Essential Statistics

This video walks you through the steps required to perform a one-way ANOVA, including what analysis choices and options you will have to make about your experiment to perform the analysis.

You will learn how to:

- Correctly enter your data for a one-way ANOVA
- Select the parameters for your analysis
- S ...

This video walks you through the steps required to perform a one-way ANOVA, including what analysis choices and options you will have to make about your experiment to perform the analysis.

You will learn how to:

- Correctly enter your data for a one-way ANOVA
- Select the parameters for your analysis
- Select the appropriate test
- Format and annotate a graph of your results

This video is part of the Essential Statistics series, presented by Dr James Clark, from the School of Cardiovascular Medicine and Sciences at King’s College London.

*Transcript:*

Hello, my name is James Clark from King's College London. In this short video I'm going to work through the steps required to undertake a one-way ANOVA in GraphPad Prism. Probably the three most used statistical tests in biomedical science are the Student T-test or T-test, regression analysis and the analysis of variance, or ANOVA.

The way you enter data in Prism to undertake both T-tests and one-way ANOVA are the same. You use the column format table, as you can see in front of us on the screen and you enter your groups into the individual columns. For instance, if I was undertaking a T-test, I would enter Group A and Group B because a T-test only compares two sets of data. Since I'm undertaking a one-way ANOVA and have three sets of data, I've entered my control data into Group A. Group B contains drug A's data and Group C contains the data from an experiment using Drug B. These three data sets have equal end numbers and I want to undertake a one-way ANOVA to see whether these means are different.

Before you undertake any parametric statistical test, it is best advised to check that your data first fit within a Gaussian normal or bell shaped distribution. GraphPad Prism allows you to undertake normality tests and we've done a normality test on these data and you can see that all three groups, Control, Drug A and Drug B pass normality tests. Therefore, we can carry out a parametric statistical analysis on these data. We can look at our data in Prism as a table or we can look at our data and represent it as a graph. Here we can see graphical presentation of our experiment, Control in blue, Drug A in red and Drug B in green.

You can immediately see that Control and Drug A look quite similar, whereas Drug B numerically appears to have a higher output. We wish to undertake a one-way ANOVA to compare these three groups.

In order to do an ANOVA, you need to select your data set and click on the analyze button. You can do that from within the graph view by clicking on analyze in the menu. You can do it from your table view by clicking on analyze from the menu or you can click on new analysis from within the results section. For the purposes of this walkthrough, we're going to click on analyze from the table view.

As soon as you click on analyze, it brings in the analyze data menu box. This allows you to select which analysis you wish to carry out on your data. We wish to do a column analysis and we wish to do a one-way ANOVA, as shown on the screen. Once you've selected one-way ANOVA, you move to the right side of the screen and make sure your data sets have been selected. It is not unusual to include multiple data sets on a single Prism table. In this occasion we only have three data sets and they're the data sets we're concerned with, so we've selected everything. You can deselect all data set or select all data set from this window or simply select the data sets you're interested in analyzing individually. Once you've selected your data sets, click okay.

There are essentially two different types of one-way ANOVA. These types depend upon the experimental design that's been undertaken. When the parameters window appears, a question you need to ask yourself is, "How was my experiment designed? Was there matching or pairing?" If so, you need to choose the second option. Each row represents matched or repeated measures data. By doing this, however, you need to ensure that your data are entered correctly. If, for instance, Subject One appears in row one in Group A, row two in Group B and back in row one in Group C, the analysis will not be correct. You need to ensure that if you have a repeated measures study that each subject appears in their own row. The data used here, albeit fictitious, are not matching or pairing, so I'm going to click on the no matching or pairing.

The second question you need to ask, "Are your data Gaussianly distributed?" We've already done a normality test on these data and we know that they are Gaussianly distributed. Therefore we can say yes. We will also assume they have equal standard deviations and we will choose yes to the next option.

The second option we have in the parameters window relates to repeated measures, but since we haven't selected this as a repeated measures study, all the options are grayed out.

The third option is to do with multiple comparisons. In other words, once we've done a one-way ANOVA and ensured there are differences between groups, we then need to find out what those differences are, using a post hoc test. A post hoc test in the context of an ANOVA is very much like individual T-tests between groups, but with some subtle mathematical modifications that make them relevant to group and pairwise analyses.

The choices we have in these follow-up tests or post hoc tests, are none, compare the mean of each column with a mean of every other column, and in the context of this experiment for instance, that will be comparing Control with Drug A, Control with Drug B, Drug A with Drug B and Drug B with Control. We can compare the mean of each column with the mean of a Control column. In other words, compare Group A, which is our Control, with Drug A and Drug B, but not compare Drug A directly with Drug B. You can of course select what your Control column is.

You can select individual pairs. So for instance, if I only want to compare Drug A with Drug B, I can click on that and choose it here. However, for the benefits of this analysis, I'm going to choose the second option and compare all columns with every other column, which is probably the most likely scenario that you would adopt in your laboratory.

The fourth option within parameters window is called options. Within the options window, you get to choose which multiple comparison post hoc test you undertake. Of course, the test you choose will result in a different P value for a given difference between groups and that is dependent upon the stringency of each of the tests. By default, Prism will recommend which test to do. For instance, here in our multiple comparisons test, Prism is recommending we undertake the Tukey test. The other options are Bonferroni, Sidak, Holm-Sidak or Newman-Keuls. Newman-Keuls is not a particularly stringent test and we certainly do not recommend using that.

We're going to use Tukey, which is a recommended test. If you're unsure what the stringency of these tests are and whether your particular data set with your end number is suitable to use for these tests, remember there is a little help button down the bottom left hand side of your window and if you click on this at any time, it will bring up the very intuitive Prism help file.

So having selected Tukey, we're going to move on to the last window, which is our optional residuals plot. We're going to leave this blank, so I'm just going to confirm that I've chosen the right multiple comparisons, the right post hoc test and my experimental design is not matching, and then click on the OK button to bring up the results window.

The results window is fairly self explanatory. There are two results windows within each result pane. We have our ANOVA results and we have our multiple comparison results. On the ANOVA results window, it reports which data sets are being analyzed, the F score from our ANOVA, a P value showing in general, the probability that there is differences between groups, the R squared value and then a series of other outputs.

Since our main concern for this experiment is what are the differences between our groups, we're going to go to our multiple comparisons window. The multiple comparisons window will give us the outcome of the post hoc tests, in this case a Tukey multiple comparison test. If we concern ourselves with the outputs listed in the second block of text, we can see that Control versus Drug A is not significant. The P value is greater than nought point nought five. Control and Drug B however, are significantly different and in addition, Drug A and Drug B are significantly different.

Now we have determined which groups are statistically different from which groups, we can annotate our graph accordingly. Using the drawing palette in Prism8 we can select lines with text and draw a horizontal line between Drug A and Drug B and using the star in the dropdown mist, we can indicate that Drug A is significantly different from Drug B treatment. We can repeat this between our Control and Drug B and indicate a level of significance.

So now we have carried out a one-way ANOVA between three data sets and annotated the graph with the results of our statistical test.

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