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).
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?

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. 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

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

6. 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)

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
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
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
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