Lesson 12 - R

1
Lesson 12 - R

• Chapter 12 Review

2
Objectives

• Summarize the chapter
• Define the vocabulary used
• Complete all objectives
• Successfully answer any of the review exercises
• Use the technology to compute required objectives

3
Key Concepts

• Expected Counts in a Goodness of Fit Test
  Ei µi npi for i 1, 2, , k
• Chi-Square Test Statistic
• (Oi Ei)2
• ?2 S ------------ for
  i 1, 2, , k Ei
• Expected Frequencies in a Test for Independence
• 
  (row total)(column total) Expected Frequency
  ------------------------------------
  table
  total

4
Marginal Distributions

• Marginal Distributions are along the end of the
  rows or the columns of a contingency table
• Marginal Distributions effectively take out the
  other variable in the table
• Marginal Distributions help calculated Expected
  values for Independence test using (through use
  of Multiplication Law of Probability)

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Requirements

• Goodness-of-Fit Test
• all E(xi) 1
• no more than 20 of E(xi) lt 5
• Independence
• same as Goodness-of-Fit Test
• Homogeneity
• same as Goodness-of-Fit Test

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Problem 1

• Which probability distribution do we use when we
  want to test the counts of a categorical
  variable?
• The normal distribution
• The chi-square distribution
• The t-distribution
• The categorical distribution

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Problem 2

• In the test of a categorical variable, to compare
  the observed value O to the expected value E, we
  use the quantity
• O E
• E O
• E2 O2
• (E O)2 / E

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Problem 3

• A contingency table has what types of marginal
  distributions?
• A row marginal distribution and a column marginal
  distribution
• A marginal distribution for each combination of
  row and column value
• One marginal distribution that summarizes the
  entire set of data
• A different marginal distribution for each
  different relative frequency

9
Problem 4

• If a contingency table has variables Gender and
  Color of Eyes, then which of the following is a
  conditional distribution?
• The number of males with blue eyes
• The number of females who have either brown eyes
  or green eyes
• The proportion of the population who are male
• The proportion of females who have blue eyes

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Problem 5

• In a contingency table where one variable is Day
  of Week and the other variable is Rainy or
  Sunny, a test for independence would test
• Whether rainy days are independent of sunny days
• Whether rainy or sunny days are independent of
  the day of the week
• Whether Sundays are independent of Saturdays
• Whether weekdays are independent of weekends

11
Problem 6

• For a study with row variable Color of Car and
  column variable Gender, if 18 of males have
  blue cars, then the null hypothesis for the test
  for homogeneity would assume that
• 18 of males have white cars
• 18 of males do not have blue cars
• 18 of females do not have white cars
• 18 of females have blue cars

12
Summary and Homework

• Summary
• We can use a chi-square test to analyze the
  frequencies from categorical data
• For the analysis of one categorical variable, we
  can use the chi-square goodness-of-fit test
• For the analysis of two categorical variables in
  a contingency table, we can
• Use the test for independence to analyze whether
  the two variables are independent
• Use the test for homogeneity to analyze whether
  the proportions are equal
• Homework
• pg 662 - 667 1, 4, 5, 11, 12, 16

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Even Homework Answers

• 4 a) Reject H0 school crime has become more
  violent sum of chi-sq is 1448.31 (way
  out in the tail!)
• 12 a) FTR H0, not enough evidence to support the
  claim that martial status and gender are
  independent pvalue 0.1811596, Chi-Sq
  Test 4.8753
• 16 a) Mohr in both positions b) Erstad
  c) Mohrs more at-bats with runners in
  scoring position dragged his overall average down
  more than Erstads.