# 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

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/

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.

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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/

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/

The analysis of variance or also known as ANOVA is a statistic test utilize in comparing means among two or more groups (Corty, 2016). There are different types of ANOVA, and they differ from each other by their functions. The most common form of ANOVA is the Between-Subjects ANOVA which is applied when analyzing the difference between independent groups on continuous level variable (Statistic Solution, n.d.). There are two types of Between-Subjects ANOVA which are one-way ANOVAs and factorial ANOVAs.

One-way ANOVA is effective in assessing the differences in one continuous variable between ONE grouping variable (Statistics Solution, n.d.). An example for one-way ANOVA would be research to assess the differences in how often the health office visit between different grades in elementary level is. This example shows that the dependent variable is how often is health office visits, and the one independent variable is the different elementary grades.

Factorial ANOVA is known for examining the multiple independent variables (Statistics Solution, n.d.). An example for this form of ANOVA would be research to assess the difference of how often the health officer visit between different grades in elementary level and the time of visits is. The dependent variable is how often the health office visits and the two independent variable is different elementary grade levels and the time of visit.

### Reference

Corty, E. (2016). Using and interpreting statistics: A practical text for the behavioral, social, and health

sciences (3rd ed.). New York, NY: Macmillan Learning.

Statistics Solutions. (n.d.). The various forms of ANOVA. Retrieved from

Analysis of variance (ANOVA) is an analysis tool used in statistics that splits an observed aggregate variability found inside a data set into two parts: systematic factors and random factors. The systematic factors have a statistical influence on the given data set, while the random factors do not. Analysts use the ANOVA test to determine the influence that independent variables have on the dependent variable in a regression study. (Will Kenton 2022). The ANOVA test allows a comparison of more than two groups at the same time to determine whether a relationship exists between them. The result of the ANOVA formula, the F statistic (also called the F-ratio), allows for the analysis of multiple groups of data to determine the variability between samples and within samples.

There are two main types of ANOVA: one-way (or unidirectional) and two-way. There also variations of ANOVA. For example, MANOVA (multivariate ANOVA) differs from ANOVA as the former tests for multiple dependent variables simultaneously while the latter assesses only one dependent variable at a time. One-way or two-way refers to the number of independent variables in your analysis of variance test. A one-way ANOVA evaluates the impact of a sole factor on a sole response variable. It determines whether all the samples are the same. The one-way ANOVA is used to determine whether there are any statistically significant differences between the means of three or more independent (unrelated) groups.

A two-way ANOVA is an extension of the one-way ANOVA. With a one-way, you have one independent variable affecting a dependent variable. With a two-way ANOVA, there are two independents. For example, a two-way ANOVA allows a company to compare worker productivity based on two independent variables, such as salary and skill set. It is utilized to observe the interaction between the two factors and tests the effect of two factors at the same time.

### Reference:

Will Kenton: Analysis of Variance, Updated May 2022 Reviewed by TOBY WALTERS

Analysis of variance (ANOVA) is a statistical method that is frequently used in experimental studies. ANOVA compares means from groups of data sets to identify the differences. ANOVA also analyzes the extent of the difference between means. Statisticians conduct ANOVA tests to confirm the significance of study findings. In essence, statisticians use ANOVA as inference to reject/accept the null hypothesis or alternative hypothesis. There are two types of ANOVA based on the number of independent variables in the ANOVA test. The two types of ANOVA include one-way and two-way ANOVA. One-way (unidirectional) ANOVA has one independent variable and assumes the two means are equal (Liu et al., 2021). This type of ANOVA examines the difference between the means of one independent variable with two levels using f-distribution (Kim, 2017). For instance, a researcher can conduct a one-way ANOVA test on several subjects for a new medication. Significant results from this ANOVA test denote the two means are unequal (Kim, 2017).

Two-way ANOVA has two independent variables. Two-way ANOVA examines the difference between means of variables with multiple levels (quantitative variable and two nominal variables). In essence, two-way ANOVA is used to describe how combined variables affect a dependent variable. Two-way ANOVA is further classified based on replication (Mishra et al., 2019). Two-way ANOVA with replication tests two groups with members of each group doing different things. For instance, a researcher can conduct two-way ANOVA with replication on patients from two different hospitals, diagnosed with a similar condition but undergoing two different treatment therapies. Two-way ANOVA without replication involves testing one group twice (before and after an intervention) (Mishra et al., 2019). For instance, a researcher can test study participants at baseline and after administering a medication intervention to identify the efficacy of the medication.

**References**

Kim TK. (2017 Feb). Understanding one-way ANOVA using conceptual figures. Korean J Anesthesiol. 70(1):22-26. doi: 10.4097/kjae.2017.70.1.22. Epub 2017 Jan 26. PMID: 28184262; PMCID: PMC5296382.

Liu, Q., & Wang, L. (2021). t-Test and ANOVA for data with the ceiling and/or floor effects. *Behavior Research Methods*, *53*(1), 264-277. https://doi.org/10.3758/s13428-020-01407- 2

Mishra, P., Singh, U., Pandey, C. M., Mishra, P., & Pandey, G. (2019). Application of student’s t-test, analysis of variance, and covariance. *Annals of cardiac anesthesia*, *22*(4), 407. doi: 10.4103/aca.ACA_94_19.