1. Examining the Relationship Between Two Variables (Bivariate Analyses)

2. 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). 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 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? What statistical analyses do we use to summarize, describe, and make inferences about the relationship?

3. 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

4. Type of Analyses Y is Continuous 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 Two-Sample t-Test or Wilcoxon Rank Sum Test. If X has k > 2 levels then Oneway ANOVA or Kruskal Wallis Test If X has k > 2 levels then Oneway ANOVA or Kruskal Wallis Test Y is Ordinal or Nominal Y is Ordinal or Nominal If Y has 2 levels then use Logistic Regression If Y has 2 levels then use Logistic Regression If Y has more than 2 levels then use Polytomous 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 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. If either X or Y has more than two levels use a Chi-square Test. X is Continuous X is Ordinal or Nominal

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

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

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

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

9. 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)

10. 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