To create an element whose value is the mean of the values in the other elements of the axis, type:

To create a standard deviation element, type:

To create a standard error element, type:

To create an error variance element, type:

All rows that are to be included in these calculations need factors. These can be defined using fac= on each row or by the option inc= on an n25 statement. If the latter, the n25 must come before the statistical statement.

When an axis contains both fac= and n25;inc=, and statistics are requested, Quantum must decide which values to use in the statistical calculations. To do this, it works backwards from the statistical element to the start of the axis looking for elements with fac= or an n25 statement. If it finds an n25 first (that is, latest in the axis), it uses the values named with inc=. If the first thing found is a group of elements with fac=, then the statistics are based on those factors. If neither is found, Quantum issues an error message to that effect.

The mean (n12) reports the mean value of the factors or values belonging to each respondent.

The standard deviation (n17) is the amount by which you would expect respondents’ answers to differ from the mean. You can apply the standard deviation to the mean at three levels. If you just take the standard deviation reported by Quantum, you would expect 67% of answers to lie within the range mean±std.dev. You can also expect that 95% of answers lie within the range mean±2std.dev, and that 99% of answers will lie within the range mean±3std.dev.

You use the standard error (n19) to estimate the mean for the population as a whole, based on the mean of your sample. You can be 95% certain that the mean score for the population as a whole will lie within the range mean±2std.err.

The sample variance (also known as the error variance) is the square of the standard error.