Performs a test of randomness of a sequence of observations (P.W. Goedhart).
Options
PRINT = string token |
Controls printed output (results); default resu |
|---|---|
NULL = scalar |
Defines the boundary between the two types; default 0 |
Parameters
DATA = variates |
Sequences of observations |
|---|---|
SAVE = pointers |
To save the number of runs, the number of positive and negative observations and the lower and upper tail probabilities of the test |
Description
The data are assumed to be in an ordered sequence of observations of two types, n1 of the first type and n2 of the second type. A run is defined to be a succession of observations of the same type. A clue to lack of randomness is provided by the total number of runs in the sequence. If the data are in random order, the expected number of runs is 1 + 2n1n2/(n1+n2). A low number of runs might indicate positive serial correlation while a high number might arise from negative serial correlation.
The DATA parameter is used to specify the sequence of observations. Observations larger than option NULL are considered to be of the first type (positive) while observation smaller than NULL are of the second type (negative). Missing values and observations that equal NULL are not taken into account. The PRINT option controls printed output, while the SAVE parameter can be used to specify a pointer containing five scalars to save the number of runs, the number of positive observations (that is, those larger than NULL), the number of negative observations and the lower and upper tail probabilities of the number of runs.
Options: PRINT, NULL.
Parameters: DATA, SAVE.
Method
When the number of observations of type one and two are both smaller than 11, exact left and right tail probabilities are taken from Table 3.1 from Draper & Smith (1981). In other cases a normal approximation with continuity correction is used.
Action with RESTRICT
The DATA variate can be restricted so that the test uses only a subset of the units.
Reference
Draper & Smith (1981). Applied Regression Analysis (second edition). Wiley, New York.
See also
Commands for: Basic and nonparametric statistics.
Example
CAPTION 'RUNTEST example',\
!t('Testing for randomness in a sequence of numbers obtained',\
'with URAND. Testing for serial correlation in a sequence of',\
'residuals.'); STYLE=meta,plain
CALCULATE uniform = URAND(7453671; 5000)
RUNTEST [NULL=0.5] uniform
VARIATE [NVALUES=20] time, response; VALUES=!(1...20), *
READ response
6.52 5.74 5.39 5.34 5.02 5.42 4.90 5.67 5.06 5.32
3.43 3.81 3.15 3.39 4.03 4.12 3.96 3.93 3.81 3.94 :
MODEL response; RESIDUALS=residual
FITCURVE [CURVE=exponential] time
RUNTEST residual