GraphPad Curve Fitting Guide

Replicates

Replicates

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Replicates

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If you entered data with replicates (in side-by-side subcolumns), Prism gives you two choice for how to deal with the replicates.

Consider each replicate as an individual point.

Fit the means of each set of replicates.

The rest of this page explains how to decide. When in doubt, choose to fit individual replicates. The other choice is only rarely useful.

Independent replicates

In most experiments, it is fair to consider each replicate to be an independent data point. Each particular replicate is subject to random factors, which may increase or decrease its value. Each random factor affects individual replicates, and no random factor affects the replicates as a group. In any kind of biochemical experiment, where each value comes from a test tube or plate well, the replicates are almost certain to be independent.

When your replicates are independent, Prism will treat each replicate as a separate point. If there are four replicates at one X value and two at another, the four replicates will automatically get twice the weight, since the program considers them to be four separate data points.

If you ask Prism to fit the mean values, rather than individual replicates, you won't get valid standard errors and confidence intervals. If you have different number of replicates at different X values, you will lose the extra weights that the points with more replicates deserve, so will get incorrect best-fit values.

Replicates that are not independent

In some experimental situations, the replicates are not independent. Random factors can affect all the replicates at once. Two examples:

You performed a binding experiment with a single tube at each concentration, but measured the radioactivity in each tube three times. Those three values are not independent. Any experimental error while conducting the experiment would affect all the replicates.

You performed a dose-response experiment, using a different animal at each dose with triplicate measurements. The three measurements are not independent. If one animal happens to respond more than the others, that will affect all the replicates. The replicates are not independent.

Treating each replicate as a separate data point would not be appropriate in these situations. Most of the random variation is between tubes (first example) or animals (second example). Collecting multiple replicates does not give you much additional information. Certainly, each replicate does not give independent information about the values of the parameters. Here is one way to look at this. Imagine that you have performed a dose-response experiment with a separate animal for each dose. You measure one animal in duplicate (for one dose) and another animal (another dose) ten times. It would be a mistake to enter those as individual values, because that would give five times more weight to the second dose compared to the first. The random factors tend to affect the animal, not the measurement, so measuring an animal ten times does not give you five times more information about the true value than measuring it two times.

Since each tube (first example, above) or animal (second example) is the experimental unit, you should enter each tube or animal once. If you measured several replicates, average these and enter the average. Don’t enter individual values. Don’t weight the means by sample size. Doing so would inflate the number of degrees of freedom inappropriately, and give you SE that are too small and CI that are too narrow. Doing so, when you have unequal number of replicates would give artificial, and undeserved, weight to the tubes or animals with more replicates, so would affect the best-fit curve and you would get less than optimal best fit parameter values.

If you are confused by the choice of fitting to individual replicates vs. the mean, choose to fit individual replicates (which is the default