Key Points

• Fisher’s 1-Way ANOVA is a basic statistical test for detecting differences in the means between two or more sample groups.
• The test itself is quite simple, and the results are easy to interpret.
• It isn’t a useful test if the variances between sample sets don’t conform to a normal distribution.

Fisher’s 1-way ANOVA is so commonplace in sampling that it is one of the first concepts learned by those studying statistics. Below, we will go over what it is, some benefits of it, and an example of how it can be used.

Overview: What Is Fisher’s (1-Way ANOVA)?

Fisher’s 1-way ANOVA is a classic analysis of variance utilized in statistics to determine if there are statistical differences between the means of two or more unrelated groups. Interestingly, while you can use it for two or more groups, the tendency is that the differences are not noticeable unless there are three groups or more.

What If Variances Aren’t Homogenous?

If you’ve got data sets where the variances don’t match up, a Fisher’s 1-way ANOVA isn’t going to benefit you. You’d be better off utilizing the

3 Benefits of Fisher’s (1-Way ANOVA)

There are some key benefits to Fisher’s 1-way ANOVA test that should be addressed:

1. Different Numbers of Observations

One of the primary benefits of 1-way ANOVA is that for each group, the number of observations can be different.

2. Simplicity

The design layout and statistical analysis are simple.

3. Extension of Another Test

This test is an extension of the independent two-sample t-test. If you know how to do that test, the 1-way ANOVA test should be easy for you.

Why Is Fisher’s (1-Way ANOVA) Important to Understand?

Fisher’s 1-way ANOVA is important to understand for the following reasons:

Less Error Than Other Tests

Understanding 1-way ANOVA is important because, while it may be similar to many two-sample t-tests, it results in fewer type-1 errors.

Homogeny

Understanding the 1-way ANOVA test is important so that you know when the test will not apply. For example, it is not suitable in situations where the experimental units are not homogenous.

Tolerates Violations

Having an understanding of 1-way ANOVA is important because it is a robust test that can tolerate violations of its normality assumptions.

An Industry Example of Fisher’s (1-Way ANOVA)

A toy company has decided to focus on its social media presence to more actively engage with its customers. The company uses Fisher’s 1-way ANOVA to see the correlations between customers that engage with their social media pages for up to half an hour, more than an hour, and more than two hours make a difference in how many of their toys they buy online.

3 Best Practices When Thinking About Fisher’s (1-Way ANOVA)

Here are some practices to keep in mind before applying Fisher’s (1-way ANOVA):

1. Factor Each Level

The population that the sample is derived from needs to be distributed normally, and all levels of the factor need to be applied to a sample.

2. Independence

Before Fisher’s can be applied, it must be determined that all of the samples are independent.

3. Variance Equality

Be sure that the variances of the population are equal.

Other Useful Tools and Concepts

Looking for some other tools to bolster your statistical analysis? You might need to brush up on the basics of ANOVA. ANOVA is a useful means of testing between sample sets to check for variances in the means, as we’ve established throughout today’s article.

Further, you might need to learn about Mood’s Median Test. This is a great way of testing for normality within a set of data points that have failed a parametric test.

Using Fisher’s 1-Way ANOVA

If you would like to use Fisher’s 1 way ANOVA, it is so commonplace that there are plenty of statistical software options available online or you can use a statistical calculator.