Statistical Tests

Title
Test of one mean
Two means comprison test
One proportion test
Two proportions comparison test
One variance test
Two variances comparison test
One correlation test
One way anova
Chi squared test of independance

What is a Statistical Test?

A statistical test provides a mechanism for making quantitative decisions about a process or processes. Generally, the purpose is to determine whether enough evidence exists to reject a null hypothesis (\(H_0\)) in favor of an alternative hypothesis (\(H_1\)).

Types of Statistical Tests

There are numerous statistical tests, each suited for different types of data and hypotheses. Some common tests include:

Z-test: Used for comparing the mean of a sample to a known value, usually in large samples.
T-test: Used to compare the means of two groups, especially useful when the sample sizes are small.
Chi-squared test: Used to determine whether there is a significant association between categorical variables.
ANOVA: Used to compare the means among three or more groups.

Hypothesis Testing Framework

The general steps in hypothesis testing are:

State the Hypotheses:
- Null hypothesis (\(H_0\));
- Alternative hypothesis (\(H_1\));
Choose the Appropriate Test: Select the statistical test that fits the data and the research question;
Set the Significance Level \(\alpha\): Commonly set at \(\alpha=5\%\);
Calculate the Test Statistic: Based on the sample data, compute a statistic according to the test type;
Decision: Reject or do not reject the null hypothesis based on the p-value or critical value.