# Calculating the grand mean of column data.

Prism does not compute the grand mean of all values on a table, either as part of column statistics or one-way ANOVA.

How to compute the grand mean with Prism

Change the data table to by an XY table, and enter X values. To do this, drop the Change menu and choose Format Data Table.

1. Enter X values. It doesn't matter which values you use, but every row with a value in the Y columns must have an X value. One suggestion: Enter the row numbers as X values. Shortcut: Drop the Insert menu and choose Create Series.
2. Click Analyze, and choose nonlinear regression. No the data are not nonlinear, and no you don't really want to fit regression. But this method can be used to find the value of the grand mean you want.
3. The first step in nonlinear regression is to choose an equation on the first (Fit) tab of the nonlinear regression dialog. Choose the horizontal line model in the Lines section.
4. In the Constrain tab of the dialog, set the constraint type to Shared value for all data sets.
5. Click OK. The "best-fit" value of Mean will be the Grand mean of all the values you entered.

Notes

The equation for this model is:  Y = Mean + 0*X. Since the X values are all multiplied by zero, it doesn't make any difference what values you enter. But it does matter than you enter an X value on each row, as rows without X values are ignored by the regression.

Why not just fit the model Y=Mean, and forget about the X values? As the name suggests, the nonlinear regression analysis was created to fit a curve to XY data, and cannot analyze data without X values in the data table and X in the equation. Adding the 0*X term is a sneaky way to get Prism to extend the nonlinear regression method in a way we didn't anticipate when we designed the analysis.

If you don't share the value of Mean, then Prism would compute one mean for each data set column. These values would be identical to those computed by the Column Statistics analysis.  if you share the value of Mean, then you get one value for the entire table. This is the grand mean.

The value computed above is the mean of all the values you entered on the data table. You'd get the same value by adding up all the values you entered, and dividing by the total number of values.

Distinguish the grand mean computed here from the mean of column means computed by first calculating the mean of each column, and then computing the mean of those means. If some columns have more values than others, those two methods will give different results. If you enter twice as many values into column A as you entered into column B, then column A will have twice the weight in the computation of the grand mean but equal weight when computing the mean of column means.

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