Standardizing Values

Obtains z-scores for each observation in a data set.

To Standardize

Here the data are in C1 ‘data’. You want to compute z-scores for each observation: z = (data - mean) / stdev. In the example a target column (the place where you will store the results) has already been determined: C2 'z' (any column will do).

You only need to identify the data column and target column to complete the standardization.

You can see here that the correct operation (Subtract mean and divide by std. dev.) is selected by default (although others are availabe). Your z-scores will be placed in the worksheet in the 'z' column.

To determine how many observations lie within a particular number of standard deviations of the mean.

One way to do this is to count. A quicker way is to use the Minitab column calculator.

The example here determines, for each observation, whether or not it lies within 2 standard deviations of the mean. You can substitute any value for 2 and do the same thing.

Begin by opening the column calculator. (Note that the z-scores are in place in C2.)

Again you need a target column. The target will indicate whether an observation’s z-score is between -2 and 2. The target column here is C3 ‘ind’.

The expression determines whether for each value it is between -2 and 2. The results get placed in column C3 ‘ind’.

A 1 appears in C3 wherever the observation is within 2 standard deviations of the mean. Note row 6, where the entry is 0. The value of 14.5774 has a z-score of -2.80. This observation does not lie within 2 standard deviations of the mean.

Finally, obtain Basic Statistics for C3. The mean of C3 is the proportion of observations that lie within 2 standard deviations of the mean.

To determine how many observations are positive (negative).

It requires the same approach using the column calculator; just enter C < 0 (or C > 0) as the expression where C designates your column.

The result is this.

Now find the mean of the values in C2 ‘neg’ and you’ll know the proportion of values that are negative.