Dr. Satyendra Singh, Department of Adminstrative Studies Welcome to the Class of Bivariate Data Analysis

Dr. Satyendra Singh, Department of Adminstrative Studies Bivariate Analysis Correlation Interval or Ratio vs. I or R e.g. GPA(i) vs. SAT(i) T-test of mean Interval or Ratio vs. Binary Nominal e.g. GPA(i) by Gender(n) Cross tabulation Nominal or Ordinal vs. N or O e.g. Gender(n) by Major(n)

Dr. Satyendra Singh, Department of Adminstrative Studies Cross Tabulations Relationship among and between variables Sample divided into subgroups gender age student status –How dependent variables vary by subgroup

Dr. Satyendra Singh, Department of Adminstrative Studies Gender by Favorite Type of Soft Drink Marginal totals –65 people prefer diet soft drink, while 35 prefer regular. –Note: sample is near to representative of the population with 54% males and 46% females. Does soft drink type depend on gender? –It would seem so from the table. –Need to compute percentages. Gender Soft Drink Type

Dr. Satyendra Singh, Department of Adminstrative Studies Gender by Preference Preference by Gender Mathematically equivalent, different messages. Soft drink preference is affected by gender. –83% of females preferred diet soft drink, while only 50% of males preferred diet soft drink. Gender is affected by soft drink preference. –58% of people who preferred diet soft drink were females, while only 42% of people who preferred diet soft drink were males. –Does this mean that preference produces gender?

Dr. Satyendra Singh, Department of Adminstrative Studies Rule: Percentage Calculations Calculate %s in the direction of the causal factor, or across the effect factor. In this case –Gender is logically the cause or independent variable Independent of whether the person drinks diet or regular pop –Preference for diet or regular pop, is logically the effect or dependent variable Dependent on gender

Dr. Satyendra Singh, Department of Adminstrative Studies Correct Calculation of Percentage Cross tabulation of gender by type of soft drink (n=100).

Dr. Satyendra Singh, Department of Adminstrative Studies Conditional Probability Probability of one event occurring given that another event has occurred or will occur. –Be careful of past and present behavior. Probability that a person prefers to drink diet pop GIVEN that they are female makes sense. Notion that a person is female GIVEN that she drinks pop does not.

Dr. Satyendra Singh, Department of Adminstrative Studies What about this one? Preference for soft drink type Perception of weight Last soft drink purchased Perception of weight

Dr. Satyendra Singh, Department of Adminstrative Studies Soft Drink Type Marginal Totals –65 people prefer to drink diet pop, while 35 prefer to drink regular pop (as before). Cross tabulation –88% of people who think they are overweight prefer to drink diet pop, while only 25% of people who think they are underweight drink diet pop. –Only 12% of people who think they are overweight drink regular pop, while 75% of people who think they are underweight drink regular pop.

Dr. Satyendra Singh, Department of Adminstrative Studies Multivariate Analysis Regression –Dependent variable: Interval or Ratio –Independent variable: Interval, Ratio, and Binary e.g. GPA(i) on SAT(i), Gender(n) ANOVA –Dependent variable: Interval or Ratio –Independent variable: Nominal or Ordinal e.g. GPA(i) on Major(n), Gender(n) Plus, Discriminant, Factor, Correspondence,Canonical, SEM