Examining the Relationship Between Two Variables (Bivariate Analyses)

What type of analysis? We have two variables X and Y and we are interested in describing how a response (Y) is related to an explanatory variable (X). What graphical displays do we use to show the relationship between X and Y ? What statistical analyses do we use to summarize, describe, and make inferences about the relationship?

Type of Displays Y is Continuous Scatterplot Comparative Boxplot Y is Ordinal or Nominal Logistic Plot 2-D Mosaic Plot X is Continuous X is Ordinal or Nominal

Correlation and Regression Type of Analyses Y is Continuous Correlation and Regression If X has k = 2 levels then Two-Sample t-Test or Wilcoxon Rank Sum Test. If X has k > 2 levels then Oneway ANOVA or Kruskal Wallis Test Y is Ordinal or Nominal If Y has 2 levels then use Logistic Regression If Y has more than 2 levels then use Polytomous Logistic Regression If both X and Y have two levels then use Fisher’s Exact Test, RR/OR, and Risk Difference If either X or Y has more than two levels use a Chi-square Test. X is Continuous X is Ordinal or Nominal

Fit Y by X in JMP Y nominal/ordinal Y continuous X continuous X nominal/ordinal

Example: Low Birthweight Study List of Variables id – ID # for infant & mother headcir – head circumference (in.) leng – length of infant (in.) weight – birthweight (lbs.) gest – gestational age (weeks) mage – mother’s age mnocig – mother’s cigarettes/day mheight – mother’s height (in.) mppwt – mother’s pre-pregnancy weight (lbs.) fage – father’s age fedyrs – father’s education (yrs.) fnocig – father’s cigarettes/day fheight – father’s height lowbwt – low birthweight indicator (1 = yes, 0 = no) mage35 – mother’s age over 35 ? smoker – mother smoked during preg. Smoker – mother’s smoking status (Smoker or Non-smoker) Low Birth Weight – infant birthweight (Low, Normal)

Example: Low Birthweight Study (Birthweight vs. Gestational Age) Y = birthweight (lbs.) Continuous X = gestational age (weeks) Continuous

Example: Low Birthweight Study (Birthweight vs Example: Low Birthweight Study (Birthweight vs. Mother’s Smoking Status) Y = birthweight (lbs.) Continuous X = mother’s smoking status (Smoker vs. Non-smoker) Nominal

Example: Low Birthweight Study (Birthweight Status vs Example: Low Birthweight Study (Birthweight Status vs. Mother’s Cigs/Day) Y = birthweight status (Low, Normal) Nominal X = mother’s cigs./day Continuous P(Low|Cigs/Day)

Example: Low Birthweight Study (Birthweight Status vs Example: Low Birthweight Study (Birthweight Status vs. Mother’s Smoking Status) Y = birthweight status (Low, Normal) Nominal X = mother’s smoking status (Smoker, Non-smoker) Nominal