Chapter 11: Inference for Distributions of Categorical Data

What information does a side by side bar chart show?

The difference between each bar.

Explain how to construct a side by side bar chart?

Label the X axis the with the categories and the Y axis with the unit of measurement.

What is the chi-square statistic?

The measure of how far the observed counts are from the expected counts.

What is the difference between the notation X2 and x2?

X 2 represents a variable squared. χ2 is a test statistic, Chi, like z or t.

How do we calculate degrees of freedom does the chi square Goodness of fit test?

df = k-1 where k represents the number of categories

As the chi-square statistic increases, what happens to the P-value?

As chi-square statistic increases, P-value decreases

What is the domain of a chi square distribution?

All positive numbers

What is the shape of a chi square distribution? What happens to the shape as the degrees of freedom increases?

The χ2 distribution only have positive values and are skewed to the right. As the degrees of freedom increases the shape becomes more normal.

State the null and alternative hypotheses for the chi-square goodness of fit test?

H0: the actual population proportions are equal to the hypothesized proportions

Ha: actual population proportions are not equal to the hypothesized proportions

What conditions must be met in order to use the chi square goodness of fit test?

SRS= Independence

10%= less then 1/10N

Large Count= all expected counts are at least 5

What is meant by a component of chi square?

A component of chi-square is one term of the sum which comprises the chi-square statistic.

What does the largest component of chi square signify?

The largest component is the part of the distribution where the largest change has occurred or where there is the largest deviation from the expected distribution.

Why is it necessary to perform follow up analysis to a chi square test?

If the χ2 tests allow us to reject the null hypothesis that all proportions are equal to the hypothesized values, we want to do a follow-up analysis to decide which of the parameters differ and to estimate how large the differences are.

What information is contained in a two-way table for a chi square test?

Counts of categories for the various populations.

How do you calculate the expected count in any cell of a two-way table when the null hypothesis is true?

Expected count= (row total)(column total)/ (grand total)

How many degrees of freedom does a chi square test for a two-way table with r rows and c columns have?

df = ( r-1 ) ( c-1 )

How do we distinguish between a chi square test of homogeneity and a chi square test of association?

Chi square test of independence which help us find whether 2 or more attributes are associated or not.

Chi square test of homogeneity is an extension of chi square test of independence which compares 2 or more sample populations.

What are the differences between a one way table and a two way table?

In a one way table we use C or T test but on a two way table we use a Chi square or homogeneity test.