Difference between one way and two way ANOVA

By Priya Chetty on February 15, 2022

When it comes to research in the field of social sciences, the Analysis of Variance test, shortly known as ANOVA is an extremely important tool. It is a technique employed to make a comparison between more than two populations. The most common variants are one-way and two-way ANOVA. In one-way ANOVA the researcher studies the effect of one element on another.

For example, studying the effect of gender on mobile phone usage. On the other hand, in two-way ANOVA, the researcher studies the effect of two concurrent elements on a third one. Studying the effect of gender and age concurrently on mobile phone usage.

The table below explains in detail the theoretical knowledge surrounding the ANOVA test to show how the one-way and two-way ANOVA methods differ.

Basis of comparisonOne-way ANOVATwo-way ANOVA
Number of Independent VariablesA one-way ANOVA only involves one factor or independent variable.A two-way ANOVA involves two independent variables and one dependent variable.
Number of Groups Of SampleThere is only one independent variable that has multiple groups. For example, ‘Age’ as an independent variable may have multiple groups:
12-18 years
19-26 years
27-35 years
Above 36 years  
Compares multiple groups of two factors.  For example, in addition to ‘Age’, ‘Gender’ may have the following multiple groups:
Male
Female
Prefer not to say
Number Of ObservationsThe number of observations (sample size) need not be the same in each group.  The number of observations (sample size) needs to be the same in each group.  
DescriptionOne-way ANOVA is a hypothesis test that allows one to make comparisons between the means of three or more groups of data.  Two-way ANOVA is a hypothesis test that allows one to make comparisons between the means of three or more groups of data, where two independent variables are considered.
EffectIt accesses only one variable at a given time.It accesses two variables at the same time. It therefore also shows whether there is any interaction effect between the independent variables.

Example How does tea consumption affect weight?

Independent variable: Tea
Green tea
Black tea
Milk tea
No tea

Dependent variable: Weight
Below 50 kg
51-70 kg
71-80 kg
Above 80 kg
How do tea consumption and exercise intensity affect weight?

Independent variable 1: Tea
Green tea
Black tea
Milk tea
No tea

Independent variable 2: Exercise intensity
High intensity
Medium intensity
Low intensity
No exercise

Dependent variable: Weight
Below 50 kg
51-70 kg
71-80 kg
Above 80 kg  
Table 1: Difference between one-way and two-way ANOVA

Applicability of one-way and two-way ANOVA 

The usage of one-way and two-way ANOVA for primary and secondary data is similar. One-way ANOVA would need only one independent variable stated in different categories while two-way ANOVA consists of more than one independent variable. Herein, the applicability mainly varies with the assumptions of the respective ANOVA test. Thus, if the dataset is fulfilling the assumptions, the respective test could be applied.

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