NPAR TESTS

NPAR TESTS
     nonparametric test subcommands
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     [ /STATISTICS={DESCRIPTIVES} ]

     [ /MISSING={ANALYSIS, LISTWISE} {INCLUDE, EXCLUDE} ]

     [ /METHOD=EXACT [ TIMER [(N)] ] ]

NPAR TESTS performs nonparametric tests. Nonparametric tests make very few assumptions about the distribution of the data. One or more tests may be specified by using the corresponding subcommand. If the /STATISTICS subcommand is also specified, then summary statistics are produces for each variable that is the subject of any test.

Certain tests may take a long time to execute, if an exact figure is required. Therefore, by default asymptotic approximations are used unless the subcommand /METHOD=EXACT is specified. Exact tests give more accurate results, but may take an unacceptably long time to perform. If the TIMER keyword is used, it sets a maximum time, after which the test is abandoned, and a warning message printed. The time, in minutes, should be specified in parentheses after the TIMER keyword. If the TIMER keyword is given without this figure, then a default value of 5 minutes is used.

• Binomial test
• Chi-square Test
  • Chi-square Example
• Cochran Q Test
• Friedman Test
• Kendall's W Test
• Kolmogorov-Smirnov Test
• Kruskal-Wallis Test
• Mann-Whitney U Test
• McNemar Test
• Median Test
• Runs Test
• Sign Test
• Wilcoxon Matched Pairs Signed Ranks Test

Binomial test

     [ /BINOMIAL[(P)]=VAR_LIST[(VALUE1[, VALUE2)] ] ]

The /BINOMIAL subcommand compares the observed distribution of a dichotomous variable with that of a binomial distribution. The variable P specifies the test proportion of the binomial distribution. The default value of 0.5 is assumed if P is omitted.

If a single value appears after the variable list, then that value is used as the threshold to partition the observed values. Values less than or equal to the threshold value form the first category. Values greater than the threshold form the second category.

If two values appear after the variable list, then they are used as the values which a variable must take to be in the respective category. Cases for which a variable takes a value equal to neither of the specified values, take no part in the test for that variable.

If no values appear, then the variable must assume dichotomous values. If more than two distinct, non-missing values for a variable under test are encountered then an error occurs.

If the test proportion is equal to 0.5, then a two tailed test is reported. For any other test proportion, a one tailed test is reported. For one tailed tests, if the test proportion is less than or equal to the observed proportion, then the significance of observing the observed proportion or more is reported. If the test proportion is more than the observed proportion, then the significance of observing the observed proportion or less is reported. That is to say, the test is always performed in the observed direction.

PSPP uses a very precise approximation to the gamma function to compute the binomial significance. Thus, exact results are reported even for very large sample sizes.

Chi-square Test

     [ /CHISQUARE=VAR_LIST[(LO,HI)] [/EXPECTED={EQUAL|F1, F2 ... FN}] ]

The /CHISQUARE subcommand produces a chi-square statistic for the differences between the expected and observed frequencies of the categories of a variable. Optionally, a range of values may appear after the variable list. If a range is given, then non-integer values are truncated, and values outside the specified range are excluded from the analysis.

The /EXPECTED subcommand specifies the expected values of each category. There must be exactly one non-zero expected value, for each observed category, or the EQUAL keyword must be specified. You may use the notation N*F to specify N consecutive expected categories all taking a frequency of F. The frequencies given are proportions, not absolute frequencies. The sum of the frequencies need not be 1. If no /EXPECTED subcommand is given, then equal frequencies are expected.

Chi-square Example

A researcher wishes to investigate whether there are an equal number of persons of each sex in a population. The sample chosen for invesigation is that from the physiology.sav dataset. The null hypothesis for the test is that the population comprises an equal number of males and females. The analysis is performed as shown below:

get file='physiology.sav'.

npar test
     /chisquare=sex.

There is only one test variable: sex. The other variables in the dataset are ignored.

