## (Basic Statistics for Citizen Data Scientist)

# Real Statistics Power Data Analysis Tool

**Real Statistics Data Analysis Tool**: The Real Statistics Resource Pack supplies the **Statistical Power and Sample Size** data analysis tool to determine the power which results from a statistical test for a specified effect size, sample size and alpha, as well as the sample size required to achieve a specified effect size, power and alpha.

To use this tool, press **Ctrl-m** and select **Statistical Power and Sample Size **from the resulting menu. The dialog box in Figure 1 will then appear.

**Figure 1 – Statistical Power and Sample Size dialog box**

You can now select one of the specified twelve tests and either the **Power** or **Sample Size** options. E.g. if you choose the **two-sample t test** and the **Power** options, you will be presented with the dialog box shown on the left side of Figure 2.

**Figure 2 – Power: two-sample t test dialog box**

Next fill in the **Input** fields, as shown on the right side of Figure 2 (retaining the default values of the **# Tails, Alpha** and **Sum Count** fields). After pressing the **OK** button you will see the results shown in **Output** area in the dialog box on the right side of the figure.

We see that the power of this test is 48.2% (we explain the other output fields elsewhere). To increase the power of the test for the given effect size, you would normally need to change from a two-tailed to a one-tailed test, increase the sample size(s), increase the alpha value or make some combination of these.

For this example if you change the **# Tails** to 2, you would increase **Power** to 60.8%. If you keep to a two-tailed test, you would need to increase alpha to .28 to obtain power of at least 80%, which is usually not very acceptable. Alternatively you could increase the sample sizes. E.g. to achieve a power of 80% you would need to increase the sample sizes to 176.

This can be determined by using the **Sample Size** option shown in Figure 1. You can do this by first pressing the **Cancel** button (on the dialog box in Figure 2) or the **x** in the upper right-hand corner of the dialog box. When the dialog box shown in Figure 1 reappears select the **Sample Size** option.

The dialog box shown on the left side of Figure 3 now appears. You need to insert .3 for the **Effect Size** and press the **OK** button. The result is shown on the right side of Figure 3, confirming that samples sizes of 176 are required. Note that the actual power achieved is a little more than 80%.

**Figure 3 – Sample size: two-sample t test dialog box**

Note that the **Sample size ratio** is set to 1, which means that the ratio *n*_{2}/*n*_{1} = 1 (where *n*_{1} = size of sample 1 and *n*_{2} = size of sample 2), i.e. the samples are equal. If we wanted the size of the second sample to be twice that of the first sample we would set **Sample size ratio** to 2.

We could also specify that sample 2 has a specific size, say 100, by using a negative value for **Sample size ratio**, -100 in this case. Note that if we fix *n*_{2}, then to achieve power of 80% for the above example, we would need a larger sample 1. In particular, we would need sample 1 to have size 695.

Statistics for Beginners – Introduction to Excel Data Analysis Tools

## Statistics for Beginners in Excel – Real Statistics Power Data Analysis Tool

Disclaimer: The information and code presented within this recipe/tutorial is only for educational and coaching purposes for beginners and developers. Anyone can practice and apply the recipe/tutorial presented here, but the reader is taking full responsibility for his/her actions. The author (content curator) of this recipe (code / program) has made every effort to ensure the accuracy of the information was correct at time of publication. The author (content curator) does not assume and hereby disclaims any liability to any party for any loss, damage, or disruption caused by errors or omissions, whether such errors or omissions result from accident, negligence, or any other cause.The information presented here could also be found in public knowledge domains.

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