Stats

Statistics

The science of collecting, organizing, and interpreting data.

Individuals

The objects on which data are collected (e.g., students, states, hospitals).

Variables

Characteristics recorded about individuals.

Quantitative Variables

Numeric values with meaningful operations (e.g., height, weight).

Categorical Variables

Groups or categories (e.g., gender, college type).

Identifier Variables

Unique values assigned to individuals (e.g., ID numbers).

Bar Charts & Pie Charts

Graphs that represent categorical data.

Histograms

Graphs that display quantitative data distributions.

Boxplots

Graphs that compare distributions and identify outliers.

Dotplots & Density Plots

Graphs that represent distributions and trends.

Mean (x̄)

Sum of all values divided by the number of values.

Median (m)

The middle value when data is ordered.

Range

Difference between the largest and smallest values.

Interquartile Range (IQR)

Difference between Q3 (75th percentile) and Q1 (25th percentile).

Standard Deviation (S)

Measures variation around the mean.

Z-Score

Measure of how far a value is from the mean in standard deviations.

68-95-99.7 Rule

Describes Normal Distribution percentages.

Explanatory Variable

The variable suspected to influence another.

Response Variable

The variable that is measured as an outcome.

Simpson’s Paradox

When a relationship between two variables reverses due to a lurking variable.

Proportion

A fraction representing part of a whole (e.g., 0.25 or 1/4).

Percent

A proportion multiplied by 100 (e.g., 0.25 = 25%).

Nominal Variables

Categories without a meaningful order (e.g., colors, names).

Ordinal Variables

Categories with a meaningful order but no consistent difference (e.g., ranking).

Natural Variables

Ordered with meaningful differences (e.g., temperature, income).

Standardizing (Z-score)

Z=X−μσ (Tells how many SDs a value is from the mean).

Shifting

Adding/subtracting a constant affects mean but not spread.

Scaling

Multiplying/dividing a constant affects both center and spread.

Correlation (R-Value)

Measures the strength of a linear relationship between two quantitative variables.

Bimodal Distribution

A distribution with two peaks.

Skewed Distribution

Distribution where one tail is longer than the other.

Symmetric Distribution

A distribution where the left and right sides are mirror images.

Five-Number Summary

Min, Q1, Median, Q3, Max that summarize a dataset.

Outliers

Data points significantly higher or lower than the rest.

Frequency Table

Table listing the number of times categories occur.

Contingency Table

Table showing frequency distribution of variables to examine relationships.

favstats()

An R function providing summary statistics.

histogram()

An R function that generates a histogram to visualize distributions.

tally()

An R function creating frequency tables for categorical data.

bwplot()

An R function generating boxplots to compare distributions.