Bi-variate #1 Cross-Tabulation PS 372

Single Variable “Typical Case” is central tendency (Mean, Mode, Median). Variability or dispersion (Variance). Overall pattern is the distribution (Histogram, Bar Charts, Pie Charts).

Two Variables Cross Tabulation Difference-of-means Analysis of Variance Correlation Analysis Regression Analysis

Steps in Two Variable Analysis Is there a statistical relationship? How strong is the relationship? What is the relationship’s direction? Is the relationship casual or not? If we know the answers we can make predictions (subject to error) if we know the value of one the two variables.

Statistical Relationship A statistical relationship between two variables exists if the values of the observations for one variable are associated or connected to the values of the observations of the other. Without a statistical relationship cannot answer the other three questions!

Statistical Relationship Always a possibility (especially with samples) that an observed relationship is due only to chance and is an inaccurate indication of what we would have observed in the entire population. It is possible to test for “statistical significance”.

Strength of Relationship Strength of relationship indicates how consistently the values of an IV variable are associated with the values of a DV! Weak and Strong relationships. Remember correlation (r).

Strength of Relationship Nil or Weak if proportion of cases across various categories of independent variable are nearly equal across categories/values of the dependent variable!!! Proportion of Men voting/non voting is nearly equal to percentage of women voting/non-voting! i.e. Gender does not explain participation at the ballot box.

Strength of Relationship Strong or Perfect relationship if proportion of cases of various categories of independent variable differ substantially across categories of the dependent variable! Perfect if ALL values for one category of the IV fall into one category of the DV…and values for another IV category fall into another category of the DV!!!

Direction of Relationship The direction or shape of the relationship tells us which values of the independent variable are associated with which values of the dependent variable, rather than simply whether the two are related.

Direction of the Relationship The direction of the relationship tells us how the values of the independent variable are associated with the values of the dependent variable Positive and Negative Relationship between Independent and DV! Need Directionality… Ordinal or Higher!

Direction of the Relationship Positive Relationship – Higher values of the Independent Variable are associated with Higher Values of the DV!!! More Literacy; More Democracy More Education; More Political Knowledge Any More????? Casinos and Crime??? Income and Campaign Contributions???

Direction of the Relationship Negative Relationship – Higher Values of the IV are associated with Lower Values of the DV! And Vice Versa! More Democracy; Less War More African Americans; Less Welfare More Income; Less Liberal Any More???? More negative ads; Less Voting

Causality That a relationship exists between independent and dependent variables does not necessarily imply causality. What do we need to prove causality? Covariance; Time Dependence; Rival Explanations!!!

What is a Crosstabulation? Crosstabulations are appropriate for examining relationships between variables that are nominal, ordinal, or dichotomous. Few Categories!!!

What is a Crosstabulation? Crosstab displays the joint distribution of values of the variables by listing the categories for one of the variables along one side (DV) and the categories for the other variables across the top (IV). Each case is then placed in the cell of the table that represents the combination of values that corresponds to its scores on the variables.

What is a Crosstabulation? Example: We would like to know if presidential vote choice in 2000 was related to race. Dependent variable: presidential vote in 2000. Voted for Bush or Gore (Nominal). Independent variable: race. Non-White and White (Nominal).

What is a Crosstabulation? To show the data we construct a table showing each case’s value for both variables by putting the independent variable across the top and the dependent variable down the side and creating a grid of boxes or cells, one for each combination of the variables.

Are Race and Vote Choice Related? Why?

Crosstab What is important in testing the hypothesis is not which cases have particular values for the independent and dependent variables, but how many have each combination of values. The number or frequency of observations in each CELL is important.

Interpretation Each cell in the table should contain two numbers. The first is the frequency of cases having that particular combination of values. By themselves the frequencies are not especially helpful.

Interpretation The second number is the relative frequency (percentage) of the column. It is important to stress that the percentages add to 100 down the columns (not the rows).

Are Race and Vote Choice Related? Why?

Strength of the Relationships Weak or Strong Relationship? How do we know relationship strength from a cross-tab??? Need to look at how values across categories of IV are distributed across values of DV!!!

Strength of the Relationships A weak relationship would be one in which the differences in the observed values of the dependent variable for different categories of the independent variable are Very Slight The weakest is one in which the joint distribution is identical for all categories of the independent variable.

Direction of the Relationships The direction of the relationship shows which values of the independent variable are associated with which values of the dependent variable. Important if the variable is ordinal. Often a critical part of testing a hypothesis.

Crosstabs Important to check to see if the IV is the columns and not the rows. Want to know proportion of values of IV that fall into different categories of the DV!!! Sometimes the independent variable is the rows to save space and for easier presentation of the table. Important that the percentage adds to 100 in each category of the IV variable (Column %)

Crosstab No matter the number of cases and categories the procedure remains the same: Separate the cases into groups based on their values for the independent variable. Compare the values of the dependent variable for those groups. Decide whether the values for the dependent variable are different for the groups.