# ANOVA / F-Test

We use the **ANOVA (Analysis of Variance) **aka **F-Test** when comparing the means of three or more groups.

**One-Way ANOVA**

A one-way ANOVA has one dependent variable and only __one independent variable__ (or factor).

A one-way ANOVA has two hypotheses:

H (null): μ = μ = μ

H (alternative): at least one of the means are not equal.

Example.

**Two-Way ANOVA**

A two-way ANOVA has one dependent variable and __two independent variables__ (factors).

A two-way ANOVA has three null and alternative hypotheses:

H (null): No relationship between Dependent variable and Factor A

H (null): No relationship between Dependent variable and Factor A

H (null): No interaction between Factor A and Factor B

H (alternative): Relationship between Dependent variable and Factor A

H (alternative): Relationship between Dependent variable and Factor B

H (alternative): Interaction between Factor A and Factor B

Examples

Calculators

The easiest way to calculate a z score, and find it's probability (p-value) is to use a statistics calculator.

**Graphing calculators**, **statistical software programs** (such as Excel, SPSS, R), or **free online calculators** are all able to Z-Tests, which give you the z-score and resulting probability for a value in a dataset.

**Next, let's take a break - and then learn more about populations, samples, and hypothesis testing.**

Contact us for practice materials regarding standard deviation, the bell curve, the empirical rule, normal probability, and more.