Calculating "Unknown" Concentrations using a Standard Curve

A standard curve is a graph relating a measured quantity (radioactivity, fluorescence, or optical density, for example) to concentration of the substance of interest in "known" samples.  You prepare and assay "known" samples containing the substance in amounts chosen to span the range of concentrations that you expect to find in the "unknown" samples.  You then draw the standard curve by plotting assayed quantity (on the Y axis) vs. concentration (on the X axis).  Such a curve can be used to determine concentrations of the substance in "unknown" samples.  Prism automates this process.

Prism can fit standard curves using nonlinear regression (curve fitting), linear regression, or a cubic spline (or LOWESS) curve. To find "unknown" concentrations using a standard curve, follow these steps:

Enter the Data

In the Welcome to GraphPad Prism dialog box, choose to Create an XY data table. Choose to format the X values as Numbers and to format the Y column for the number of replicates in your data.  For our example, choose Enter and plot a single Y value for each point.

Enter data for the standard curve.  In our example, shown below, we entered concentrations for the "known" samples into the X column, rows 1-5, and the corresponding assay results into the Y column. Just below the standard curve values, starting in row 6, enter the assay results for the "unknown" samples into the Y column, leaving the corresponding X cells blank.  Later, Prism will fit the standard curve and then report the unknown substance concentrations using that curve.

Fit the Curve

Click on the Analyze button. From the XY analyses category, select Simple linear regression if you are using our example data (or if you are analyzing data that you suspect are curvilinear, choose Nonlinear regression [curve fit]).

In the Parameters: Simple Linear Regression dialog box, check the box labeled Interpolate unknowns from the standard curve, because we want our unknown concentrations to be provided. 

When you click OK, Prism performs the fit and creates a results sheet.

View the Results

Prism displays the results in various tabs.  The default view (Tabular results) shows the defining parameters for the curve of best fit.  

Switch to the Interpolated X values tab (in early Prism releases, this was "Standard curve X from Y").

Prism reports the corresponding X value for each unpaired Y value on your data sheet.

Add Unknowns to your Graph

Prism's automatic graph includes the data from the data sheet and the curve, as seen below.

To add the "unknowns" to the graph, switch to the Graphs section of your project.

Click on the Change button and then select Data Sets on Graph. The dialog box shows all data and results tables that are represented on the graph.  Click on the Add button.

From the drop-down list at the top of the Add Data Sets to Graph dialog box, select ...Simple linear regression of Data...  as seen below.

Press OK to return to the graph. If you want the "unknowns" represented as spikes projected to the X axis (rather than data points), double-click on the graph to bring up the Format Graph dialog.  From the "Data set" drop-down list, select ...Simple linear regression of Data..., and adjust the options shown in the screenshot below. 

Here are the standard curve results -- Unknowns are represented as spikes on the graph; numerical results are reported as an embedded table.  The illustration includes some formatting changes not discussed here.