In this guide, I will explain how to perform a One-Way ANOVA test in GraphPad Prism. I will also show you how to interpret and report the results.

# Assumptions of a One-Way ANOVA test

Before running a One-Way ANOVA test in GraphPad Prism, it is best to ensure the data meets the following assumptions.

- The dependent variables should be measured on a continuous scale (either interval or ratio).
- There should be three or more independent (non-related) groups.
- There are no outliers present in the dependent variable.
- The dependent variables should be normally distributed. See how to test for normality in GraphPad Prism.
- The dependent variables should have homogeneity of variances. In other words, their standard deviations need to be approximately the same.

# Setting up the GraphPad sheet

To perform a One-Way ANOVA test in GraphPad Prism you will need to enter groups of data into separate columns. Upon opening GraphPad Prism, select the ‘**Column**’ type for the ‘**New Table & Graph**’ option. Then select ‘**Enter replicate values, stacked into columns**’ as the ‘**Enter/import data**’ choice.

Alternatively, you can go to ‘**File > New > New Data Table & Graph …**’.

# Example dataset

I will use a theoretical example of comparing the age at which three groups of individuals encountered a certain disease (disease X). The groups are stratified by their genotype (AA, AG, GG) for a certain gene. In total, I have 6 data points for each group. Each group’s data is separated into different columns.

The null hypothesis for this example will be:

**“There is no difference in the age of disease X contraction between the three genotypes”.**

And the alternative hypothesis will be:

**“There is a difference in the age of disease X contraction between the three genotypes”.**

## Performing the test

- To perform a One-Way ANOVA test in GraphPad Prism, first, go to ‘
**Insert > New Analysis …**’.

2. This will open a new window. Here you need to tell GraphPad which test to perform. Select the ‘**One-way ANOVA (and nonparametric)**’ analysis under the ‘**Column analyses**‘ section. Double check that the datasets are ticked on the right window to be included in the test. Click the ‘**OK**’ button.

3. The next window will ask you to specify which test to perform. In this case, select the ‘**No matching or pairing**’ option, under the ‘**Experimental design**‘ header. Next, select ‘**Yes. Use ANOVA**’ under the ‘**Assume Gaussian distribution**’ header below.

4. Next, click the ‘**Multiple comparisons**‘ tab at the top. Select the ‘**Compare the mean of each column with the mean of every other column**‘ option. This will enable post-hoc testing to be carried out to determine where, if any, the significance lies.

5. Finally, click the ‘**Options**‘ tab at the top of the window. Ensure the ‘**Correct for multiple comparisons: Confidence intervals and significance. Recommended.**‘ option is selected, found under the ‘**Multiple comparisons test**‘ header. Then, select the appropriate post-hoc method to use. Tukey testing is selected as default, as is recommended by GraphPad, however, there is also the option to run Bonferonni and Sidak methods.

Also, I recommend selecting the ‘**Report multiplicity adjusted P value for each comparison**‘ option, under the ‘**Multiple comparisons**‘ header. The P values presented will then be adjusted.

Finally, click the ‘**OK**‘ button to run the One-Way ANOVA test.

# Output (ANOVA)

The results are split into two sheets: ‘**ANOVA**‘ and ‘**Multiple comparisons**‘. Click on the first sheet to see the results of the overall ANOVA test.

Focus on the output under the ‘**ANOVA summary**‘ header. Each output is as follows:

**F**– The F statistic.**P value**– The P value of the One-Way ANOVA test.**P value summary**– A summary of the p-value as represented by asterisks. These are useful to signify the level of significance on graphs, for example.**Are differences amoung means statistically significant? (P<0.05)**– A straight yes or no answer to was there any significance.**R square**– The R square value.

There are also other outputs reported in this sheet underneath, such as the F tests (Brown-Forsythe and Barlett’s).

# Interpretation (ANOVA)

By looking at the ‘**Significantly different? (P<0.05)**’ output, a ‘**Yes**’ is given which means that the results are significantly different from each other. The exact P value is given next to ‘**P value**’. In this case, a P value of <0.0001 is a very significant result.

Therefore, we accept the alternate hypothesis and reject the null hypothesis.

However, it is not known what groups explain the significance, simply that there is a difference between the three groups. This is where you now look at the results of the post-hoc tests.

# Output (post-hoc)

Next, open the results of the post-hoc tests by clicking the ‘Multiple comparisons’ results sheet.

Focus on the output under the ‘**Tukey’s multiple comparisons test**‘ header. Each group comparison is listed in a separate row. Since we have three groups, there are three possible comparisons. The results presented are as follows:

**Mean Diff.**– The difference between the two means.**95% CI of diff.**– The 95% confidence intervals for the difference.**Significant?**– A Yes or No answer as to whether the comparison is significance, i.e P < 0.05.**Summary**– The summary of the significance presented as asterisks.**Adjusted P Value**– The adjusted P value for the comparison.

The other useful output to look at is the ‘**Test details**‘ table which reports the descriptive statistics for each comparison, such as the mean and n number of each group.

# Interpretation (post-hoc)

By looking at the three comparisons, and focussing on the ‘**Significant?**‘ and ‘**Adjusted P Value**‘ columns, there are two significant results. Specifically, the comparison between groups AA vs AG and AA vs GG were significant. There was no difference between the AG vs GG groups.

# Reporting

To report the results of a One-Way ANOVA, it is appropriate to state the overall ANOVA test result first, followed by any post-hoc tests performed. An example of the reporting can be seen below.

The degrees of freedom (Df) can be found in the Brown-Forsythe test results table.

GraphPad Prism version used: 6