Stats Topic 5

Question 1

Single Categorical Variable

Answer 1

• Frequency data represents the count of observations in each category.
• The distribution is often visualized using bar charts or frequency tables.

Question 2

Joint Distribution for Two Categorical Variables

Answer 2

• Examines how data is distributed across combinations of two categorical variables.
• Represented using contingency tables or stacked bar charts.

Question 3

Chi-Square Tests

Answer 3

Chi-square tests are used to determine whether observed categorical data differs from what is expected.

Question 4

Chi-Square Goodness-of-Fit Test:

Answer 4

• Tests whether the observed distribution of a single categorical variable matches an expected distribution.
• Example: Checking if the color distribution of M&M’s matches the expected proportions provided by the company.
• Formula:
  𝑂: is the observed frequency and
  𝐸: is the expected frequency.

Question 5

Chi-Square Test of Independence

Answer 5

Determines whether there is an association between two categorical variables.
Example: Testing if a person’s preference for a drink is related to their gender.
Degrees of Freedom (df) calculation
where
𝑟: is the number of rows and
𝑐: is the number of columns in the contingency table.

Question 6

Statistical Significance

Answer 6

A p-value less than 0.05 leads to rejecting the null hypothesis, indicating a significant association or deviation from the expected distribution.

Question 7

Reporting the Results

Answer 7

When reporting the chi-square test results, include:

1) The type of test used.
2) The null and alternative hypotheses.
3) The observed and expected frequencies.
4) The chi-square statistic and degrees of freedom.
5) The p-value and conclusion (whether to reject or fail to reject the null hypothesis).