A one-way ANOVA is used to determine whether or not there is a statistically significant difference between the means of three or more independent groups.
When reporting the results of a one-way ANOVA, we always use the following general structure:
- A brief description of the independent and dependent variable.
- The overall F-value of the ANOVA and the corresponding p-value.
- The results of the post-hoc comparisons (if the p-value was statistically significant).
Here’s the exact wording we can use:
A one-way ANOVA was performed to compare the effect of [independent variable] on [dependent variable].
A one-way ANOVA revealed that there [was or was not] a statistically significant difference in [dependent variable] between at least two groups (F(between groups df, within groups df) = [F-value], p = [p-value]).
Tukey’s HSD Test for multiple comparisons found that the mean value of [dependent variable] was significantly different between [group name] and [group name] (p = [p-value], 95% C.I. = [lower, upper]).
There was no statistically significant difference between [group name] and [group name] (p=[p-value]).
The following example shows how to report the results of a one-way ANOVA in practice.
Example: Reporting the Results of a One-Way ANOVA
Suppose a researcher recruits 30 students to participate in a study. The students are randomly assigned to use one of three studying techniques for the next month to prepare for an exam. At the end of the month, all of the students take the same test.
The researcher then performs a one-way ANOVA to determine if there is a difference in mean exam scores between the three groups.
The following table shows the results of the one-way ANOVA along with the Tukey post-hoc multiple comparisons table:
Here is how to report the results of the one-way ANOVA:
A one-way ANOVA was performed to compare the effect of three different studying techniques on exam scores.
A one-way ANOVA revealed that there was a statistically significant difference in mean exam score between at least two groups (F(2, 27) = [4.545], p = 0.02).
Tukey’s HSD Test for multiple comparisons found that the mean value of exam score was significantly different between technique 1 and technique 2 (p = 0.024, 95% C.I. = [-14.48, -0.92]).
There was no statistically significant difference in mean exam scores between technique 1 and technique 3 (p=0.883) or between technique 2 and technique 3 (p=0.067).
Things to Keep in Mind
Here are a few things to keep in mind when reporting the results of a one-way ANOVA:
Use a descriptive statistics table.
It can be helpful to present a descriptive statistics table that shows the mean and standard deviation of values in each treatment group as well to give the reader a more complete picture of the data.
For example, SPSS produces the following descriptive statistics table that shows the mean and standard deviation of exam scores for students in each of the three study technique groups:
Only report post-hoc results if necessary.
If the overall p-value of the ANOVA is not statistically significant, then you will not conduct post-hoc multiple comparisons between groups. This means you obviously don’t have to report any post-hoc results in the final report.
If you do have to conduct post-hoc tests, the Tukey HSD test is the most commonly used one but occasionally you may use the Scheffe or Bonferroni test instead.
Round p-values when necessary.
As a general rule of thumb, the overall F value and any p-values in ANOVA results are rounded to either two or three decimal places for brevity.
No matter how many decimal places you choose to use, be sure to be consistent throughout the report.
Additional Resources
The following tutorials explain how to report other statistical tests and procedures in APA format:
How to Report Two-Way ANOVA Results (With Examples)
How to Report Cronbach’s Alpha (With Examples)
How to Report t-Test Results (With Examples)
How to Report Chi-Square Results (With Examples)
How to Report Pearson’s Correlation (With Examples)
How to Report Regression Results (With Examples)
very informative
Your content is very detailed and yet simple to follow. Thanks a lot Zach for all the great work!
Thank you!
Hi. Can you help me in reporting more than three groups? Does it come the same way as this.
Thank you, for the explanation on the ANOVA and Post Host results writing
I find this platform very educative and would like to learn more on how to interpret more statistical information under you. Thanks
This was extremely helpful! Thank you!
Guide me on how t- can be used in comparison of variables
Thank you! Bless your soul. 🙂
I gained some knowledge
zach thank you for the guide to report anova results , you are a legend.
If the results of ANOVA contradict that of the post-hoc. ANOVA is significant but the post hoc is not, how do I report the results?????
I have recently been criticised for using p<= 0.05 as a cut off point for significance and referred to several statistical papers in biomedical and social science for this viewpoint (eg Greenland et al 2016, Huilbert et al 2019). What is your viewpoint? my science field is agriculture.
Hi Jay…The criticism of using **p ≤ 0.05** as a cutoff for statistical significance is part of an ongoing discussion in many scientific fields, including agriculture. The debate revolves around the over-reliance on arbitrary thresholds and the misinterpretation of p-values in research.
Here’s an overview of the criticism and some perspectives tailored to your field:
—
### **Criticism of p ≤ 0.05**
1. **Arbitrary Threshold**:
– The p ≤ 0.05 threshold is an arbitrary standard set historically, not a universal indicator of meaningful results. It doesn’t reflect the magnitude or practical significance of effects.
– Greenland et al. (2016) and Hurlbert et al. (2019) argue that rigidly adhering to p ≤ 0.05 oversimplifies the complexity of scientific evidence.
2. **False Dichotomy**:
– The threshold promotes a binary “significant/not significant” thinking, ignoring that p-values close to 0.05 (e.g., 0.049 and 0.051) are essentially indistinguishable.
3. **Lack of Context**:
– In isolation, p-values do not account for study design, sample size, or the context of the research question.
—
### **Recommendations for Moving Beyond p ≤ 0.05**
#### 1. **Report the Exact p-Value**:
– Instead of labeling results as “significant” or “not significant,” report the exact p-value and let readers interpret the evidence within the study’s context.
#### 2. **Focus on Effect Sizes**:
– Include measures of effect size (e.g., Cohen’s d, η², or confidence intervals). Effect sizes provide information on the magnitude of the observed effect, which is crucial in applied fields like agriculture.
#### 3. **Use Confidence Intervals**:
– Confidence intervals offer a range of plausible values for the effect size, giving a clearer picture of the uncertainty around the estimates.
#### 4. **Integrate Prior Knowledge**:
– Use p-values in conjunction with prior evidence, domain expertise, and biological relevance to interpret results, especially in applied research like agriculture.
#### 5. **Emphasize Replicability**:
– Consider the likelihood of replicating the results. A single p-value cannot ensure reliability across studies.
#### 6. **Shift to a Bayesian Framework**:
– Bayesian statistics provide probabilistic interpretations and incorporate prior knowledge. Although less common in agricultural sciences, Bayesian approaches are gaining traction for their flexibility and transparency.
#### 7. **Pre-Register Analysis Plans**:
– Clearly state hypotheses, methods, and p-value thresholds (if any) before data collection to minimize bias and p-hacking.
—
### **Specific to Agriculture**
In agriculture, the practical significance of results often outweighs statistical significance. For example:
– A small increase in yield due to a treatment may be statistically “non-significant” but could be meaningful if it translates into tangible economic benefits for farmers.
– Conversely, a statistically “significant” pH change might be irrelevant if it doesn’t impact crop performance.
Thus, interpreting results should consider both statistical metrics and their practical, biological, or economic implications.
—
### **My Viewpoint**
While p-values (including p ≤ 0.05) remain a useful tool, their interpretation must be nuanced and integrated with other statistical and contextual insights. For agricultural research:
1. Avoid rigid adherence to thresholds.
2. Report p-values, effect sizes, and confidence intervals.
3. Discuss findings in terms of their practical implications, especially for stakeholders like farmers, policymakers, or industry professionals.
This balanced approach ensures that your research is statistically rigorous while remaining relevant and actionable.