Chapter 9: Q82SE (page 522)

What is the difference between a one-way ANOVA and atwo-way ANOVA?

Short Answer

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A two-way ANOVA has two independent variables, whereas a one-way ANOVA only has one factor or independent variable.

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Individuals must differentiate between a one-way and two-way ANOVA in this question.

A description of the one- and two-way ANOVA

One-way ANOVA:A direct ANOVA is a statistical test that evaluates just one independent variable or factor while comparing the variance in the group means within a sample. It is a hypothesis-based test that assesses various competing hypotheses regarding our data. Here, need to have a question about our data for which we are looking for an answer before developing a hypothesis.

Adventuresome scientists studying a population of walruses, for instance, might ponder the question, "Do our walruses weigh more in early or late mating season?" The "month of mating season" is the independent variable or factor in this case (both terms refer to the same thing). Our independent variables in an ANOVA are organized into categorical categories. For instance, there would be four groups to analyze the researchers looking at walrus weight in December, January, February, and March.

Two-way ANOVA: A two-way ANOVA is a hypothesis-based test, just like a one-way ANOVA. The two-way ANOVA, on the other hand, divides each sample into two definite groups due to its dual definition. Assuming that the interrogation is, "Does walrus sex affect whether they are heavier during early or late mating season?"A two-way ANOVA is an option for researchers.

In this case, there are two factors: "month in mating season" and "sex of walrus" are both factors. Once more, individuals must take the number of groups in each factor into account; there will only be two groups for "sex": "male" and "female”.

Consequently, the two-way ANOVA investigates the influence of two factors (month and sex) on a dependent variable, in this case, weight, and whether the two factors interact to affect the continuous variable.

The distinction between one- and two-way ANOVA

The primary purpose of a one-way ANOVA is to make it possible to compare three or more means equally. A two-way ANOVA is made to evaluate how two independent variables interact with one another.

A two-way ANOVA has two independent variables, whereas a one-way ANOVA only has one factor or independent variable.

	One-way ANOVA	Two-way ANOVA
Definition	A test makes it possible to compare the means of at least three data sets.	A test enables comparisons between the means of three or more data groups and considers two independent variables.
Independent variables	One	Two
Which comparison is being made?	The average of three or more independent groups on a dependent group	A dependent variable and different groups of two independent variables interact.
Number of sample groups	At least three.	There should be several samples for each variable