Chi Square Distribution

ChSquare Distribution review

What does chi-square statistic measure?

The distance between values from the observed and expected counts.

What happens to the skewness of the chi square distribution as the df change?

As df decrease, the skewness (to the right) increases, and as df increase, the skewness decreases and the distribution becomes more normal.

Degrees of freedom for a chi square test for goodness of fit?

df = number of categories minus 1

What are the different types of chi square tests?

Goodness of Fit, Homogeneity, Independece

What is a goodness of fit test?

Testing if sample data fits a distribution from a population with a normal distribution (ONE population)

What is a test for independence?

Goal is to determine whether two categorical variables are associated

What is a test for homogeneity?

Goal is to compare distributions of a categorical variable for multiple populations (are they the same?)

A test for goodness of fit has…

A random sample of n and 1 population

A test for homogeneity has…

1 categorical variable and 2 populations

A test for independene has…

2 categorical variable and 1 population

How do you state the null hypothesis for a goodness of fit chi square test?

Equality Statement:

Ho: p1 = p2 =p3 =p4…

and Define parameters (p1, p2, p3, p4…)

“where p1, p2, p3, p4, etc. are the…”

How do you state the alternative hypothesis for a goodness of fit chi square test?

Inequality Statement: (In words)

Ha: “At least one of the proportions is not the same as specified in the null hypothesis”

What are the conditions of a Chi-square goodness of fit test?

Independence:

Random sample/randomized experiment

When sampling without replacement, n ≤ 10% of N

\
Chi Square Distribution:

All expected counts should be greater than 5

How do you find expected counts of a chi square test statistic?

Proportions from null times sample size

Ex: .452(40); .292(40); .256(40)

How do you find expected counts using a two-way table?

(row total)(column total)÷ table total

How do you state the null hypothesis for a chi square test of homogeneity?

Ho: There is no difference in the distribution of (context)

How do you state the alternative hypothesis for a chi square test of homogeneity?

Ha: There is a difference in the distribution of (context)

How do you state the null hypothesis for a chi square test of independence?

Ho: There is no association between (context of two varaibles)

How do you state the alternative hypothesis for a chi square test of independence?

Ha: There is an association between (context of two variables)

What are the conditions of a Chi-square homogeneity test?

Independence:

Stratified random sample or randomized experiment

When sampling without replacement, n ≤ 10% of N

\
Chi Square Distribution:

All expected counts should be greater than 5

What are the conditions of a Chi-square independence test?

Independence:

Single Random Sample

When sampling without replacement, n ≤ 10% of N

\
Chi Square Distribution:

All expected counts should be greater than 5

How do you find the p value of a chi square test for independence or homogeneity?

Use table C:

degrees of freedom

(number of rows -1)x(number of columns -1)