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Examining the Relationship Between Two Variables

This document delves into the examination of the relationship between two variables, X and Y, through bivariate analyses. It outlines how to graphically display and statistically analyze the relationship between an explanatory variable (X) and a response variable (Y). Various types of graphical displays and statistical analyses are discussed based on the nature of Y (nominal/ordinal or continuous) and X (nominal/ordinal or continuous). Examples from a low birthweight study illustrate the application of these methods, focusing on the impacts of gestational age and maternal smoking on birthweight.

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Examining the Relationship Between Two Variables

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  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

  4. Type of Analyses

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

  6. 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 ? (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) Example: Low Birthweight Study

  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

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