# Creating an estimation plot of the results of an unpaired t test

Ho and colleagues showed a new way to present results of a t-test, that they call an "estimation plot". It is designed to display the raw data and the confidence interval for the difference between means, and thus put less emphasis on the P-value (1). Below is the example plot they presented.

On the left is a scatter plot of the control (C) and treated (T) raw data. The right side shows the 95% confidence interval. The right axis has the same interval (but different starting place) as the left axis. The red dot shows the difference between the two means, and the red line shows the 95% confidence interval of that difference. The Gaussian curve (sideways) shows the probability distribution of the difference between the two means, demonstrating that the 95% cutoff is arbitrary. Since the 95% confidence interval doesn't quite cross zero, this shows that with 95% confidence (if you accept a bunch of standard assumptions) you can say that the difference between population means is greater than zero. But you can see that the two distributions overlap substantially and that the 95% CI goes quite close to zero. Thus it is obvious that any conclusion from these data is pretty weak. In contrast, if you only saw a graph of the two means with SEM error bars and an asterisk denoting statistical significance, you might have been quite misled into thinking the evidence is stronger than it actually is.

GraphPad Prism cannot (yet) make an estimation plot automatically. The rest of this page shows how, with a bit of fussing, you can get Prism to make an estimation plot (without the Gaussian curve). The example is Figure 7 of a 2010 review by GraphPad's founder Harvey Motulsky and two colleagues(2). Download the Prism file.

Follow these steps with Prism 8 to enter and analyze the data.

- Enter the raw data into columns A and B of a new Column data table and enter column titles.
- Run the unpaired t test. On the options tab, choose the option to graph the CI of the difference between means and the option to report descriptive statistics for each data set.
- The analysis will create a new graph of the CI. You won't need this graph, so delete it.
- Go to the unpaired t test results. Next to the two tabs for tabular results and descriptive statistics, click the down arrow to open a menu and check the option to display the results for the mean diff plot.
- Go to the tab for the mean difference plot, select all three values, and copy to the clipboard.
- Go to the data table, position the insertion point in row 1 of column C, and use Edit..Paste Transpose. Enter "95% CI" as the column title. Now the table looks like this:

To make the graph, you need to do the following within the Format Graph and Format Axes dialogs (these instructions assume you are pretty familiar with Prism).

- Change data set C to be plotted as a bar showing median and range. Yes, that is right. The data represent the mean difference and its 95% CI. But the graph just sees three numbers, so you want to plot the the median of the three numbers, the middle one, with error bars extending down to the smallest value and up to the largest value.
- Check the option to draw a vertical line to be plotted between the second and third data set. Do this at the bottom of the Data Sets On Graph tab of the Format Graph dialog.
- Add a right Y-axis. You want this axis to have the same range (max-min) and interval as the left Y axis, but with an offset to make the bar baseline to be aligned with the smaller of the two sample means. Set the bottom (minimum) of the right Y-axis to equal -1 times the smaller of the two group means. You can see the group means on the descriptive statistics tab of the t test. For these datasets, the smaller mean is 30.17, so set the axis minimum to -30.17. Set the top of the right axis to be the top of the left Y-axis (80) minus the smaller of the two means, 30.17, which is 49.83.
- Draw a short line to serve as the base of the bar in the right half of the graph.

Let us know if you'd like us to automate these steps in a future release.

1. Ho, J., Tumkaya, T., Aryal, S., Choi, H., and Claridge-Chang, A. (2019). Moving beyond P values: data analysis with estimation graphics. Nat. Methods *16*: 565–566.

2. Michel, M.C., Murphy, T.J., and Motulsky, H.J. (2020). New Author Guidelines for Displaying Data and Reporting Data Analysis and Statistical Methods in Experimental Biology. Molecular Pharmacology *97*: 49–60.

Keywords: estimation graph estimating plot estimating graph