Advanced tables and statistics > Z, T and F tests > Newman-Keuls test
 
Newman-Keuls test
Quick reference
To request a Newman-Keuls test, type:
stat=nksig_level
on the tab statement. sig_level may be 90, 95 or 99.
More information
The standard Newman-Keuls test (as described in Winer, Statistical Principles in Experimental Design) is a table-level statistic that can be used as an alternative to T-tests when you want to compare the differences between the means of two or more samples of the same size.
The test is produced by the option stat=nknn option on the tab statement, where nn is 90, 95 or 99 depending on the level at which results are required. The column axis defines the groups to be compared. The row axis must include a base element, a mean (n12) and a standard deviation (n17) — these require fac= options on the axis elements or an n25 element with the inc= option. For details about these elements, see Statistical functions and totals.
Notes
▪This statistic calculates Q-values at the 90%, 95% or 99% level, as defined on the tab statement. A triangular matrix of Q-values is produced with values for each pair of means. It is labeled with the text ‘NEWMAN-KEULS STATISTICS’ followed by the level at which the values have been calculated.
▪This statistic uses the sum of totalizable rows and the input to the mean and standard deviation rather than the base and the mean and standard deviation themselves.
▪If the axis being tested contains fac= and inc=, Quantum scans backwards through the axis from the stat=t1 element and uses whichever of the two it finds first; that is, whichever of fac= or inc= occurs closest to, but still before, the statistical element.
▪Where a Q value is significant at the chosen level, an asterisk is printed underneath the value.
▪The formula adjusts for the fact that in practice sample sizes are seldom identical by using the harmonic mean of the sample sizes. This approach is described by Snedecor and Cochran in Statistical Methods and by Miller in Simultaneous Statistical Inference. However, it should be noted that this test is inappropriate when sample sizes differ markedly.
Example
The following table uses the same row and column axes as those used for the Two-Sample T-test (see ). It was created by the statement:
tab hours vcr;stat=nk95
Q15 Hours per week spent watching TV
Base: All Respondents
                   Base      Does not own a        Owns a video
                             video recorder            recorder
Base                305                 181               124
Under 5 hours        45                  24                21
5-6 hours            93                  50                43
7-10 hours           62                  40                22
11-15 hours          51                  31                20
16+ hours            54                  36                18

Mean              2.921               3.028             2.766
Std. Deviation    1.330               1.335             1.314
NEWMAN-KEULS STATISTICS (95%)
                            Owns a video
Has no video                2.392
The results show that, at the 95% level, there is no evidence of a difference between the mean scores.
See also
Z, T and F tests