Examining the Relationship Between Two Variables

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
Fit Y by X in JMP
In the lower left corner of the Fit Y by X dialog
box you will see this graphic which is the same
as the more stylized version on the previous
slide.
Y Variable/Response Data Type
X Variable/Predictor Data Type
5
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
6
Type of Analyses
Y is Continuous Correlation and Regression - Parametric or Nonparametric If X has k 2 levels then Two-Sample t-Test or Wilcoxon Rank Sum Test. If X has k gt 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 Fishers Exact Test, RR/OR, and Risk Difference/AR If either X or Y has more than two levels use a Chi-square Test. McNemars Test (dependent)
X is Continuous X is Ordinal or Nominal
7
Fit Y by X in JMP
Y nominal/ordinal Y continuous
X continuous X nominal/ordinal
8
Example Low Birthweight Study(Note This is
not NC one)

• 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 mothers age
• mnocig mothers cigarettes/day
• mheight mothers height (in.)
• mppwt mothers pre-pregnancy
• weight (lbs.)

• fage fathers age
• fedyrs fathers education (yrs.)
• fnocig fathers cigarettes/day
• fheight fathers height
• lowbwt low birth weight indicator
• (1 yes, 0 no)
• mage35 mothers age over 35 ?
• (1 yes, 0 no)
• smoker mother smoked during preg.
• (1 yes, 0 no)
• Smoker mothers smoking status
• (Smoker or Non-smoker)
• Low Birth Weight birth weight
• (Low, Normal)

Continuous Nominal
9
Example Low Birthweight Study(Birthweight vs.
Gestational Age)
Y birthweight (lbs.) Continuous X
gestational age (weeks)Continuous
10
Regression and Correlation Analysis from Fit Y by
X
11
Example Low Birthweight Study(Birthweight vs.
Mothers Smoking Status)
Y birthweight (lbs.) Continuous X mothers
smoking status (Smoker vs. Non-smoker) Nominal
12
Independent Samples t-Test from Fit Y by X
13
Example Low Birthweight Study(Birthweight
Status vs. Mothers Cigs/Day)
Y birthweight status(Low, Normal)Nominal X
mothers cigs./day Continuous
P(LowCigs/Day)
14
Logistic Regression from Fit Y by X
15
Example Low Birthweight Study(Birthweight
Status vs. Mothers Smoking Status)
Y birthweight status(Low, Normal)Nominal X
mothers smoking status (Smoker,
Non-smoker)Nominal
16
Independent Samples p1 vs. p2 - Fishers Exact,
Chi-square, Risk Difference, RR, OR
Skipped the arrows this time, everything should
self-explanatory. Notice the OR is upside-down
and needs reciprocation. OR 1/.342 2.92
17
Summary

• In summary have seen how bivariate relationships
  work in JMP and in statistics in general.
• We know that the type of analysis that is
  appropriate depends entirely on the data type of
  the response (Y) and the explanatory variable or
  predictor (X).