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What are the differences between one-way and two-way ANOVA?
Posted May 20, 2022
Answer
| Basis of Diefferentiation | One-way ANOVA | Two-way ANOVA |
| Definition | A statistical test used to determine how one factor affects a response variable | A statistical test used to determine how two factors affect a response variable, and whether or not there is an interaction effect between the two factors on the response variable |
| Number of independent variables or factors | Involves only one independent variable or factor | Involves two independent variables or factors |
| What the test compares | Compares three or more levels (conditions) of one independent variable or factor | Compares the effect of multiple levels of two independent variables or factors |
| Number of observations required | Do not need to be the same in each group | Need to be equal in each group |
| Compliance with principles of design of experiments | Need to comply with only two principles of design of experiments - replication and randomization | Need to comply with all three principles of design of experiments -replication, randomization, and local control |
| Purpose | To determine whether the data collected for one dependent variable are close to the common mean | To determine whether the data collected for two dependent variables converge on a common mean derived from two categories |
| When the test is used | Used when there is only one independent variable with multiple levels | Used when there are two independent variables with multiple levels |
| Example | Testing the relationship between watering frequency and plant growth | Testing the relationship between watering frequency and sunlight exposure on plant growth |
Additional resources
Two-way ANOVA for scalar trajectories, with experimental evidence of non-phasic interactions