ANOVA, known in full as, Analysis of Variance, is a statistical test that helps researchers discover and analyze the differences of the mean values of more than two groups. One-way ANOVA is a type of ANOVA that applies one independent variance. This blog post will discuss One-way ANOVA in depth.
Definition: One-way ANOVA
ANOVA, which is short for, Analysis of Variance is a statistical test that analyzes the differences between the means of three or more groups.4 Therefore, one-way ANOVA is a statistical method that uses one independent variable to test the differences in the means of more than two groups.2
One-way ANOVA: Function
The key role of One-way ANOVA is to analyze data from field studies, experiments, and quasi-experiments.3 This statistical test helps determine if there is notable statistical evidence that proves a significant difference between the means of the associated populations.3
Using One-way ANOVA
You can use One-way ANOVA when your collected data features one categorical independent variable and a single quantitative dependent variable. Furthermore, your independent variables should contain at least three levels.4 ANOVA will help you determine if the dependent variable changes depending on the independent variable level.
How does One-way ANOVA work?
A One-way ANOVA applies the following hypotheses:
- Null hypothesis: μ1 = μ2 = μ3 = … = μk, this implies that all the population means are equal
- Alternative hypothesis: at least one of the population means is not equal to the rest.
ANOVA typically works hand in hand with:
F-tests – they are great for statistical significance. These tests allow you to compare several means simultaneously. With f-tests, the error is calculated for an entire group of comparisons instead of individually.
One-way ANOVA: Assumptions
For the outcomes of One-way ANOVA to be valid, the assumptions below apply:
Each sample is obtained from a normally-distribution population.1
The data was obtained using statistically valid sampling techniques. Therefore, there are no hidden correlations between the observations.
Equality of variances
The variance within all the groups in the comparison are similar in each group. Barlett’s test will help verify this assumption.3
One-way ANOVA: Beginning
You can perform One-way ANOVA by hand. However, this approach is challenging and cumbersome with several observations.1 Therefore, the R statistical program may come in handy. This program is free, powerful, and readily available.
One-way ANOVA: Interpretation of the results
You can check out a summary of a statistical model in R by utilizing the summary () command.2 It should provide the following summary R code:
The output of an ANOVA usually gives you an estimate of the dependent variable variation that the independent variable can explain.2
|mean error||The initial column lists the independent variable together with the model residuals also known as the model error.|
|Df||The column labeled Sq showcases the total variation or sum of squares between the group and the overall mean expressed by the variable.|
|Sq||The column labeled Sq showcases the total variation or sum of squares between the group and the overall mean expressed by the variable.|
|Mean Sq||The column labeled Mean Sq showcases the sum squares’ means, which are found by dividing the summation of the squares by the freedom degrees.|
|F value||The F value column represents the test statistic from the F test.|
|Pr(>F)||The Pr(>F) column represents the F statistic’s p-value, which indicates the likelihood of the calculated F value occurring in the null hypothesis.|
One-way ANOVA: Post-hoc testing
One-way ANOVA will show you if there is a difference in the independence variable levels. However, it does not tell you how significant the difference is. This is where the Post-hoc (Tukey’s Honestly-Significant Difference) test comes in. This test runs comparisons among each group in pairs using a conservative error estimate.3
The Post-Hoc test code is: TukeyHSD(one.way)
- The table reports the tested model and lists the differences among the groups in pairs.
- The soil section shows the mean differences for each level.
- The pairwise comparisons display the level with the highest yield.
One-way ANOVA: Reporting the test results
In one-way ANOVA, the reported results should feature a small description of the following: tested variables, f value, freedom degrees, and each independent variable’s p-value. The report should also have a detailed explanation of the mean of the results.4
One-way ANOVA is a statistical test that compares the means of more than three independent groups to determine if a significant statistical difference exists between the means of the corresponding populations.
ANOVA (Analysis of Variance) is a statistical test that analyzes the differences between the means of three or more groups.
You can use computer programs to run one-way ANOVA tests because doing so by hand can be cumbersome.
The difference between One-way ANOVA and two-way ANOVA is that the latter contains two independent variables.
1 Statology. “One Way ANOVA: Definition, Formula, and Example.” December 27, 2018. https://www.statology.org/one-way-anova/.
2 JMP Statistical Discovery. “One Way ANOVA.” Accessed February 16, 2023. https://www.jmp.com/en_us/statistics-knowledge-portal/one-way-anova.html.
3 Kent State University. “SPSS TUTORIALS: ONE WAY ANOVA.” January 27, 2023. https://libguides.library.kent.edu/SPSS/OneWayANOVA.
4 Wall Street Mojo. “One Way ANOVA Definition.” Accessed February 16, 2023. https://www.wallstreetmojo.com/one-way-anova/.