab").
For most of you it is your very first one. Congratulations!

9.  You will decide on the general causal status of the three way crosstabulation. Is it:

direct
joint
statistical interaction
intervening
spurious or
suppressed?

    Accessing an online database (the General Social Survey file) and the SDA system.
    Running univariate frequency and percentage distributions.
    Using a selection filter to select only two years: here, 1972 and 2002
    Recoding the values of a variable into fewer values.
    Conducting a crosstabulation to generate:

• A bivariate percentage table
• Chi-Square
• Many correlation coefficients

NEW FEATURES include:

• Adding a third "layer" or control variable to your crosstabulations.
• Examining partial tables and "physical control."
• Examining the form (linear, monotonic, nonlinear) of a relationship.
• Assessing what kind of causal processes MAY be operating in these non-experimental data.

---

Use the RIGHT toe of your mouse to click on this link:
 
 

http://www.icpsr.umich.edu/GSS/

When the menu opens on the link, click on:         Open in New Window

Click on the  button to pull up the statistical program selection screen.
 

Remember: WHAT YOU SEE BELOW IS A NONWORKING COPY.  YOU MUST GO TO THE NEW PAGE THAT OPENS ON YOUR MONITOR TO ACCESS THE SDA PROGRAM.

You can always switch back to this screen by clicking on the box at the very bottom of the monitor screen that reads "Assignment 4". Or you can print out the pages of Assignment 4.

Once again, you will bring up the "radio buttons" screen to select an analytic option, in this case, Frequencies or crosstabulation. The directions that you place in the SDA boxes will direct the program to perform a series of crosstabulations.
 

Study: GSS 1972-2002 Cumulative Datafile Select an action: Browse codebook in this window Frequencies or crosstabulation Comparison of means Correlation matrix Comparison of correlations Multiple regression Logit/Probit List values of individual cases Recode variables (into public work area) Compute a new variable List/delete derived variables Download a customized subset

Suggestion for running analysis programs: Click the "Open Extra Codebook Window" button above. This allows you to "copy-and-paste" the names of variables you wish to analyze from the codebook window to the analysis windows.

Return to SDA Home Page

In the Study: GSS 1972-2002 Cumulative Datafile screen that opens: first click on:
 

Open Extra Codebook Window

to open up the codebook window. Remember to click on the "Standard Codebook" link.

Use the radio button to select Frequencies or crosstabulation. Then, click on :
 

Start

so that you have the SDA program window active as well.
 

PRELIMINARY FREQUENCIES

REMEMBER! The first step in working with data is to ALWAYS display the total frequencies on all the variables that you plan to analyze for a particular research project.
 
 

After you have accessed the Current Population Survey data and the SDA system, be sure to run the original frequencies for:

1.sex

2. degree and

3. year

Obtain the frequencies ONLY. (This includes percentages too!) You DO NOT need measures of central tendency, dispersion, or other univariate measures for this assignment.

BE SURE TO IMMEDIATELY PRINT THESE FREQUENCIES PAGES AND INCLUDE THEM WITH YOUR OUTPUT.

See the directions below for "what goes in the boxes" below the SDA Program box.
 

RUNNING YOUR SDA SHORT PROGRAM FOR CROSSTABULATIONS

Pull up the window for the SDA Program Screen. Again for your review, below is the example screen for running frequencies or crosstabulations that appeared when you clicked the "START" button on the SDA beginning window.

We can be reasonably sure that time will influence educational level in the United States because people in more recent years are better educated. Most states and the federal government have tried to prevent high school dropouts and encourage high school graduates to attend college.  I cannot imagine any circumstances under which one's level of education would influence year (try the "giggle factor" here if nothing else).

We can be totally sure that neither the study year nor someone's level of education will influence  whether they are male or female! On the other hand, one sex or the other may have increased their educational level disproportionately over time.

FIRST, you will run the crosstabulation between degree and sex.

Row: degree

Make sex your Column: variable

REMEMBER: Where it says Selection Filter(s):  put: year (1972,2002)
to select only respondents from 1972 and 2002.

Be sure that the "Column" box is checked under Percentaging:

Now, click on the boxes to the LEFT of:

"Statistics"                    AND
"Question text"

If you like, you can change the number of decimal places ONLY for statistics to "4".
However there is a good  chance this won't work and you will only get 2 decimal places anyway under statistical significance...

Click on the gray box at the bottom left that says:
 

Run the Table

IMMEDIATELY PRINT THESE PAGES BEFORE YOU BEGIN THE THREE-WAY CROSSTABULATION RUN BELOW!

THE BOX BELOW WILL NOT WORK TO RUN YOUR PROGRAM.  YOU MUST GO TO THE NEW PAGE THAT OPENS ON YOUR MONITOR TO RUN YOUR PROGRAM.

 

Now for the three-way crosstabulation. You will also be able to get the BIVARIATE crosstabulation of degree by year for the total sample from this run. It will be the VERY LAST TABLE (and include all the valid cases) on the run output.

In the Row box, type: degree

degree goes in the "row" line because it is your dependent variable.

Next to the Column: line, type: year
This will make year, your independent variable, the column variable, per MOST conventions.

