Tables

One way to describe relationships is with tables. Tables depict relationships between variables. The simplest table depicts the

relationship between one dependent variable and one independent variable.

One dependent variable of interest to political scientists studying elections is vote choice: Some people vote for the Democratic candidate, other people vote for the Republican.

Every election year the NES draws a representative sample of the American electorate to study voting behavior. All told about 1500 people are randomly sampled and interviewed.

Let's treat whether a citizen voted for Republican or Democratic in a recent presidential election as our dependent variable.

Vote Choice by Gender

Number of cases Percent of cases by IV

VOTE Male Female N Male Female %

Democratic 240 224 464 53% 61% 56.7%

Republican 212 143 355 47% 39% 43.3%

Total 452 367 819 100% 100% 100%

Basic Rules for Constructing and

Interpreting Crosstabulations 1. Determine the title: Write a clear description in which the Dependent Variable

comes first, then the Independent Variable(s).

EG, “Presidential Vote by Gender"

Reader should be able to tell what is being compared without reading the accompanying

text. Here we are looking at vote choice as a function of gender.

2. Next, Determine categories for the Dep and Ind Vars, here Vote Republican or Democratic. Vote choice is a (categorical) dichotomous variable. The Ind Var can also be broken down as a dichotomy -- Male or Female, producing a 2 by 2 table, with each "cell" -- a, b, c, or d -- showing the number of people in each category.

3. Next, Label the Columns and Rows. Here is a key question. Which should be the column variable, which the row? By convention the Independent variable (Gender) is the column variable. The DV makes up the rows – with title on left.

4. Next Important decision: Which way to calculate percentages.

Vote Choice by Income

Low income

Med income

High income

Vote Rep. 41% 49% 66%

Vote Dem. 59% 51% 34%

Total 100% 100% 100%

Vote Choice by Party ID

VOTE Republican Independent Democrat

Rep. Pres. 89% 40% 7%

Dem. Pres.

11% 60% 93%

Total % 100% 100% 100%

Reading and Interpreting Tables

Crosstabs with Controls

CONTROLLING for a THIRD VARIABLE

Main effects: Partisanship, Income, & Gender (each of the factors influenced vote choice )

Concept called “control variables” will help us answer an important question: How do the different independent variables interact?

Interactions: Gender and Party ID Gender and income Party ID and income

Vote by Party ID, Controlling for Gender

Male Female

Vote: Rep Ind Dem Rep Ind Dem

Rep. 95% 73% 24% 95% 55% 23%

Dem. 5% 27% 76% 5% 45% 77%

Total 100% 100% 100% 100% 100% 100%

Vote by Income, Controlling for Gender

Male Female

Vote: Low Med High Low Med High

Rep. 47% 61% 67% 38% 51% 65%

Dem. 53% 38% 33% 62% 49% 35%

Total 100% 100% 100% 100% 100% 100%

Vote by Income, Controlling for Party ID

Republican Independent Democratic

Vote: Low Med High Low Med High Low Med High

Rep. 94% 93% 96% 56% 65% 71% 17% 25% 25%

Dem. 6% 7% 4% 44% 35% 29% 83% 75% 75%

Total N 33 76 115 34 63 86 99 137 98

Total % 100% 100% 100% 100% 100% 100% 100% 100% 100%

Effects of Controlling for a Third Variable: four possibilities when

controlling for a 3rd Variable

I. The independent effect is maintained

II. The now you see it now you don’t effect

III. Something from nothing effect

IV. The stretch and shrink effect

The Independent Effect Maintained:

Vote Choice by Religion

Protestant Catholic

Republican 58% 25%

Democrat 42% 75%

Vote by Religion, Controlling for Income

Low Income High Income

Prot. Cath. Prot. Cath.

Rep. 54% 20% 67% 35%

Dem. 46% 80% 33% 65%

Now you see it now you don’t effect

Congressional Vote by Union Membership

Non-UnionUnion

Member

Republican 50% 42%

Democrat 50% 58%

Congressional Vote by Union Membership, Controlling for Income

Below Median Income Above Median Income

Non-Union Union Non-Union Union

Rep 33% 32% 58% 56%

Dem 67% 68% 42% 44%

Attitude toward Urban Renewal

by Party Identification

Republican Democrat

Pro Urban Renewal

50% 52%

Anti Urban Renewal

50% 48%

Something from Nothing Effect

Attitude toward Urban Renewal by Party Identification, Controlling for Income

Below Median Income Above Median Income

Republican Democrat Republican Democrat

Pro Urban Renewal 40% 45% 58% 67%

Anti Urban Renewal 60% 55% 42% 33%

Support for Aggressive Foreign Policy

by Gender

Male Female

Ease Relations

42% 67%

Get Tougher 58% 33%

The Stretch and Shrink Effect

Support for Aggressive Foreign Policy by Gender, Controlling for Region

South North

Male Female Male Female

Ease 30% 67% 58% 68%

Tough 70% 33% 42% 32%