Practice Test: Statistics Lectures 3–6 and R Labs 2–3

Vocabulary practice flashcards covering statistical hypothesis testing, errors and power, Normal models, data display principles, and descriptive summary statistics from Lectures 3–6 and R Labs 2–3.

Type I Error

The mistake of rejecting the null hypothesis ($H_0$) when it is actually true; its probability is denoted by the significance level ($\alpha$).

Type II Error

The mistake of failing to reject the null hypothesis ($H_0$) when it is actually false; its probability is denoted by $\beta$.

Power

The probability of rejecting the null hypothesis ($H_0$) when it is false, calculated as $1 - \beta$.

Significance Level ($\alpha$)

The predetermined threshold for the probability of committing a Type I error (rejecting $H_0$ when $H_0$ is true), chosen before data collection.

P-value

The probability of observing data at least as extreme as the observed sample results, assuming that the null hypothesis ($H_0$) is true.

Effect Size

The distance between the true population parameter and the null hypothesis value; larger values increase the power of a statistical test.

Large Counts Condition (One-Proportion)

A condition for using the Normal model in a one-proportion test, requiring that both expected counts, $n \cdot p_0$ and $n \cdot (1 - p_0)$, are at least $10$.

Large Counts Condition (Two-Proportions)

A requirement for testing the difference between two proportions stating that the counts of successes and failures in each independent group must all be at least $10$.

z-Score

A standardized measure that describes the number of standard deviations a data value falls above or below the mean.

68-95-99.7 Rule

An empirical rule for Normal models stating that approximately $68\%$ of observations lie within $1\,\text{SD}$, $95\%$ within $2\,\text{SD}$, and $99.7\%$ within $3\,\text{SD}$ of the mean.

Area Principle

A data display principle stating that the visual area occupied by a graphic element must correspond directly to the magnitude of the data value it represents.

Histogram

A graphical display of quantitative data that divides values into adjacent bins and uses the heights of bars to show frequencies or relative frequencies, revealing distribution shape.

Stemplot

A display for quantitative data that separates each value into a leading digit (stem) and a final digit (leaf), showing the shape of the distribution while retaining the original data values.

Skewed to the Left

A distribution shape in which the tail extends farther toward the lower values on the left side, typically pulling the mean below the median.

Skewed to the Right

A distribution shape in which the tail extends farther toward the higher values on the right side, typically pulling the mean above the median.

Five-Number Summary

A concise summary of a quantitative distribution consisting of the minimum, first quartile ($Q1$), median, third quartile ($Q3$), and maximum.

Interquartile Range (IQR)

A resistant measure of spread calculated as the distance between the third and first quartiles ($\text{IQR} = Q3 - Q1$), containing the central $50\%$ of the data.

1.5 \times IQR Rule

A criterion designating an observation as an outlier if it lies below $Q1 - 1.5 \times \text{IQR}$ or above $Q3 + 1.5 \times \text{IQR}$.

Boxplot

A visual display of the five-number summary featuring a central box between $Q1$ and $Q3$, a line at the median, whiskers extending to the most extreme non-outlier points, and individual marks for outliers.

Shift (Adding a Constant)

The transformation of adding a constant to every observation, which increases measures of position (mean, median) by that constant while leaving measures of spread ($\text{SD}$, $\text{IQR}$) unchanged.