How do I use the four parameters logistic regression to compare two samples
The four parameters parallel lines logistic regression allows comparing the regression lines of two samples (typically a standard sample, and a sample that is currently being studied). Of course, this tool can also be used to fit a four parameter logistic curve to a unique sample.
The example treated here is an medical case where a molecule is being injected at a given concentration, and where the concentration of type of cells in the blood is being measured. An Excel sheet with both the data and the XLSTAT-Dose results can be downloaded by clicking here.
To activate the parameters logistic regression dialog box, start XLSTAT, then select the XLSTAT-Dose/Four parameters logistic regression command, or click on the corresponding button of the "XLSTAT-Dose" toolbar (see below).
When you click on the button, a dialog box appears. Select the data on the Excel sheet. The "Dependent variable" is here the concentration of cells, and the "Explanatory variable" is the Log of the concentration of the injected molecule. As we selected the column titles of all variables, we have selected the option "Column labels included".
In the "Options" tab, we uncheck the Dixon's test because we do not think that there are Outliers in our data.
The computations begin once you have clicked on the "OK" button. The results are displayed on a new sheet as requested in the first dialog box.
Interpreting the results of a four-parameter logistic regression
The first table gives the descriptive statistics of the selected data.
The a table displays the results of the F test that is performed to check if the two curves are parallel.
We see here that the two curves cannot be considered as being parallel. This indicates that there is a significant difference between the samples.
However we see that the goodness of fit statistics are high (see table below). This means that the difference the samples is well explained by the difference between the slope parameters c1 and c2.
The fitted parameters are displayed in the table below.
After the tables that contains the predictions and residuals for both samples, the two regression curves are displayed, enabling a visual comparison of the samples.
We can see that the strongest differences responsible for the significant difference between the samples are in the [1.6, 2] for the log of the concentration.
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