STAT 164 - 3RD LE - CHAPTER 5.4

CHI-SQUARE TEST

considered as the most commonly used member of the non-parametric family of tests that deals with counts or frequencies

CHI-SQUARE TEST

does not require assumptions about parameters (mean or variance) nor test hypotheses about population parameters

CHI-SQUARE GOODNESS-OF-FIT TEST

Which Analysis of Count Data?

An agriculturist wants to determine if the reported proportions of adults who said that genetically modified food was safe (35%), not safe (52%) or no opinion at all (13%) are true in their locality

CHI-SQUARE GOODNESS-OF-FIT TEST

Which Analysis of Count Data?

The percentage of Americans with each blood type are as follows: 0 (43%), A (40%), B (12%), and AB (5%). Red Cross Organization wants to check if the Filipino population follows the same divisions.

CHI-SQUARE GOODNESS-OF-FIT TEST

Which Analysis of Count Data?

Investigating if the observed phenotypic ratios in a dihybrid cross of heterozygous individuals follow the expected 9:3:3:1 ratio.

CHI-SQUARE GOODNESS-OF-FIT TEST

Which Analysis of Count Data?

Determining whether cats equally prefer different brands of cat food. Will the preference for each of the 5 brands of cat food be equal, with 20 cats preferring each brand, among a group of 100 cats?

CHI-SQUARE GOODNESS-OF-FIT TEST

used to test whether a frequency distribution fits a specific pattern

Assumption

• The expected frequency for each category must be at least 5.

CHI-SQUARE GOODNESS-OF-FIT TEST

determines whether observed frequencies of a categorical data collected from a single sample matches the expected distribution.

• Tests only a single sample/set of samples

CHI-SQUARE GOF TEST, Test of Hypothesis

provide the following:

• Ho (in words):

• Ha (in words):

• Test Procedure:

• Test Statistic:

• Decision Rule:

CHI-SQUARE GOF TEST, provide the following:

• Ho (in words):

• Ha (in words):

• Decision Rule:

• Test Statistic:

Then provide the following:

• Decision:

• Conclusion:

CHI-SQUARE GOF TEST, provide the following:

• Ho (in words):

• Ha (in words):

• Decision Rule:

• Test Statistic:

Then provide the following:

• Decision:

• Conclusion:

CHI-SQUARE TEST OF HOMOGENEITY

Which Analysis of Count Data?

A geneticist wanted to determine if the distribution of phenotypic traits is consistent or different between two groups of individuals, each group having a unique genotype.

CHI-SQUARE TEST OF HOMOGENEITY

Which Analysis of Count Data?

There are three possible behaviors that may occur when dogs are subjected to a certain stimulus. An animal behavior researcher wanted to know if the proportions of these three behaviors are equal between domesticated dogs and wild dogs.

CHI-SQUARE TEST OF HOMOGENEITY

Which Analysis of Count Data?

To understand patterns of biodiversity, a study investigated whether the number of species is consistent among different types of habitat

CHI-SQUARE TEST OF HOMOGENEITY

Which Analysis of Count Data?

In a clinical trial, the response to a new drug was tested between blood cancer patients and skin cancer patients. They observed if the drug will be effective with adverse effects, effective without adverse effects, ineffective with adverse effects, or ineffective without adverse effects.

CHI-SQUARE TEST OF HOMOGENEITY

used to test whether the proportions for a variable are equal when several samples are selected from different and independent populations

• CHI-SQUARE TEST OF HOMOGENEITY

• CHI-SQUARE TEST OF INDEPENDENCE

CHI-SQUARE TEST OF HOMOGENEITY, Test of Hypothesis

provide the following:

• Ho (in words):

• Ha (in words):

• Test Procedure:

• Test Statistic:

• Decision Rule:

CHI-SQUARE TEST OF HOMOGENEITY, provide the following:

• Ho (in words):

• Ha (in words):

• Decision Rule:

• Test Statistic:

Then provide the following:

• Decision:

• Conclusion:

CHI-SQUARE TEST OF HOMOGENEITY, provide the following:

• Ho (in words):

• Ha (in words):

• Decision Rule:

• Test Statistic:

Then provide the following:

• Decision:

• Conclusion:

CHI-SQUARE TEST OF INDEPENDENCE

Which Analysis of Count Data?

A researcher wishes to determine whether there is a relationship between the gender of an individual and the amount of alcohol consumption (low, moderate, high).

CHI-SQUARE TEST OF INDEPENDENCE

Which Analysis of Count Data?

A wildlife conservationist wanted to assess whether the class of vertebrate is associated with whether it is endangered or threatened

CHI-SQUARE TEST OF INDEPENDENCE

Which Analysis of Count Data?

An inheritance study wanted to determine whether presence of genetic markers is associated with the stages of a specific disease.

CHI-SQUARE TEST OF INDEPENDENCE

Which Analysis of Count Data?

A clinical trial assessed whether there is significant association between the dose of a drug and the occurrence of adverse side effects.

CHI-SQUARE TEST OF INDEPENDENCE

• also called Chi-square Test of Associatio

• hypothesizes about the presence of a relationship or association between two qualitative variables observed from a single sample.

independent groups; related variables

If Chi-square test of homogeneity uses _____________, Chi-square test of independence uses _____________ since both were observed from a single set of units.

CHI-SQUARE TEST OF INDEPENDENCE, Test of Hypothesis

provide the following:

• Ho (in words):

• Ha (in words):

• Test Procedure:

• Test Statistic:

• Decision Rule:

CHI-SQUARE TEST OF HOMOGENEITY, provide the following:

• Ho (in words):

• Ha (in words):

• Decision Rule:

• Test Statistic:

Then provide the following:

• Decision:

• Conclusion:

CHI-SQUARE TEST OF HOMOGENEITY, provide the following:

• Ho (in words):

• Ha (in words):

• Decision Rule:

• Test Statistic:

Then provide the following:

• Decision:

• Conclusion:

What is the condition needed for each of the following measures of association and their corresponding formula?

• Phi coefficient

• Contingency coefficient

• Cramer’s V

Solve and interpret for the appropriate measures of association.