--- /dev/null
+# NPAR TESTS
+
+```
+NPAR TESTS
+ nonparametric test subcommands
+ .
+ .
+ .
+
+ [ /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.
+
+<!-- toc -->
+
+## 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.
+
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