15.11 MEANS

MEANS [TABLES =]
      {var_list}
        [ BY {var_list} [BY {var_list} [BY {var_list} … ]]]

      [ /{var_list}
         [ BY {var_list} [BY {var_list} [BY {var_list} … ]]] ]

      [/CELLS = [MEAN] [COUNT] [STDDEV] [SEMEAN] [SUM] [MIN] [MAX] [RANGE]
        [VARIANCE] [KURT] [SEKURT]
        [SKEW] [SESKEW] [FIRST] [LAST]
        [HARMONIC] [GEOMETRIC]
        [DEFAULT]
        [ALL]
        [NONE] ]

      [/MISSING = [INCLUDE] [DEPENDENT]]

You can use the MEANS command to calculate the arithmetic mean and similar statistics, either for the dataset as a whole or for categories of data.

The simplest form of the command is

MEANS v.

which calculates the mean, count and standard deviation for v. If you specify a grouping variable, for example

MEANS v BY g.

then the means, counts and standard deviations for v after having been grouped by g are calculated. Instead of the mean, count and standard deviation, you could specify the statistics in which you are interested:

MEANS x y BY g
      /CELLS = HARMONIC SUM MIN.

This example calculates the harmonic mean, the sum and the minimum values of x and y grouped by g.

The CELLS subcommand specifies which statistics to calculate. The available statistics are:

• MEAN The arithmetic mean.
• COUNT The count of the values.
• STDDEV The standard deviation.
• SEMEAN The standard error of the mean.
• SUM The sum of the values.
• MIN The minimum value.
• MAX The maximum value.
• RANGE The difference between the maximum and minimum values.
• VARIANCE The variance.
• FIRST The first value in the category.
• LAST The last value in the category.
• SKEW The skewness.
• SESKEW The standard error of the skewness.
• KURT The kurtosis
• SEKURT The standard error of the kurtosis.
• HARMONIC The harmonic mean.
• GEOMETRIC The geometric mean.

In addition, three special keywords are recognized:

• DEFAULT This is the same as MEAN COUNT STDDEV.
• ALL All of the above statistics are calculated.
• NONE No statistics are calculated (only a summary is shown).

More than one table can be specified in a single command. Each table is separated by a ‘/’. For example

MEANS TABLES =
      c d e BY x
      /a b BY x y
      /f BY y BY z.

has three tables (the ‘TABLE =’ is optional). The first table has three dependent variables c, d and e and a single categorical variable x. The second table has two dependent variables a and b, and two categorical variables x and y. The third table has a single dependent variables f and a categorical variable formed by the combination of y and z.

By default values are omitted from the analysis only if missing values (either system missing or user missing) for any of the variables directly involved in their calculation are encountered. This behaviour can be modified with the /MISSING subcommand. Three options are possible: TABLE, INCLUDE and DEPENDENT.

/MISSING = INCLUDE says that user missing values, either in the dependent variables or in the categorical variables should be taken at their face value, and not excluded.

/MISSING = DEPENDENT says that user missing values, in the dependent variables should be taken at their face value, however cases which have user missing values for the categorical variables should be omitted from the calculation.

15.11.1 Example Means

The dataset in repairs.sav contains the mean time between failures (mtbf) for a sample of artifacts produced by different factories and trialed under different operating conditions. Since there are four combinations of categorical variables, by simply looking at the list of data, it would be hard to how the scores vary for each category. Example 15.4 shows one way of tabulating the mtbf in a way which is easier to understand.

get file='repairs.sav'.  means tables = mtbf       by factory by environment.

Example 15.4: Running MEANS on the mtbf score with categories factory and environment

The results are shown in Result 15.3. The figures shown indicate the mean, standard deviation and number of samples in each category. These figures however do not indicate whether the results are statistically significant. For that, you would need to use the procedures ONEWAY, GLM or T-TEST depending on the hypothesis being tested.

	N	Percent	N	Percent	N	Percent
	Cases
	Included	Excluded	Total
mtbf * factory * environment	30	100.0%	0	.0%	30	100.0%
Manufacturing facility	Operating Environment	Mean	N	Std. Deviation
0	Temperate	7.26	9	2.57
Tropical	7.47	7	2.68
Total	7.35	16	2.53
1	Temperate	13.38	6	7.77
Tropical	8.20	8	8.39
Total	10.42	14	8.26
Total	Temperate	9.71	15	5.91
Tropical	7.86	15	6.20
Total	8.78	30	6.03

Result 15.3: The mtbf categorised by factory and environment

Note that there is no limit to the number of variables for which you can calculate statistics, nor to the number of categorical variables per layer, nor the number of layers. However, running MEANS on a large numbers of variables, or with categorical variables containing a large number of distinct values may result in an extremely large output, which will not be easy to interpret. So you should consider carefully which variables to select for participation in the analysis.