Chapter 2: Generalization and Inference for a Single Quantitative Variable

Flashcards covering key vocabulary and concepts for inference involving a single quantitative variable, including summary statistics, types of data skew, hypothesis testing components, and the theory-based approach with standardized statistics and standard error.

Summary Statistics

Statistics calculated from a sample that provide numeric information about the sample.

Mean / Average

Calculated by adding up all the values first, then dividing by the total number of values.

Median

The 'middle' value when data is ordered, where half of the data is above and half is below.

Outliers

Unusual data points in a dataset.

Robust (summary statistic)

A summary statistic whose value does not change much when outliers are included.

Skew

A description for a distribution that is not symmetric.

Right skewed

A distribution where the tail is on the right, pulling the mean toward the longer tail.

Left skewed

A distribution where the tail is on the left, pulling the mean toward the longer tail.

Sample mean (ҧ𝑥)

The observed statistic calculated from a sample.

Sample Standard Deviation (𝑠)

A measure of the spread of data in a sample.

Population Mean (𝜇)

The hypothesized value for the average of an entire population.

Population Standard Deviation (𝜎)

A measure of the spread of data in an entire population.

Parameter (for quantitative variable)

Represents the 'long-run average' in a given context (symbolized by 𝜇).

Null Hypothesis (𝐻0 for quantitative)

States that the long-run average of the context is equal to a previously known number.

Alternative Hypothesis (𝐻𝐴 for quantitative)

States that the long-run average of the context is greater than, less than, or different from a previously known number.

Standard Error (SE)

An approximation of the standard deviation of the sample mean, calculated as s / √n (where 's' is sample standard deviation and 'n' is sample size).

Standardized Statistic

Calculates how many standard deviations from the null value that the observed statistic falls.

t-statistic

A type of standardized statistic used for quantitative variables when the population standard deviation is unknown, calculated as (sample mean − population mean) / Standard Error.

t distribution

A reference distribution used with the t-statistic for quantitative data, different from the Z (Standard Normal) distribution.

Validity Conditions (Theory Based Approach for Quantitative Data)

One of two conditions must hold: 1) The quantitative variable should have a symmetric distribution, OR 2) The sample size is ≥ 20 and the sampling distribution is not strongly skewed.