# “Statistical test used to examine differences among two or more groups by comparing the variability between groups with the variability within each group,”

The textbook definition for the analysis of variance according to the authors of Understanding Nursing Research is the “Statistical test used to examine differences among two or more groups by comparing the variability between groups with the variability within each group,” (Grove, 2015, p. 500). In further explanation, it is a calculation of the squared average difference from the mean. It is the second step of the mathematical calculations utilized to determine the standard deviation. The first step of the process is calculating the mean. The mean is finding the average amount from collected scores of one sample group. This serves, as the standard at which the data collected should be based. In further calculations, the next step is to determine the variance. The variance utilizes each number in the sample and describes the difference of each number from the mean or average number. To calculate the variance, the number is squared and then averaged for results. These results provide a range for the standard deviation, or in other terms provides a range of what is “normal” range for the data that is being analyzed. It provides the standard deviation for what is above normal and what is below normal. For those that have never had a statistics class before this can be useful when determining what the normal range is for a sample based on the sample data collected. It’s beneficial because it allows a range from above and below average. With this range it can allow a variety that is accepted in the normal range and also what is out of the normal standard.

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Developed by statistician Ronal Fisher, the Analysis of Variance (ANOVA) is a statistical procedure that tests two or more differing groups in an experiment. An ANOVA’s purpose is to determine if the results of the experiment are significant. In other words, the results help determine whether to reject the null hypothesis or to accept the alternate hypothesis. The procedure helps establish the difference between the groups being tested. Examples of when you might want to test different groups are the following. For example- A manufacturer has two different processes to make light bulbs. They want to know if one process is better than the other.

There are two main types of the ANOVA test: one-way and two-way. One-way or two-way refers to the number of independent variables (IVs) in your Analysis of Variance test. The one-way test has one independent variable with 2 levels, and is used when you want to test two groups to see if there’s a difference between them.

Two-way has two independent variables and can have multiple levels. It used when you have one group and you’re double-testing that same group. For example, you’re testing one set of individuals before and after they take a medication to see the results of the medicine.