STAT Exam 3 Vocab and Terminology

α

Significance level

μ

Population mean

μ₁ - μ₂

Population Difference in Means

μ_d

Population mean difference

x̄

Sample mean

x̄₁ - x̄₂

Sample Difference in Means

d̄

Sample mean difference

n

Sample size

σ²

Population variance

s²

Sample variance

σ/√n

Standard error of sample mean

p

Population proportion

p̂

Sample proportion

L(θ)

Likelihood

Statistical Inference

The process of drawing conclusions about a population based on a sample taken from that population

Point Estimation

The process of finding a single number to use as our best guess for the value of the unknown population parameter

Confidence Intervals

A range of values that describes the uncertainty surrounding an estimate of a parameter

Standardization

Transforming a variable by subtracting its mean and dividing by its standard deviation to produce a Z-score

Point Estimator

a statistical function applied to sample data that produces a single numerical value which serves as the best estimate of an unknown population parameter

Point Estimate

The specific numerical value produced by applying a point estimator based on sample data

Population Parameter

An unknown value that describes the population

Sample Statistics

Estimates the population parameter to make inferences using sample data

Discrete Random Variable

A variable that can only take on a countable number of distinct values

Continuous Random Variable

A variable that can take on any value within a given range or interval

Population

The complete set of all individuals or observations of interest in a study

Sample

A subset of the population selected to represent and draw conclusions about the population

Likelihood Function

A function of the parameter(s) rather than of the observed data

Maximum Likelihood Estimation

The method of estimating a population parameter by finding the value (best guess) that makes the observed data most probable

Expected Value

The long-run average value of a random variable, calculated as the weighted average of all possible outcomes

Variance

A measure of the spread of a distribution, calculated as the average squared deviation from the mean

Standard Error

The standard deviation of a statistic

Population Distribution

The distribution describing the values and their probabilities for an entire population

Sample Distribution

The distribution of values observed in a particular sample drawn from the population

Sampling Distribution

The probability distribution of a statistic like a mean or proportion across many repeated samples

Null Hypothesis

A statement describing a claim about a population constant; the default assumption of no effect or no difference

Alternative Hypothesis

A statement describing the researcher’s suspicions about the claim; the claim that contradicts the null hypothesis, representing the effect or difference the researcher is trying to detect

P-Value

The probability of observing our sample result or more extreme results, assuming the null hypothesis is true.

Test Statistic

A numerical value calculated from the sample data that’s used to decide whether to reject the null hypothesis

Power

The probability that the test rejects the null hypothesis when a specific alternative hypothesis is true; Power = 1 - Type 2 Error (β)

Type 1 Error

Rejecting the null hypothesis when it is actually true (false positive); determined by alpha, α

Type 2 Error

Failing to reject the null hypothesis when it is actually false (false negative); determined by beta, β

Statistical Power

The ability to detect a difference, given that one exists