Hypothesis Testing: Principles and Applications

Hypothesis Testing

A statistical method used to make decisions based on data by testing a null hypothesis against an alternative hypothesis.

Null Hypothesis (H0)

The hypothesis that specifies a particular value of a parameter, often representing the status quo.

Alternative Hypothesis (H1 or HA)

The hypothesis that specifies other possible values of a parameter, representing a deviation from the null hypothesis.

Test Statistic

A value calculated from sample data used to evaluate the null hypothesis.

P-value

The probability of observing a test statistic as extreme or more extreme than the one calculated, assuming the null hypothesis is true.

Significance Level

A pre-specified threshold used to decide whether to reject the null hypothesis, typically set at 0.05.

One Sample t-test

A test used to determine if the mean of a single population differs from a specified value when the population standard deviation is unknown.

Two Sample t-test

A test used to compare the means of two populations.

Analysis of Variance (ANOVA)

A statistical method used to compare the means of more than two groups.

F-test

A test used in linear regression to assess the significance of the overall model.

Likelihood-Ratio Test

A general hypothesis test used to compare nested models in statistical analysis.

Wald Test

A hypothesis test used in logistic regression to test if a single parameter is equal to zero.

Breusch-Pagan Test

A test used to assess homoscedasticity (constant variance) in the errors of a linear model.

Degrees of Freedom

A parameter that affects the shape of certain statistical distributions based on sample size.

Standard Error

The estimated standard deviation of the sampling distribution of a statistic.

Multiple Testing

The need to adjust the significance level when performing multiple hypothesis tests to control the family-wise error rate.

Causality

The principle that hypothesis tests can only detect associations but cannot establish causality.

Model Hierarchy

The rule that interaction effects should be tested first before testing main effects in statistical models.