Hypothesis Testing
A method of statistical inference used to determine whether there is enough evidence in a sample to draw conclusions about a population parameter.
The Process
- 1
State the Hypotheses
Formulate the null hypothesis (H₀) and the alternative hypothesis (H₁)
- 2
Select Significance Level
Choose the significance level (α), commonly 0.05 or 0.01
- 3
Calculate Test Statistic
Compute the appropriate test statistic (t, z, χ², F, etc.)
- 4
Find the p-value
Determine the probability of observing the test statistic or more extreme under H₀
- 5
Make a Decision
Reject H₀ if p-value < α, otherwise fail to reject H₀
- 6
State Conclusion
Interpret the result in the context of the original problem
Key Concepts
Null Hypothesis (H₀)
The statement being tested, typically representing no effect or no difference
Alternative Hypothesis (H₁)
The statement we're looking for evidence to support
Significance Level (α)
The probability threshold for rejecting H₀, representing the risk of Type I error
p-value
The probability of observing the test statistic or something more extreme if H₀ is true
Type I Error
Rejecting H₀ when it is actually true (false positive)
Type II Error
Failing to reject H₀ when it is actually false (false negative)
Common Hypothesis Tests
t-test
Tests hypotheses about means when the population standard deviation is unknown
z-test
Tests hypotheses about means when the population standard deviation is known
Chi-Square Test
Tests for independence between categorical variables or goodness of fit
ANOVA
Tests for differences among means of three or more groups
F-test
Tests for equality of variances between two populations
Wilcoxon Rank-Sum
Non-parametric alternative to t-test for comparing two independent samples