Inference of 2-way Tables

Review…

New Stuff: 2-Way Tables  Looking for Significant difference across 2 variables instead of just 1 (hence, 2-way)  Example: TreatmentNo RelapseYes Relapse Desipramine1410 Lithium618 Placebo420

Cells, Rows and Columns…

Examples : Cocaine  We want to see if there is a significant difference between two possible treatments and a placebo in treating cocaine addiction  Data is in the table below: TreatmentNo RelapseYes Relapse Desipramine1410 Lithium618 Placebo420

Examples , continued…  Find the Row and Column Totals: TreatmentNoYesTotal Desipramine Lithium61824 Placebo42024 Total:244872

Examples , continued… TreatmentNoYesTotal Desipramine Lithium61824 Placebo42024 Total:244872

Examples , continued…  Observed and Expected counts: TreatmentNoYes OEOE Desipramine Lithium Placebo482016

Examples , continued…  Calculate the statistic: TreatmentNoYes OEOE Desipramine Lithium Placebo Total:

Examples : continued…

Examples : Easier

Examples : Easier…

 Difference in a two way table can mean two different things: 1. Homogeneity (Sameness) 2. Association/Independence (Relationship)  Use the Purpose or Context to determine if we are looking for Association or Homogeneity

Homogeneity:  Many SRS’s are drawn from several populations of interest  Observations are recorded for a single categorical variable, within their population  Commonly used to compare several population proportions  The null hypothesis states there is no difference between population proportions  Examples: Treatments and Results

Association Studies:  A single SRS is drawn from a population  Observations are classified in a matrix of two variables  The null hypothesis states that there is not a relationship between the two variables  Examples: Grades and Sleep, Attendance and Grades,

Practice:  Page 766: – 13.28