Fitting a Gaussian distribution to a frequency distribution

Why fit a Gaussian distribution to your data?

Does you data follow a Gaussian distribution? One way to answer that question is to perform a normality test on the raw data. Another approach is to examine the frequency distribution or the cumulative frequency distribution.

Fitting a Gaussian distribution

To fit the frequency distribution, you have to specify that the distribution be plotted as an XY plot, so the bin centers are X values (and not just row labels). Then click Analyze, choose nonlinear regression, and choose the Gaussian family of equations and then the Gaussian model.

The results depend to some degree on which value you picked for bin width, so we recommend fitting the cumulative distribution as explained below.

Fitting a cumulative Gaussian distribution

The cumulative Gaussian distribution has a sigmoidal shape.

To fit the frequency distribution, you have to specify that the distribution be plotted as an XY plot, so the bin centers are X values (and not just row labels). Then click Analyze, choose nonlinear regression, and choose the one of the cumulative Gaussian models from the selection of Gaussian models. Prism offers separate models to use for data expressed as percentages, fractions or number of observations. With the last choice, you should constrain N to a constant value equal to the number of values.

The graph below shows the cumulative distribution of the sample data (in percents) fit to the cumulative Gaussian curve. The observed distribution is plotted with red circles and the fit distribution is a blue curve. The two are superimposed, so hard to distinguish.

Plotting on a probability axis

Below, the same graph is plotted using a probability Y axis. To do this, double-click on the Y axis to bring up the Format Axis dialog, drop down the choices for scale in the upper right corner, and choose "Probability (0..100%). The cumulative Gaussian distribution is linear when plotted on probability axes. At the top right of the graph, the cumulative distribution is a bit higher than predicted by a Gaussian distribution. This discrepancy is greatly exaggerated when you plot on a probability axis.