I was reading a synopsis where a student used 1 way ANOVA and 2way Anova, while seeing the effect of independent variable on dependent variable. Is this possible while 1way ANOVA is used to compare more than three groups and 2way is ahead of this. Or that synopsis is objectionable?
The model behind a 2w-ANOVA with interactions is equivalent to the 1w-ANOVA over all level-combinations. It's sometimes easier to adress a particular contrast via a 1w-formulation. However, the 1w-formulation does not give you the usually interesting interactions.
A 2w-ANOVA without interactions is different to the 1w-ANOVA, because it pools across the levels of the other factor.
Just to recap and add something.
To compare means between two groups, t-test and ANOVA give the same results.
Moreover, ANOVA is useful in case of more groups and/or interaction to be tested
Regarding the assumptions, one is the normality, but do not be strict with normality test that are not usually powerful. Look to the symmetry and, if possible, increase the replications.
Other assumption is the homoscedasticity. It is the most stringent assumption to be tested.
Regarding p-value, do not be strict to “classic” p-values. There are a lot of papers that explain how to use correctly the p-value, and one of them is attached.
Thank you for valuable guidance Jochen Wilhelm sir and Roberto Molteni sir.
1. A one-way ANOVA is primarily designed to enable the equality testing between three or more means. A two-way ANOVA is designed to assess the interrelationship of two independent variables on a dependent variable.
2. A one-way ANOVA only involves one factor or independent variable, whereas there are two independent variables in a two-way ANOVA.
3. In a one-way ANOVA, the one factor or independent variable analyzed has three or more categorical groups. A two-way ANOVA instead compares multiple groups of two factors.
4. One-way ANOVA need to satisfy only two principles of design of experiments, i.e. replication and randomization. As opposed to Two-way ANOVA, which meets all three principles of design of experiments which are replication, randomization, and local control.
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