Hypothesis Testing Study Guide

A set of vocabulary flashcards based on key concepts and terms related to hypothesis testing.

Hypothesis

A testable prediction about relationships, effects, or differences.

Null Hypothesis (H₀)

States there is no change, no effect, no relationship, no difference.

Alternative Hypothesis (H₁)

States there is a change, effect, relationship, or difference.

Two-tailed Hypothesis

Tests for any difference (≠).

One-tailed Hypothesis

Tests for a directional difference (> or <).

Significance Level (α)

Pre-set cutoff (usually 0.05), the probability of Type I error.

p-value

Probability of observing the data (or more extreme) if H₀ is true.

Critical Value

The z or t cutoff that defines the rejection region for H₀.

Test Statistic

The calculated z or t score from your data, compared to the critical value.

Type I Error (α)

Rejecting H₀ when it is true (false positive).

Type II Error (β)

Failing to reject H₀ when it is false (false negative).

Power (1 – β)

Probability of correctly rejecting H₀ when H₁ is true.

Z-Test Statistic

Used when the population standard deviation (σ) is known and the sample is large.

t-Test Statistic

Used when the population standard deviation (σ) is unknown.

Independent Samples

Comparing two independent groups for differences in means.

Reject H₀ Decision Rule

If p < α, then reject the null hypothesis.

Fail to Reject H₀ Decision Rule

If p ≥ α, then fail to reject the null hypothesis.

Critical Value Rule

Defines rejection regions for hypothesis testing.

Normal Distribution

A probability distribution that is symmetric about the mean.

Degrees of Freedom (df)

Calculated as n - 1 for a single sample.

Significance Level Interpretation

The maximum risk of Type I error that a researcher is willing to take.

Power of a Test

The ability of a test to correctly reject a false null hypothesis.

Two-sample t-test

Used to compare the means of two independent samples.

Z-Critical Value

The value that defines the cutoff for the significance level in z-tests.

t-Critical Value

The value that defines the cutoff for the significance level in t-tests.

Population Mean (μ)

The mean of the entire population from which a sample is taken.

Sample Mean (x̄)

The average of the sample data.

Standard Deviation (σ)

A measure of the amount of variation or dispersion in a set of values.

Sample Standard Deviation (s)

An estimate of the standard deviation of the population based on the sample.

Test Region

The part of the distribution where we reject the null hypothesis.

Rejection Region

The range of values for the test statistic that leads to rejection of H₀.

Error Types

Refers to Type I and Type II errors in hypothesis testing.

Directionality in Testing

Refers to whether a test is one-tailed or two-tailed.

Hypothesis Formulation

The process of stating the null and alternative hypotheses.

Sample Size (n)

The number of observations in a sample used for hypothesis testing.

Comparison of Means

Analyzing the difference between two sample means.

Testing Procedure Steps

The systematic approach followed in hypothesis testing.

Interpretation of Findings

Understanding what statistical outcomes imply about hypotheses.

p-value Calculation

The method to determine the probability associated with the observed data.

Significance Threshold

The predetermined level at which results are considered statistically significant.

Statistical Significance

When the p-value is less than the significance level.

Effect Size

A quantitative measure of the magnitude of a phenomenon.

Confidence Interval

A range of values used to estimate the true parameter value.

Test Assumptions

The conditions that must be met for the results of a test to be valid.

Null Hypothesis Example

H₀: μ₁ = μ₂ (no difference between means).

Alternative Hypothesis Example

H₁: μ₁ ≠ μ₂ (a difference exists between means).

Decision Criteria

Rules established to determine whether to reject or fail to reject H₀.

One-tailed Test Example

H₁: μ > 100 (looking for an increase).

Two-tailed Test Example

H₁: μ ≠ 100 (looking for any change).

Statistical Analysis

The process of collecting and interpreting data to derive conclusions.

Comparison to Critical Value

How the test statistic relates to the z or t-critical values.

Research Hypothesis

The hypothesis that the researcher aims to support.

Null Hypothesis Rejection

The conclusion reached when the evidence suggests H₀ is false.

Retaining Null Hypothesis

The conclusion reached when evidence does not support rejecting H₀.

Robustness of Test

The ability of a statistical test to produce valid results under diverse conditions.

Statistical Power Determinants

Factors influencing the likelihood of correctly rejecting H₀.

Random Sample

A sample that fairly represents a population because each member has an equal chance of inclusion.