Bivariate Descriptive Analysis First step in analyzing your data Three components Cross-tabulations and frequency distributions Significance testing Correlations Initial look at how the data fits together and the relationships between the data Always done before the regressions because lends a framework for the analysis

Crosstabs Have already done in lab What do they Mean? Measure of how two variables and therefore two concept categories overlap/relate Example white race versus poverty income may be 14% African American versus poverty income may be 27% Thus fewer whites live in poverty than African Americans BY THIS DATA

Data and Samples Cannot assume that the data are representative Need to be cautious about statements such as “this relates to that” in a certain way

Rates versus Raw numbers Raw numbers do not reflect the relative strength of the relationships and should never be used in data explication Rates are relative comparisons regardless of the numbers and better reflect relationships

General descriptives are valuable too Mean Median Mode Each for each variable—dependent and independent General Idea of the distribution of each Variance and Standard deviation

Graphs Helpful only if they show a clear delineation or difference in the data

Descriptives versus Regressions Descriptives are raw measures that do not give precision Regressions give more precise relationships between independent and dependent variables Can show those relationships CONTROLLING for other variables Descriptives have no such controls

Correlations Measures of association Measures of the strength and direction of a relationship between two variables or concepts statistically Need to know what kind of variable you have Nominal, ordinal, scale

Nominal Correlations Lambda 0 to 1 Zero means unrelated 1 means completely overlapping (the same) Usually in between Which variables? All the dichotomous variables (ones and zeros) you just made If comparing two nominals use lambda DOES NO SHOW DIRECTION

Ordinals Not applicable here Comparison of two ordinal variables Use Spearman’s Rho or Gamma Gamma ranges from -1 to +1 Shows direction and strength—larger number (-/+) then stronger relationship

Interval/Scale Variables Need Mean, Variance, Range and Standard deviation as frequency measures PRE concept Association measures are r-squared and Pearson’s r T-test and p value associations for significance Very high r value means auto-correlation (the variables measure the same thing)

Nominal and Ordinal Use Chi-square If Scale or interval use T test for significance testing These test difference and likeness If not significant (p>0.05) then the concepts and the variables used are not arrayed differently and may not be significant to the regression

Chi-square Lambda and Gamma issues Need for ordinal and Nominal variables If Lambda is zero (rare) the ONLY measure of association and significance that is valuable Differences in Chi-square models will be discussed with regression models Non-parametric measure of association and difference—compares two variables with know frequencies of distribution –does the data relate or not together?

Significance Testing Defined as the likelihood that a relationship between two variables in a sample exists in the population the sample is designed to represent Inference is the Strength of that relationship Measures of Goodness of Fit—how do the parameters chosen fit together (well or not well)

Making Sense of This Frequencies—what does the data say is the distribution of EACH of your variables Crossatbulations—what are the relationships between sets of two of your variables, how do they cross relate Association tests—are the two variables related in some way Significance tests—what is the strength of that two-way relationship