One way ANOVA and Two way ANOVA

The analysis of variance that is used to compare three or more means is called a ONE-WAY ANALYSIS OF ANOVA since it contains only one variables.
We used F-test to test a hypothesis concerning the means of three or more population.
when we comparing two means, t-test would be used.
Now in this case, we are using F-test for one-way analysis, since we are comparing three or more means.....

the assumption for F-test comparing three or more means:
1. the populations from which the amples were obtained must be normally or approx. normally distributed.
2. the samples must be independent of each other.
3. the variances of populations must be equal.

the following hypotheses should be used:
Ho: mean 1 = mean 2 = mean 3 = ... = mean p
Ha: At least one mean is different from the others.

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The two-way analysis of variance is an extension of the one-way analysis of variance.
It involves two independent variabes. The independent variables are also called factors.

We used two-way ANOVA to determine if there is a significant different in the main effects or interaction.

For example, suppose a reasercher wishes to test the effect of two different types of plant food and two different types of soil on the growth of certain plants. The two independent variables are the types of plant food anf the type of soil, while the dependent variables is the plant growth. Other factors, such as water, temperatre, and sunlight, are held constant.

The two-way ANOVA has several hypotheses:
1. Ho: there is no interaction between food type and soil type on plant growth.
Ha: there is an interaction between food type and soil type on plant growth.

2. Ho: There is no different in means of height of plants grown using different foods.
Ha: There is a different in means of height of plants grown using different foods.

3. Ho: There is no different in means of height of plant grown in different soil types.
Ha: There is a different in means of height of plant grown in different soil types.


the assumption for two-way ANOVA:
1. the populations from which the amples were obtained must be normally or approx. normally distributed.
2. the samples must be independent of each other.
3. the variances of populations must be equal.
4. the groups must be equal in sample size.