In the output, shown below, the summary box shows that in the sample, there are more males than females. However the significance of chi-square result is greater than 0.05—the most commonly accepted p-value—and therefore there is not enough evidence to reject the null hypothesis and one must conclude that the evidence does not indicate that there is an imbalance of the sexes in the population.

             Sex of subject
┌──────┬──────────┬──────────┬────────┐
│Value │Observed N│Expected N│Residual│
├──────┼──────────┼──────────┼────────┤
│Male  │        22│     20.00│    2.00│
│Female│        18│     20.00│   ─2.00│
│Total │        40│          │        │
└──────┴──────────┴──────────┴────────┘

         Test Statistics
┌──────────────┬──────────┬──┬───────────┐
│              │Chi─square│df│Asymp. Sig.│
├──────────────┼──────────┼──┼───────────┤
│Sex of subject│       .40│ 1│       .527│
└──────────────┴──────────┴──┴───────────┘

Cochran Q Test

     [ /COCHRAN = VAR_LIST ]

The Cochran Q test is used to test for differences between three or more groups. The data for VAR_LIST in all cases must assume exactly two distinct values (other than missing values).

The value of Q is displayed along with its asymptotic significance based on a chi-square distribution.

Friedman Test

     [ /FRIEDMAN = VAR_LIST ]

The Friedman test is used to test for differences between repeated measures when there is no indication that the distributions are normally distributed.

A list of variables which contain the measured data must be given. The procedure prints the sum of ranks for each variable, the test statistic and its significance.

Kendall's W Test

     [ /KENDALL = VAR_LIST ]

The Kendall test investigates whether an arbitrary number of related samples come from the same population. It is identical to the Friedman test except that the additional statistic W, Kendall's Coefficient of Concordance is printed. It has the range [0,1]—a value of zero indicates no agreement between the samples whereas a value of unity indicates complete agreement.

Kolmogorov-Smirnov Test

     [ /KOLMOGOROV-SMIRNOV ({NORMAL [MU, SIGMA], UNIFORM [MIN, MAX], POISSON [LAMBDA], EXPONENTIAL [SCALE] }) = VAR_LIST ]

The one sample Kolmogorov-Smirnov subcommand is used to test whether or not a dataset is drawn from a particular distribution. Four distributions are supported: normal, uniform, Poisson and exponential.

Ideally you should provide the parameters of the distribution against which you wish to test the data. For example, with the normal distribution the mean (MU) and standard deviation (SIGMA) should be given; with the uniform distribution, the minimum (MIN) and maximum (MAX) value should be provided. However, if the parameters are omitted they are imputed from the data. Imputing the parameters reduces the power of the test so should be avoided if possible.

In the following example, two variables score and age are tested to see if they follow a normal distribution with a mean of 3.5 and a standard deviation of 2.0.

  NPAR TESTS
        /KOLMOGOROV-SMIRNOV (NORMAL 3.5 2.0) = score age.

If the variables need to be tested against different distributions, then a separate subcommand must be used. For example the following syntax tests score against a normal distribution with mean of 3.5 and standard deviation of 2.0 whilst age is tested against a normal distribution of mean 40 and standard deviation 1.5.

  NPAR TESTS
        /KOLMOGOROV-SMIRNOV (NORMAL 3.5 2.0) = score
        /KOLMOGOROV-SMIRNOV (NORMAL 40 1.5) =  age.

The abbreviated subcommand K-S may be used in place of KOLMOGOROV-SMIRNOV.

Kruskal-Wallis Test

     [ /KRUSKAL-WALLIS = VAR_LIST BY VAR (LOWER, UPPER) ]

The Kruskal-Wallis test is used to compare data from an arbitrary number of populations. It does not assume normality. The data to be compared are specified by VAR_LIST. The categorical variable determining the groups to which the data belongs is given by VAR. The limits LOWER and UPPER specify the valid range of VAR. If UPPER is smaller than LOWER, the PSPP will assume their values to be reversed. Any cases for which VAR falls outside [LOWER, UPPER] are ignored.

The mean rank of each group as well as the chi-squared value and significance of the test are printed. The abbreviated subcommand K-W may be used in place of KRUSKAL-WALLIS.

