What is ANOVA (Analysis of Variance), Types, Assumptions and Uses – A Quick Guide For Biomedical Researchers

What is ANOVA (Analysis of Variance)?

ANOVA, which stands for Analysis of Variance, is a statistical method used to analyze data from studies with multiple groups. ANOVA is widely used in biomedical research to compare means across multiple groups in order to determine whether the differences observed are statistically significant.

Assumptions of ANOVA

Before performing an ANOVA, you will need to check whether its underlying assumptions are met. The assumptions of ANOVA are as follows:

• Normality: The data within each group should be normally distributed.
• Homogeneity of variance: The variance of the data within each group should be equal.
• Independence: The observations within each group should be independent.
• Random sampling: Observations within each group have been sampled randomly and are independent of each other.

Uses of ANOVA in Biomedical Research

ANOVA is a useful tool for biomedical researchers to compare means across multiple groups. It can be used to analyze data from experiments that involve testing the effectiveness of a new drug, comparing the survival rates of different treatments for a disease, or analyzing the efficacy of a new medical device.

Reporting an ANOVA in Your Paper

When reporting an ANOVA in your paper, it is important to include the following information:

1. The number of groups being compared
2. The sample size for each group
3. The mean and standard deviation for each group
4. The F statistic and its associated p-value
5. The post-hoc tests performed, if any
6. A measure of effect size, such as eta-squared, partial eta-squared, or omega-squared
7. Many style guides also require degrees of freedom to be reported. Check this against your target journal’s requirements.

Here’s an example of how to report an ANOVA result:
F(2,34) = 2.51, p = .003, η² = .04

Note that “F” and “p” may need to be italicized depending on the style used by your target journal.

Posthoc Comparisons for ANOVA

While an ANOVA test indicates that there is a significant difference among the means of the groups, it does not provide information about which specific groups are different from each other. This is where post-hoc tests play an important role.

Post-hoc tests are used to identify which specific groups have significantly different means from each other. The most commonly used posthoc tests for ANOVA are the Tukey HSD (Honestly Significant Difference) test, Bonferroni correction, and Scheffé test.

These tests adjust for the increased probability of a type 1 error when multiple pairwise comparisons are performed. They allow for a more detailed examination of the differences between groups and help to avoid making erroneous conclusions based on a single comparison.

Post-hoc tests are useful when the objective is to compare groups after the initial ANOVA analysis has identified a significant difference among them. However, it is important to note that conducting multiple post-hoc tests can increase the probability of making a type 1 error. Therefore, the researcher should carefully select the appropriate test and adjust the p-value accordingly to avoid making false conclusions.

Types of ANOVA tests

Depending on your study design, there are various types of ANOVAs you can use. Here’s a quick explanation of each:

One-way ANOVA

One-way ANOVA is used to compare the means of three or more groups to determine if there is a significant difference between them. It examines whether there are any statistically significant differences between the means of the groups.

Two-way ANOVA

Two-way ANOVA is used to determine the interaction effects between two independent variables on a dependent variable. It is used to analyze the effects of two factors on the mean response of the dependent variable.

Three-way ANOVA

Three-way ANOVA is used to examine the effect of three independent variables on a dependent variable. It determines whether the interaction between the three independent variables has a significant effect on the dependent variable.

Repeated-measures ANOVA

Repeated measures ANOVA is used to analyze data in which the same individuals are measured multiple times under different conditions. It is used to determine whether there is a significant difference between the means of two or more related groups and to assess whether any change over time is statistically significant.

ANOVA vs ANCOVA

ANCOVA, which stands for Analysis of Covariance, is similar to ANOVA, but includes an additional variable that is used to adjust for differences in the groups being compared. ANCOVA is useful when there are variables that can affect the outcome of the experiment but are not of primary interest. ANOVA, on the other hand, assumes that the groups being compared are independent and does not account for any confounding variables.

ANOVA vs MANOVA

MANOVA, which stands for Multivariate Analysis of Variance, is a statistical method used to analyze data that has multiple dependent variables. ANOVA, on the other hand, is used to analyze data with a single dependent variable. MANOVA is useful when multiple outcome measures are being considered, such as in a clinical trial where multiple parameters are being measured to evaluate the efficacy of a drug.

Are you unsure whether to opt for ANOVA, MANOVA, or ANCOVA? Get guidance from an expert biostatistician, through Editage’s Statistical Analysis & Review Services.