Chi-square Test of Independence for Discrete Data Flashcards
It is one of the most popular methods for testing hypotheses on discrete data.
Chi-square
It only requires simple summary statistics such as frequencies and percentages.
Chi-square
What are used to get meaningful insight from discrete data?
Some chi-square statistics and contingency tables
Examples where chi-square can be used
A researcher want to know if the performance of a firm (loss, breakeven, profit) is dependent on which country (low, middle, high income) it is located in.
Three different types of chi-square analysis
Chi-square for:
- goodness of fit
- homogeneity
- independence
It is used to test the hypothesis that two categorical variables are independent of each other.
Chi-square test of independence
It is used to test if there is no association between the two categorical variables.
Chi-square test of independence
What must be constructed and used to get meaningful insight from the data?
Contingency table
What is the basis of the chi-square test of independence?
The difference between the observed frequency and the expected frequency of each cell of the contingency table.
These are frequencies obtained from the performance of an ecperiment.
Observed frequencies
It is denoted by O.
Observed frequencies
It is denoted by E.
Expected frequencies
These are frequencies that are expected to obtain if the null hypothesis is true.
Expected frequencies
It is calculated by multiplying the total of the roq by the total of the column to which the cell belongs and then dividing by the total sample size.
Expected frequencies
It presents the data in rxc tables.
Contingency Tables
R is what?
number of rows
C is what?
number of columns
What is the table if the row varibale has three categories and the column variable has two categories?
3x2 table
CSCCMC
Hypothesis Testing Using Chi-square
- Construct the contingency table.
- State the hypotheses and set the alpha level.
- Calculate the degree of freedon and the criticial value.
- Calculate the Chi-square value.
- Make a statistical decision.
- Conclude.
Formula for df of a chi-square
df = (r-1)(c-1)
Decision rule using the Fcritical value.
Chi-square value ≤ critical value : Fail to reject the null hypothesis
Chi-square value > critical value : Reject the null hypothesis
Decision rule using the p-value.
p-value ≤ significance level : reject null hypothesis
p-value > significance level : fail to reject null hypothesis