Mann-Whitney U Test

     [ /MANN-WHITNEY = VAR_LIST BY var (GROUP1, GROUP2) ]

The Mann-Whitney subcommand is used to test whether two groups of data come from different populations. The variables to be tested should be specified in VAR_LIST and the grouping variable, that determines to which group the test variables belong, in VAR. VAR may be either a string or an alpha variable. GROUP1 and GROUP2 specify the two values of VAR which determine the groups of the test data. Cases for which the VAR value is neither GROUP1 or GROUP2 are ignored.

The value of the Mann-Whitney U statistic, the Wilcoxon W, and the significance are printed. You may abbreviated the subcommand MANN-WHITNEY to M-W.

McNemar Test

     [ /MCNEMAR VAR_LIST [ WITH VAR_LIST [ (PAIRED) ]]]

Use McNemar's test to analyse the significance of the difference between pairs of correlated proportions.

If the WITH keyword is omitted, then tests for all combinations of the listed variables are performed. If the WITH keyword is given, and the (PAIRED) keyword is also given, then the number of variables preceding WITH must be the same as the number following it. In this case, tests for each respective pair of variables are performed. If the WITH keyword is given, but the (PAIRED) keyword is omitted, then tests for each combination of variable preceding WITH against variable following WITH are performed.

The data in each variable must be dichotomous. If there are more than two distinct variables an error will occur and the test will not be run.

Median Test

     [ /MEDIAN [(VALUE)] = VAR_LIST BY VARIABLE (VALUE1, VALUE2) ]

The median test is used to test whether independent samples come from populations with a common median. The median of the populations against which the samples are to be tested may be given in parentheses immediately after the /MEDIAN subcommand. If it is not given, the median is imputed from the union of all the samples.

The variables of the samples to be tested should immediately follow the = sign. The keyword BY must come next, and then the grouping variable. Two values in parentheses should follow. If the first value is greater than the second, then a 2-sample test is performed using these two values to determine the groups. If however, the first variable is less than the second, then a k sample test is conducted and the group values used are all values encountered which lie in the range [VALUE1,VALUE2].

Runs Test

     [ /RUNS ({MEAN, MEDIAN, MODE, VALUE})  = VAR_LIST ]

The /RUNS subcommand tests whether a data sequence is randomly ordered.

It works by examining the number of times a variable's value crosses a given threshold. The desired threshold must be specified within parentheses. It may either be specified as a number or as one of MEAN, MEDIAN or MODE. Following the threshold specification comes the list of variables whose values are to be tested.

The subcommand shows the number of runs, the asymptotic significance based on the length of the data.

Sign Test

     [ /SIGN VAR_LIST [ WITH VAR_LIST [ (PAIRED) ]]]

The /SIGN subcommand tests for differences between medians of the variables listed. The test does not make any assumptions about the distribution of the data.

If the WITH keyword is omitted, then tests for all combinations of the listed variables are performed. If the WITH keyword is given, and the (PAIRED) keyword is also given, then the number of variables preceding WITH must be the same as the number following it. In this case, tests for each respective pair of variables are performed. If the WITH keyword is given, but the (PAIRED) keyword is omitted, then tests for each combination of variable preceding WITH against variable following WITH are performed.

Wilcoxon Matched Pairs Signed Ranks Test

     [ /WILCOXON VAR_LIST [ WITH VAR_LIST [ (PAIRED) ]]]

The /WILCOXON subcommand tests for differences between medians of the variables listed. The test does not make any assumptions about the variances of the samples. It does however assume that the distribution is symmetrical.

If the WITH keyword is omitted, then tests for all combinations of the listed variables are performed. If the WITH keyword is given, and the (PAIRED) keyword is also given, then the number of variables preceding WITH must be the same as the number following it. In this case, tests for each respective pair of variables are performed. If the WITH keyword is given, but the (PAIRED) keyword is omitted, then tests for each combination of variable preceding WITH against variable following WITH are performed.