What is the difference between one way and two way ANOVA?

ANOVA stands for Analysis of Variance. It is quite important when it comes to research in economics, biology, and sociology among many other disciplines.

**The core difference between one way and two way ANOVA is that one-way Anova is a hypothesis test used to test the equality of three or more population means simultaneously using variance whereas two-way Anova is a statistical technique wherein, the interaction between factors, influencing variable can be studied.**

The technique employed in the research can be one way or two way ANOVA. The lesson provides the core difference between one way and two way ANOVA.

**What Is One Way ANOVA?**

One way ANOVA refers to a test where one categorical variable or single factor is taken into consideration. The technique helps to compare the means of three or more samples.

The null hypothesis (H_{0}) is the equality in all population means, while alternative hypothesis (H_{1}) will be the difference in at least one mean.

**Main Assumptions of One Way ANOVA**:

- The measurement of the dependent variable is an interval or ratio level.
- Two or more than two categorical independent groups in an independent variable.
- Independence of samples
- Homogeneity of the variance of the population.

**What Is Two Way ANOVA?**

Two way ANOVA is a hypothesis test that examines the impact of two independent factors on a dependent variable.

The test deals with the study of inter-relationship between independent variables that influence the value of dependent variables.

**Main Assumptions of Two Way ANOVA**

- Normal distribution of the population from which the samples are drawn.
- Measurement of the dependent variable at a continuous level.
- Two or more than two categorical independent groups in two factors.
- Categorical independent groups should have the same size.
- Independence of observations
- Homogeneity of the variance of the population.

**Read More: Difference between If-else and Switch Case**

**Comparison Chart: One Way Vs Two Way ANOVA**

Basic Terms |
One Way ANOVA |
Two Way ANOVA |

Meaning | Refers to a test where one categorical variable or single factor is taken into consideration. | Refers to a hypothesis test that examines the impact of two independent factors on a dependent variable. |

Independent Variable | One | Two |

Comparisons | Three or more samples | Effect of multiple levels of two factors |

Number of observations | No need to be the same in each group | Need to be equal in each group |

Design of experiment | Need to satisfy only two principles | All three principles must be satisfied |

**Main Difference between One Way and Two Way ANOVA**

- The number of groups of samples in on way ANOVA is three or more while two way has multiple samples in each variable
- The number of the independent variables in one way ANOVA is one while in two way ANOVA is two.
- The design of the experiment in one way ANOVA need to satisfy only two principles while in two way ANOVA all the three principles
- The number of observation in one way ANOVA need not to be the same while in two way ANOVA need to be equal in each group.
- One way ANOVA refers to a hypothesis test where one categorical variable or single factor is taken into consideration while two ways is a hypothesis test that examines the impact of two independent factors on a dependent variable.

**Comparison Video**

**Summary**

The core difference between one way ANOVA and Two Way ANOVA is the one way has one independent variable while two way has two independent variables. Besides that, the number of observation in one way needs not to be same while in two way need to be equal in each group.

**More Sources and References**

- https://medium.com/@StepUpAnalytics/anova-one-way-vs-two-way-6b3ff87d3a94
- https://www.investopedia.com/terms/t/two-way-anova.asp
- https://en.wikipedia.org/wiki/One-way_analysis_of_variance