Two-way ANOVA (Without Replication)

#Two-wayANOVAwithoutreplication
This video shows how to solve Two-way ANOVA (without replication).
Two-way ANOVA without replication is a statistical method used to analyze the effects of two categorical independent variables on a continuous dependent variable, where each combination of the two independent variables has only one observation.
For example, suppose you want to analyze the effect of two factors, A and B, on the yield of a chemical reaction. You perform the reaction several times, but each time you only measure the yield once under each combination of the two factors. In this case, you have a two-way ANOVA without replication design.
The steps to perform a two-way ANOVA without replication are as follows:
Set up the null hypothesis: The null hypothesis is that the means of the different combinations of the two factors are equal.
Calculate the sum of squares (SS) for each source of variation: SS(A), SS(B), and SS(AB), which represent the variation due to factor A, factor B, and the interaction between A and B, respectively.
Calculate the degrees of freedom (df) for each source of variation: df(A) = a - 1, df(B) = b - 1, and df(AB) = (a - 1) x (b - 1), where a and b are the number of levels for factors A and B, respectively.
Calculate the mean squares (MS) for each source of variation: MS(A) = SS(A) / df(A), MS(B) = SS(B) / df(B), and MS(AB) = SS(AB) / df(AB).
Calculate the F-statistic for each source of variation: F(A) = MS(A) / MS(Error), F(B) = MS(B) / MS(Error), and F(AB) = MS(AB) / MS(Error), where MS(Error) is the mean square error, which measures the variation due to random error.
Determine the critical value of the F-distribution with degrees of freedom (df(A), df(Error)) for factor A, (df(B), df(Error)) for factor B, and (df(AB), df(Error)) for the interaction, using a significance level (alpha) of your choice.
Compare the F-statistics to the critical values: If F(A) is greater than the critical value, factor A is significant; if F(B) is greater than the critical value, factor B is significant; if F(AB) is greater than the critical value, the interaction is significant.
If a factor or interaction is significant, perform post-hoc tests to determine which levels of the factor or factors are significantly different.
Interpret the results in the context of your study.
It is important to note that two-way ANOVA without replication assumes that the data are normally distributed and that the variances are equal across all groups
Please watch previous videos on ANOVA with the following link:
How to calculate One-Way ANOVA
• How to Calculate ONE W...
ANOVA (Analysis of Variance) | Simple and in-depth explanations
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Mean Comparison test after ANOVA
Tukey's (HSD) Post-Hoc
• What is ANOVA (Analysi...

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