UCLA  STAT 13
 Introduction to Statistical Methods for the Life and Health Sciences

Chapter 11:  Tables of Counts

Chapter 11:  Tables of Counts

1-dimensional tables –
classify n-individuals in J-categories

1-dimensional tables cont.

Chi-Square Test – goodness of fit test

Example of 1D table – Three blood types

Example of 1D table – rolling a single die

Slide 9

Slide 10

Slide 11

Slide 12

The Chi-square distribution

Lotto after 399 numbers have been drawn –
Do some numbers appear more frequently in LOTTO?

Lotto after 399 numbers have been drawn –
Do some numbers appear more frequently in LOTTO?

 Review

Review

Two-way tables

Melanoma by Site and Type, e.g., 4.6.2

Proportions of all 400 patients
entry = count/400

Remember plot/graph/look at your data first!

Remember plot/graph/look at your data first!

From the row totals we get ….

Slide 24

Example - Blood types

Example - Blood types

Row distributions

Slide 28

Slide 29

Notation

Chi-Square Test
(for either homogeneity or independence)

Chi-square test output – Cancer Type/Site

Comments

Comments

Comments

Degrees of freedom – since there are n-1 free parameters, for colums and rows, row/comun sums must equal 1 (or n)

Dangers of collapsing tables -Simpson’s paradox

Chapter 11 Summary

General Ideas about Chi-Square Tests

Chi-square tests cont.

Warning about Chi-square

One-Dimensional Tables

One-dimensional tables cont.

Two-Way Tables

Warning

Two-way tables cont.

Row distributions

Column Distributions

Whole-table Proportions