Next to the Control: line, type: sex

Be sure to switch "sex" to the Control: line. This will make sex your control variable. This command will generate you THREE crosstabulation tables for the association between degree level and time:

• The first is only for Men
• The second is only for Women
• The third is for both sexes combined

Next to Percentaging: be sure the little box to the LEFT of "Column" is checked.
(Click to check this box if it is blank.)

This WILL produce column percents because you have both rows and columns.

Now, click on the boxes to the LEFT of:

"Statistics"                    AND
"Question text"

Remember to ONLY use the P or Pearson Chi-Square for this assignment.
Also recall that if you choose to use Phi for any of your correlations, that you can easily calculate it if you:

(1) Take the Pearson Chi-Square and
(2) Divide it by the casebase (n), then
(3) Take the SQUARE ROOT of the result at Step 2.

That's it, that's Phi.
If you want Phi-squared instead, just stop at Step 2.

Use the Cramer's V correction in the denominator if you have a 3 by 3 size table OR LARGER. The phi formula will work for a "2 by anything" table.

Now click the gray box at the bottom left that says:
 

Run the Table

Here is your output for your first multivariate crosstabulation run using the SDA system.

Go ahead and print your "three-way crosstab" NOW so that you have these pages to study while you complete this assignment. They also form part of the Assignment 4 that you will turn in to me.
 
 

Your printed output (2 points maximum) for:

• the frequency distributions on sex, degree, and year
• the crosstabulation between sex and degree (with accompanying statistics)
• the crosstabulation between degree and year (with accompanying statistics)
• the three-way crosstabulation between degree and year within categories of sex (Male or Female)

(1) (2 points) Which correlation coefficient should you use to measure any association between degree and sex? BRIEFLY, WHY should you use that particular correlation coefficient? [If you use phi, examine the table size to see if you should use Cramer's V instead.]

(2) (1 point) Was there any association between degree and sex in your table for the total sample? (Was the association real or accidental?)(Was the association zero or non-zero--these three questions are equivalent.)

(3) (1 point) What was that significance level for the association between degree and sex? (Remember:  a row of .00s or 1.00 here really means p < .01.)

(4) (1 point) Was this relationship curvilinear (non-linear), monotonic, approximately linear, or couldn't you tell? [This is often called the FORM of the relationship.] How did you know?

(5) (1 point) What was the numeric value of this correlation? Describe the strength [and direction if applicable] of this association in words.
 

(6) (2 points) Which correlation coefficient should you use to measure any association between year and degree? BRIEFLY, WHY should you use that particular correlation coefficient? [If you use phi, examine the table size to see if you should use Cramer's V instead.]

(7) (1 point) Was there any association between year and degree in your table for the total sample? (Was the association real or accidental?) Remember, the crosstabulation table for males and females combined will be the THIRD table in your program output.

(8) (1 point) What was that significance level for the association between year and degree? (Remember:  a row of .00s or 1.00 here really means p < .01.)

(9) (1 point) Was this relationship curvilinear (non-linear), monotonic, approximately linear, or couldn't you tell? [This is often called the FORM of the relationship.] How did you know?

(10) (1 point) What was the numeric value of this correlation? Describe the strength [and direction if applicable] of this association in words.

Now, what happens when you use your control variable?

(11) (1 point) Use the same kind of correlation coefficient that you chose for part (6) above [NOT part (1)]. What were the numeric values of the correlations between year and degree for:

• (A) Males and
• (B) Females separately?

(13) (1 point) What were the levels of statistical significance for each of the two correlations in part (11)?

(14) (1 point) Describe the strength of each correlation (direction, form if applicable) in part (11) in words.

(15) (2 points) What are your causal conclusions about the type of relationship considering all three variables together?

Do you have an extraneous relationship, a joint relationship, an interaction effect, an intervening (indirect) relationship, a spurious relationship, or a suppressed relationship?

Remember, you can make ONLY ONE CHOICE from among the outcomes immediately above. (If your correlations for Males and Females differ by at least |.10| , you have an interaction effect and that is what you must call it.)

In a sentence or so, discuss the reasoning behind your decision.
 

(1) the highest values for both the independent and the dependent variables and the bottom right-hand cell contains the lowest values for both the independent and the dependent variables OR
(2) the top left-hand cell contains the lowest values for both the independent and the dependent variables and the bottom right-hand cell contains the highest values for both the independent and the dependent variables.

Obviously this is not a problem if one of your variables is nominal in the cross-tab table but it could be a problem if both your variables are at least ordinal. Because the top left-hand cell is low for both variables in this example (year = 1972 and degree = less than high school) your correlation coefficient this time around will be OK.

However, in other variable codings (e.g., the top left-hand cell is "high-low"), the sign of the correlation coefficient may be reversed and the analyst must change the signs of the correlation coefficients. Be alert to this issue in analyses you may do later on for theses, dissertations, conference papers, reports, articles, etc. and how your independent and dependent variables are coded. Remember that computers are robots and they go by table position, they don't really know which cells you meant were the "high"  cells. SPSS and SAS follow similar conventions for tables.
 
 

READINGS AND ASSIGNMENTS

OVERVIEW

Susan Carol Losh November 2, 2004
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