Stats - Section 2.1 Quiz

A set of practice questions (Question and Answer style) covering descriptive statistics for one and two categorical variables, as well as related visualizations and examples from the lecture notes.

What is Descriptive Statistics (also known as exploratory data analysis)?

Methods to summarize and visualize data; the choice of summaries/visualizations depends on whether variables are categorical or quantitative.

What are the two broad variable types considered in descriptive statistics?

Categorical and quantitative (numerical) variables.

For one categorical variable, what are the main summary statistics?

Proportion, frequency table, and relative frequency table.

For one categorical variable, what visualizations are typically used?

Bar chart and pie chart.

What is a frequency table?

A table that shows the number of cases in each category.

What is a proportion in a category?

The proportion is the count in that category divided by the total; for samples use p-hat, for populations use p.

What is a relative frequency table?

A table showing the proportion of cases in each category; the numbers sum to 1.

In the Water Preferences data, what is the total number of observations used to compute the relative frequencies?

100 (the counts 10, 25, 41, and 24 sum to 100).

What is a bar chart as used in one categorical variable analysis?

A chart where the height of each bar represents the number (or proportion) of cases in that category.

What is a pie chart as used in one categorical variable analysis?

A chart where each slice’s relative area represents the category’s proportion.

What is a two-way table?

A table that displays counts for combinations of two categorical variables; it doesn’t matter which variable is in rows or columns.

What is a difference in proportions?

The difference between two proportions calculated for different levels of the other categorical variable (e.g., proportion of females in a relationship minus proportion of males in a relationship).

How is the difference in proportions computed in the example with relationship status?

Difference = (proportion of females in a relationship) − (proportion of males in a relationship); numerically, 32/42 − 63/108 = 0.762 − 0.583 = 0.179.

What is a side-by-side bar chart?

A visualization where bars for the two categories are displayed side by side for comparison.

What is a segmented (stacked) bar chart?

A bar chart where each bar is segmented (stacked) to show the distribution within the categories.

What are the two categorical variables used in the university students example?

Relationship status and gender.

In the Vitamin D injections study, what are the two categorical variables?

Type of vitamin D injection (Calcitriol vs Paricalcitol) and survival outcome (Survived vs Died).

What do p-hat and p represent in proportions?

p-hat is the proportion estimated from a sample; p is the population proportion.

What is the difference between Descriptive Statistics and Inferential Statistics?

Descriptive Statistics summarize and visualize data; Inferential Statistics draw conclusions about a population from a sample.

Does it matter which variable is displayed in the rows or columns of a two-way table?

No; it does not matter which variable is in rows or columns.

What is a two-way table’s total in the provided example (the sex and relationship status data)?

169.