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The type II error or beta is less studied but is of great importance. In fact, it represents the probability that one does not reject the null hypothesis when it is false. We cannot fix it up front but, based on other parameters of the model, we can try to minimize it. The power of a test is calculated as 1-beta and represents the probability that we reject the null hypothesis when it is false.
We therefore wish to maximize the power of the test. XLSTAT calculates the power (and beta) when other parameters are known. For a given power, it also allows to calculate the sample size that is necessary to reach that power. The statistical power calculations are usually done before the experiment is conducted. The main application of power calculations is to estimate the number of observations necessary to properly conduct an experiment.
This example aims to estimate the necessary sample size in classical clinical trials.
When organizing a trial, the first question that arises is the number of patients to be included in order to obtain statistically valid results.
Three types of trials can be studied:
Once you have clicked on the OK button, the calculations begin and the results are displayed.
The first table shows the main results followed by their interpretation.
We can see that 945 patients are required, which means two groups of at least 473 patients.
The simulation plot gives you more information on the evolution of the sample size depending on power.
A new treatment has been obtained which has way fewer side effects than the classical treatment. We wish to be sure that both treatments are equivalent. To do so, we should test that both treatments are in the same range of results.
We use equivalence testing. An equivalence limit should be defined. Here, we define an equivalence limit of 10%.
The outcome is the fact that a patient is cured or not. This is a binary outcome. We suppose that the control group (with the oldest treatment) and the treatment group (with the new treatment) have a recovery rate of 60%. We wish to estimate necessary sample size for a level of 5% and a power of 0.9.
Choose the objective Find the sample size, then select the equivalence trial and the binary outcome. The alpha is 0.05. The desired power is 0.9. The % of success for both groups is 60% and the equivalence limit is equal to 10%.
Once you have clicked the OK button, the calculations begin and results are displayed.
The first table shows the main results followed my their interpretation.
We can see that 1038 patients are necessary, which means two groups of at least 519 patients.
The simulation plot gives you more information on the evolution of the sample size depending on power.
A new treatment has been obtained; it is cheaper than the actual treatment. We wish to be sure that the new treatment has an at least equal or a little bit less efficient effect than the actual treatment. To do so, we should test that the new treatment is better or slightly worse than the original treatment.
We use non-inferiority testing. A non-inferiority limit should be defined. In our case we define a non-inferiority limit of 8%.
The outcome is the fact that a patient is cured or not. It is a binary outcome. We suppose that the control group (with the oldest treatment) has a recovery rate of 70% and the treatment group (with the new treatment) has a recovery rate of 75%. We wish to estimate the needed sample size for a level of 5% and a power of 0.9.
Choose the objective Find the sample size, then select the non-inferiority trial and the binary outcome. The alpha is 0.05. The desired power is 0.9. The % of success for the control group is 70% and the % of success for the treatment group is 75%. The non-inferiority limit is equal to 8%.
Once you have clicked on the OK button, the calculations begin and the results are displayed.
The first table shows the main results followed by their interpretation.
We can see that the analysis need to be run on 302 patients to reach a power of 0.9.
The simulation plot gives you more information on the evolution of the sample size depending on power.
By using XLSTAT Power features, you can obtain the necessary sample size for three types of trials. We have seen that non-inferiority trials are less restrictive but are also more controversial.
XLSTAT enables you to find the power and the sample size when the outcome variable is continuous and to represent many simulation plots.
If you are a licensed XLSTAT user, to activate XLSTAT-R all you need to do is install XLSTAT 2017.6 or later. If you are not a licensed user, you should install the XLSTAT trial version, or, if you have already used a trial in the past, you need to order a license.
Once R is installed, go to XLSTAT > Advanced features > XLSTAT-R and click on one of the existing functions. See an example below.The corresponding feature dialog box opens:Then, you simply need to select the data and configure the dialog box like in standard XLSTAT function. Click OK to launch the computations. If you have never set up analysis in XLSTAT before, have a look at an example here.
As part of this procedure, you will need to edit XML files. We recommend that you use Sublime (Windows and Mac) or Notepad++ (Windows only), or any editor that takes into account the file format and can make the difference between code parts and user inputs.
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Discover the seamless integration of XLSTAT into Excel, enhancing your data analysis capabilities. This powerful add-on provides advanced statistical functions right within your spreadsheet environment.
XLSTAT is a comprehensive statistical software solution that functions as an Excel add-on, allowing users to perform advanced data analysis and create custom reports. To install, visit the Free Trial page and download the latest version of XLSTAT. The installation process is quick, taking only a few minutes. Users have the option to install XLSTAT for all computer users or for a single session. Once installed, XLSTAT integrates seamlessly with Microsoft Excel.
After installation, you can activate XLSTAT by entering a license key. If you are a new user, you can start with a 14-day free trial by using a trial license key. To keep the software up to date, download and install the latest version of XLSTAT. This ensures you have access to the latest features and improvements for efficient data processing and statistical analysis.
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