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Statistics Terms Explained

35+ core statistics terms in plain English — hypothesis testing, distributions, regression, and confidence intervals. Built for intro statistics students.

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A

Alternative Hypothesis
The claim that there is an effect or difference in the population; it is what a hypothesis test looks for evidence to support, in contrast to the null hypothesis.

B

Bias
A systematic error that causes a sample or estimate to consistently differ from the true population value.
Binomial Distribution
A discrete probability distribution giving the number of successes in a fixed number of independent trials, each with the same probability of success.

C

Central Limit Theorem
The principle that the sampling distribution of the sample mean approaches a normal distribution as the sample size grows, regardless of the population's shape.
Chi-Square Test
A test that compares observed counts with expected counts to assess goodness of fit or whether two categorical variables are associated.
Confidence Interval
A range of values, calculated from sample data, that is likely to contain the true population parameter at a stated confidence level, such as 95%.
Confounding Variable
An outside variable related to both the explanatory and response variables that can distort their apparent relationship.
Correlation
A measure of the strength and direction of the linear relationship between two quantitative variables, ranging from -1 to +1.

D

Degrees of Freedom
The number of values in a calculation that are free to vary after constraints are applied; used to determine the shape of distributions such as t and chi-square.
Descriptive Statistics
Methods that summarize and describe the features of a data set, such as the mean, median, and standard deviation.

E

Effect Size
A measure of the magnitude of a difference or relationship that does not depend on sample size.
Empirical Rule
In a normal distribution, roughly 68%, 95%, and 99.7% of values fall within one, two, and three standard deviations of the mean.

H

Hypothesis Test
A procedure that uses sample data to decide whether there is enough evidence to reject a null hypothesis.

I

Inferential Statistics
Methods that use sample data to draw conclusions or make predictions about a larger population.
Interquartile Range (IQR)
The difference between the third quartile (75th percentile) and the first quartile (25th percentile), measuring the spread of the middle 50% of the data.

M

Mean
The arithmetic average of a data set, found by adding all values and dividing by the number of values.
Median
The middle value of an ordered data set; it is resistant to outliers.
Mode
The value that occurs most frequently in a data set.

N

Normal Distribution
A symmetric, bell-shaped continuous probability distribution defined by its mean and standard deviation.
Null Hypothesis
The default assumption that there is no effect or no difference; a hypothesis test evaluates whether the data provide enough evidence to reject it.

O

Outlier
A data point that lies unusually far from the other values in a data set.

P

p-Value
The probability of obtaining results at least as extreme as those observed, assuming the null hypothesis is true.
Population
The entire group of individuals or items about which conclusions are to be drawn.

R

R-Squared (R²)
The proportion of the variation in the response variable that is explained by a regression model.
Regression Analysis
A method for modeling the relationship between a response variable and one or more explanatory variables.

S

Sample
A subset of a population from which data are actually collected.
Sampling Distribution
The distribution of a statistic, such as the sample mean, across all possible samples of the same size drawn from a population.
Significance Level (α)
The threshold probability, commonly 0.05, below which the null hypothesis is rejected; it equals the probability of a Type I error when the null hypothesis is true.
Simple Random Sample
A sample chosen so that every possible sample of the given size has an equal chance of being selected.
Standard Deviation
A measure of how spread out values are around the mean, expressed in the same units as the data.
Standard Error
The standard deviation of a sampling distribution; it estimates how much a sample statistic varies from sample to sample.
Statistical Significance
A result that is unlikely to have occurred by chance alone, typically judged by a p-value below a chosen significance level.

T

t-Test
A test that compares means using the t distribution, typically when the population standard deviation is unknown and the sample is small.
Type I Error
Rejecting a null hypothesis that is actually true; a false positive.
Type II Error
Failing to reject a null hypothesis that is actually false; a false negative.

V

Variance
A measure of spread: the average of the squared deviations from the mean, dividing by n for a population or by n - 1 for a sample; it is the square of the standard deviation.

Z

Z-Score
The number of standard deviations a value lies above or below the mean.

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