ANOVA Test Basics: 5 Types of ANOVA Tests for Data Analysis

An ANOVA test is a parametric analysis of variance test. It’s one tool among many (like chi-square tests, T-tests, or Z-tests) you can use to create a general linear model of data to depict how different inputs affect your control group.

To conduct an ANOVA test, you can use large or small sample sizes—the only caveat is that the sample sizes for each of your variable sets must be the exact same. This allows you to maintain a homogeneity of variance among all your different sets of data. It also makes it simpler to determine an overall mean between them as a result.

An ANOVA test works by comparing how different forms of input can affect your dependent variable.

For example, suppose you’re a psychological researcher who wants to see whether people with depression respond best to therapy or medication. You can make your hypothesis testing even more sophisticated by introducing various levels into each grouping. In other words, you could test how much of an effect different styles of therapy or types of medication affect your control group over a period of time.

Various types of ANOVA tests differ in terms of the number of independent variables they use. Here are five tests you can use to measure ANOVA:

1. 1. One-way ANOVA test: By utilizing a normal distribution, you can run a one-way analysis of variance (or ANOVA) test in a straightforward way. Set up a null hypothesis as a baseline first. Proceed to note the degrees of freedom the independent variable group causes in your dependent one against this initial hypothesis. Set up an alternative hypothesis from the get-go if you project there’ll be a reasonable amount of change in your variables.
2. 2. MANOVA test: This form of test is ideal if you plan to take a high number of categorical variables into account. The acronym MANOVA stands for multivariate analysis of variance. Some tests even use up to seven independent variables, leading to significant differences worth keeping track of in each case.
3. 3. Repeated measures ANOVA test: In this ANOVA test, you take sample means from at least three different sets of test statistics and compare them against one another. This way, you can look for any key and critical values and notate their statistical significance level as well. You do so primarily through utilizing repeated F-tests.
4. 4. Two-way ANOVA test: Also known as a factorial ANOVA test, this two-way approach measures the interaction effect between two different groups (or independent variables) on a control group. It does so in part by using F-ratios with two mean square values related to each group.
5. 5. Two-way ANOVA test with replication: Just as with a typical two-way ANOVA test, you’ll study the effect size of two separate datasets. The main difference arises in the fact this test requires you to run multiple studies with different groups of people, while still using the same response variables.

ANOVA tests help you better understand data and statistics. Keep the steps for this basic tutorial in mind as you conduct this statistical test:

• Assign variables. Start by deciding on your dependent variable group. This will remain constant throughout all your experimentation. Move on to define your independent variables. Keep in mind the amount you use will likely lend themselves to specific types of ANOVA tests. The goal is to eventually get an F-value (or F-statistic)—or a set of these values—you can understand by the end of the test.
• Choose levels. Within your independent group variables, decide how many different levels of information for which you’d like to test. For instance, if your goal is to see how people respond to heart medication, your variable group would be this type of medicine in a general sense and your levels would likely be specific forms or brands of heart medication.
• Collect data points. To build your F-distribution, start running the test and keep track of data over time. See what the main effects of the independent variables are. At this phase of statistical analysis, your goal should be to collect as much data as possible rather than to assign value to it.
• Decide which test to use. Make sure you’re using the appropriate form of ANOVA test to collect all your population mean differences. If you’re just collecting one group, a simple one-way test can suffice. Alternatively, if you’re using multiple different independent variables, a two-way or MANOVA approach might be more useful.
• Parse through your data set. After you gather all your data, go through your test results. See if they hew closely to the standard deviation common to most statistical analysis or give you unpredictable results. If you’re using multiple different independent variables, see if you have equal variances or wide differences between each. If something seems wrong, consider mounting a regression campaign to see where things went awry. You can always conduct some post-hoc tests as well.

ANOVA tests share a fair amount of overlap with T-tests. One-sample T-tests, as well as two-sample T-tests, can double as ANOVA tests. At a bare minimum, both approaches can yield similar information and results. The key difference between the statistical techniques is that both paired T-tests and unpaired T-tests only use up to two sets of independent variables, whereas ANOVA tests can utilize far more sets of data.

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