*PUB 550 Compare the various types of ANOVA by discussing when each is most appropriate for use*

PUB 550 Compare the various types of ANOVA by discussing when each is most appropriate for use

By comparing the variance-adjusted means of two or more categorical groups, an ANOVA test can establish if there is a statistically significant difference between them. ANOVA also divides the independent variable into two or more groups, which is an important component. As an illustration, one or more groups may be predicted to impact the dependent variable, whilst another group might be employed as a control group and not predicted to do so.

Only when there is no association between the participants in any sample is it possible to run an ANOVA. Accordingly, participants from the first group cannot also be found in the second group (e.g., independent samples/between-groups). Equal sample sizes must be used for each of the various groups/levels. Only when the dependent variable is regularly distributed—that is, when the intermediate scores are most often, and the extreme values are least frequent—can an ANOVA be performed. There must be equal population variances (i.e., homoscedastic). When a population’s standard deviation or range, for example, is similar across populations, the term “homogeneity of variance” is used.

ANOVA tests come in several forms. A “One-Way” and a “Two-Way” are the two that are used the most. How many independent variables you include in your test will determine how these two categories differ from one another.

An Analysis of Variance test using more than one independent variable, or “factor,” is known as a factorial ANOVA. Additionally, it might be used to describe several independent variable levels. One factor (the treatment) but two levels are present in an experiment with a treatment group and a control group, for instance (the treatment and the control). The phrases “two-way” and “three-way” denote how many variables or levels are in your test. Due to the test’s complicated and challenging to understand findings, four-way ANOVA and higher are rarely utilized.

### Reference:

ANOVA Test: Definition, Types, Examples, SPSS. (2022). Statistics How To. Retrieved from:

https://www.statisticshowto.com/probability-and-statistics/hypothesis-testing/anova/

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Corty (2016) states that Analysis of Variance (ANOVA) is a test that compares two groups in a study. ANOVA test is needed to reduce TYPE 1 errors. The errors are more common with multiple variables. A one-way ANOVA is used when assessing for differences in one continuous variable between ONE grouping variable. For example, a one-way ANOVA would be appropriate if the goal of research is to assess for differences in job satisfaction levels between ethnicities. With a one way ANOVA, there are two hypothesis types: null and alternative hypothesis.

A two-way ANOVA is, like a one-way ANOVA, a hypothesis-based test. However, in the two-way ANOVA each

sample is defined in two ways, and resultingly put into two categorical groups.Two-way ANOVA can be used to examine the interaction between the two independent variables. Interactions indicate that differences are not uniform across all categories of the independent variables. For example, females may have higher IQ scores overall compared to males, but this difference could be greater in African countries compared to North American countries. Two-way ANOVAs are also called factorial ANOVAs. Interaction effects represent the combined effects of factors on the dependent measure. When an interaction effect is present, the impact of one factor depends on the level of the other factor. Interaction effects occur when the effect of one variable depends on the value of another variable. Interaction effects are common in regression analysis, ANOVA, and designed experiments. Given the specifics of the example, an interaction effect would not be surprising.

### References:

Corty, E. (2016). *Using and interpreting statistics: A practical text for the behavioral, social, and health sciences *(3rd ed.). New York, NY: Macmillan Learning. ISBN-13: 978-1464107795

First, it is important define ANOVA. As defined by Corty (2016), ANOVA stands for analysis of (statistical) variance and is a family of statistical tests that can compare the mean of at least two or more groups. ANOVA is important because it helps to minimize type I error, when comparing the means of multiple groups, it also compares all means at once and can identify if there is a statistically significant difference between two variables. Sixsigmastats (2018) discuss that “ANOVA is used when X is categorical and Y is a continuous data type

One type of testing is called *between subjects, one-way ANOVA *it is used when there is just one explanatory variable and you are comparing the means between two or more independent samples. Any time the term *between-subjects* is used it indicates there are independent samples.

Two way ANOVA can be *between-subjects* as previously discussed or can be *within-subjects* which is used for dependent samples. As discussed by sixsigmastats (2018) two way ANOVA has two categorical independent factors.

Factorial ANOVA is a type testing that is involves more than one variable and can also be called multiple way ANOVA (Corty, 2016). This includes such testing as three-way and four way ANOVA. Another name these test can be called N-way ANOVA as discussed by sixsigmastats (2018) where each factor can have multiple factors and there is more than 1 independent categorical factor.

### References

Corty, E. (2016). *Using and interpreting statistics: A practical text for the behavioral, social, and health sciences *(3rd ed.). New York, NY: Macmillan Learning. ISBN-13: 978-1464107795

Sixsigmastats, (2018). 3 Types of ANOVA Analysis. https://sixsigmastats.com/3-types-anova-analysis/

A one-way ANOVA is used when assessing for differences in one continuous variable between ONE grouping variable. For example, a one-way ANOVA would be appropriate if the goal of research is to assess for differences in depression between ethnicities. In this example, there is only one dependent variable (depression) and ONE independent variable (ethnicity). The null hypothesis could be that there is no relationship between depression and ethnicity. The alternative hypothesis could be that there is a strong associative relationship between ethnicity and depression. Due to possible type I error, I would not recommend studying multiple groups at one time. Corty (2016) suggests that when testing multiple groups, its best to use the ANOVA testing method instead of the T-Test because of the time efficient that is versus doing like 10 T-tests.

### References:

Corty, E. (2016). *Using and interpreting statistics: A practical text for the behavioral, social, and health sciences *(3rd ed.). New York, NY: Macmillan Learning. ISBN-13: 978-1464107795

Analysis of Variance (ANOVA) test is a statistical test used to determine if there is a statistically significant difference between two or more categorical groups by testing for differences in means using a variance.

Another Key part of ANOVA is that it splits the independent variable into two or more groups (simply psychology, 2022). There are different types of ANOVA tests. The two most common are a “One-Way” and a “Two-Way.” The difference between these two types depends on your test’s number of independent variables.

A one-way ANOVA has one categorical independent variable (also known as a factor) and a normally distributed continuous through interval or ratio level dependent variable. The independent variable divides cases into two or more mutually exclusive levels, categories, or groups. The one-way ANOVA test for differences in the means of the dependent variable is broken down by the levels of the independent variable. An example of a one-way ANOVA includes testing a therapeutic intervention (CBT, medication, placebo) on the incidence of depression in a clinical sample (simply psychology, 2022). A two-way ANOVA is very similar to A one-way ANOVA because it is also normally distributed continuously through interval or ratio level dependent variable and independent variables, also known as a factor. A two-way ANOVA is also called a factorial ANOVA. An example of A two-way Anova is testing the effects of social contact (high, medium, low), job status (employed, self-employed, unemployed, retired), and family history (no family history, some family history) on the incidence of depression in a population (simply psychology, 2022).

### Reference:

Simply Psychology, 2022, ANOVA test: Definition & Uses. https://www.qualtrics.com/experience-management/research/anova/