Statistics Refresher – Key Vocabulary

This set of flashcards covers essential vocabulary from the Statistics Refresher chapter, including measurement scales, descriptive statistics, the normal curve, standard scores, correlation, and meta-analysis.

Measurement

Assigning numbers or symbols to characteristics of objects or people according to explicit rules.

Scale

A set of numbers or symbols whose properties model the measured characteristics.

Sample Space

All possible values a variable can assume.

Discrete Scale

A scale with countable values; no values exist between adjacent points.

Continuous Scale

A scale that can take any real value within its range, including fractions and decimals.

Measurement Error

Variation in scores caused by factors other than the trait being measured.

Nominal Scale

Categorizes observations into mutually exclusive, unordered groups (e.g., gender, zip codes).

Ordinal Scale

Ranks observations in a meaningful order without equal intervals between ranks.

Interval Scale

Has equal units throughout the scale but no true zero point (e.g., Celsius temperature).

Ratio Scale

Has equal intervals and an absolute zero, allowing meaningful ratios (e.g., weight, time).

Class Interval

A range of scores grouped together in a frequency distribution.

Frequency Distribution

A table or graph showing how often each score or group of scores occurs.

Grouped Frequency Distribution

A frequency distribution in which scores are combined into class intervals.

Histogram

A graph of contiguous bars representing the frequency of class intervals for quantitative data.

Bar Graph

A graph with separated bars used for categorical data frequencies.

Frequency Polygon

A line graph that connects points representing class-interval frequencies.

Raw Score

An untransformed, original test score.

Distribution

The arrangement of scores or data points, often shown graphically or in tables.

Measure of Central Tendency

A statistic that indicates the center of a distribution (mean, median, mode).

Mean (Arithmetic Mean)

Sum of all scores divided by the number of scores; the average.

Median

The middle score when all scores are ordered; 50% lie above and below.

Mode

The most frequently occurring score in a distribution.

Measure of Variability

Statistic describing spread of scores (range, SD, variance, etc.).

Range

Difference between the highest and lowest scores.

Interquartile Range (IQR)

Distance between the first (Q1) and third quartiles (Q3); middle 50% of data.

Semi-Interquartile Range

Half of the interquartile range; (Q3 – Q1) / 2.

Mean Absolute Deviation (MAD)

Average of the absolute deviations of scores from the mean.

Variance

Mean of the squared deviations from the mean; symbol s² or σ².

Standard Deviation (SD)

Square root of variance; average distance of scores from the mean.

Skewness

Degree of asymmetry in a distribution (positive or negative).

Positive Skew

Distribution with a long tail to the right; few high scores.

Negative Skew

Distribution with a long tail to the left; few low scores.

Kurtosis

Degree of peakedness or flatness of a distribution.

Leptokurtic

A distribution that is more peaked than normal (high kurtosis).

Platykurtic

A distribution that is flatter than normal (low kurtosis).

Mesokurtic

A distribution with kurtosis similar to the normal curve.

Normal Curve

A theoretical, symmetric, bell-shaped distribution with mean = median = mode.

Tail (of a Distribution)

The extreme ends of a distribution beyond ±2 SDs from the mean.

Standard Score

A raw score transformed to a scale with preset mean and SD for easy comparison.

z Score

Standard score with mean 0 and SD 1; indicates SD units above or below the mean.

T Score

Standard score with mean 50 and SD 10; no negative values.

Stanine

Nine-unit standard score scale with mean 5 and SD ≈2; each unit = ½ SD.

Deviation IQ

Intelligence score standardized to mean 100, SD 15 (or sometimes 16).

Linear Transformation

Score conversion that preserves the exact proportional relationships among scores.

Nonlinear Transformation

Conversion that alters proportional relationships, often used to normalize skewed data.

Normalized Standard Score

A score derived after transforming a non-normal distribution to fit the normal curve.

Coefficient of Correlation (r)

Numeric index (−1 to +1) showing strength and direction of relationship between two variables.

Coefficient of Determination (r²)

Proportion of variance in one variable predictable from the other; r squared.

Pearson r

Product-moment correlation for linear relationships between two continuous variables.

Spearman Rho (ρ)

Rank-order correlation used with ordinal data or small samples.

Scatterplot

Graph plotting paired scores (X, Y) to visualize correlation.

Outlier

A data point that lies far from other observations and can distort statistics.

Restriction of Range

Limiting score variability, often reducing observed correlations.

Meta-Analysis

Statistical method combining results of multiple studies to estimate overall effect size.

Effect Size

Quantitative measure of the strength of a phenomenon, often a correlation coefficient.