
FREQUENCY TESTName:
The frequency test is defined as follows.
For the frequency within a block test, we partition the input values into N=[n/m] nonoverlapping blocks with n denoting the number of observations and m the number of observations within a block. Any unused observations are discarded. The frequency within a block test is then defined as follows.
where <y> is the response variable being tested; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
<SUBSET/EXCEPT/FOR qualification> where <y1> ... <yk> is a list of 1 to 30 response variables; and where the <SUBSET/EXCEPT/FOR qualification> is optional. The keyword MULTIPLE is optional. The frequency test will be performed on each response variable and these response variables can be matrices. The TO syntax is supported for the variable list.
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <x1> ... <xk> is a list of 1 to 6 groupid variables; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax will crosstabulate the groupid variables and performs the frequency test for each unique combination of crosstabulated values. For example, if X1 has 3 levels and X2 has 2 levels, there will be 6 frequency tests performed. This syntax does not support matrix arguments and the keyword REPLICATED is required (to distinguish this from the MULTIPLE case). The TO syntax is supported for the variable list.
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable being tested; and where the <SUBSET/EXCEPT/FOR qualification> is optional. The length of the block is set by entering the command
before entering the FREQUENCY BLOCK TEST command.
<SUBSET/EXCEPT/FOR qualification> where <y1> ... <yk> is a list of 1 to 30 response variables; and where the <SUBSET/EXCEPT/FOR qualification> is optional. The keyword MULTIPLE is optional. The frequency block test will be performed on each response variable and these response variables can be matrices. The TO syntax is supported for the variable list.
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <x1> ... <xk> is a list of 1 to 6 groupid variables; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax will crosstabulate the groupid variables and performs the frequency block test for each unique combination of crosstabulated values. For example, if X1 has 3 levels and X2 has 2 levels, there will be 6 frequency block tests performed. This syntax does not support matrix arguments and the keyword REPLICATED is required (to distinguish this from the MULTIPLE case). The TO syntax is supported for the variable list.
FREQUENCY TEST Y1 TO Y10 REPLICATED FREQUENCY TEST Y X1 X2
LET M = 20
LET A = FREQUENCY TEST CDF Y LET A = FREQUENCY WITHIN A BLOCK TEST Y LET A = FREQUENCY WITHIN A BLOCK TEST CDF Y Enter HELP STATISTICS to see what commands can use these statistics.
LET P = 0.5 LET Y = BINOMIAL RANDOM NUMBERS FOR I = 1 1 1000 FREQUENCY TEST Y
For the frequency within a block test, it is additionally recommended that the block size should be at least 20 and it should also be greater than or equal to 0.01 times the sample size. It is recommended that the number of samples within a block be less than 100.
2011/3: Support for MULTIPLE option 2011/3: Support for REPLICATION option 2011/3: Support for matrix arguments and the TO syntax 2011/3: Output reformatted, added support for RTF output 2011/3: Support for SET WRITE DECIMALS 2011/3: Added FREQUENCY TEST statistics LET N = 1 LET P = 0.5 LET Y1 = BINOMIAL RANDOM NUMBERS FOR I = 1 1 200 LET P = 0.58 LET Y2 = BINOMIAL RANDOM NUMBERS FOR I = 1 1 200 LET P = 0.65 LET Y3 = BINOMIAL RANDOM NUMBERS FOR I = 1 1 200 LET P = 0.85 LET Y4 = BINOMIAL RANDOM NUMBERS FOR I = 1 1 200 SET WRITE DECIMALS 4 . FREQUENCY TEST Y1 FREQUENCY TEST Y1 Y2 Y3 . LET M = 20 FREQUENCY BLOCK TEST Y1The following output is generated: ************************* ** FREQUENCY TEST Y1 ** ************************* Frequency Test for Randomness Response Variable: Y1 H0: The Data Are Random Ha: The Data Are Not Random Summary Statistics: Number of Observations: 200 Sum of +1 and 1 Values: 6.0000 Frequency Test Statistic: 0.4242 CDF Value: 0.6643 PValue: 0.6713 Conclusions  Null Null Confidence Test Critical Hypothesis Hypothesis Level Statistic Value (+/) Conclusion  Random 50.0% 0.4242 0.6744 ACCEPT Random 75.0% 0.4242 1.1503 ACCEPT Random 90.0% 0.4242 1.6448 ACCEPT Random 95.0% 0.4242 1.9599 ACCEPT Random 97.5% 0.4242 2.2414 ACCEPT Random 99.0% 0.4242 2.5758 ACCEPT Random 99.9% 0.4242 3.2905 ACCEPT ******************************* ** FREQUENCY TEST Y1 Y2 Y3 ** ******************************* Frequency Test for Randomness Response Variable: Y1 H0: The Data Are Random Ha: The Data Are Not Random Summary Statistics: Number of Observations: 200 Sum of +1 and 1 Values: 6.0000 Frequency Test Statistic: 0.4242 CDF Value: 0.6643 PValue: 0.6713 Conclusions  Null Null Confidence Test Critical Hypothesis Hypothesis Level Statistic Value (+/) Conclusion  Random 50.0% 0.4242 0.6744 ACCEPT Random 75.0% 0.4242 1.1503 ACCEPT Random 90.0% 0.4242 1.6448 ACCEPT Random 95.0% 0.4242 1.9599 ACCEPT Random 97.5% 0.4242 2.2414 ACCEPT Random 99.0% 0.4242 2.5758 ACCEPT Random 99.9% 0.4242 3.2905 ACCEPT Frequency Test for Randomness Response Variable: Y2 H0: The Data Are Random Ha: The Data Are Not Random Summary Statistics: Number of Observations: 200 Sum of +1 and 1 Values: 30.0000 Frequency Test Statistic: 2.1213 CDF Value: 0.9830 PValue: 0.0338 Conclusions  Null Null Confidence Test Critical Hypothesis Hypothesis Level Statistic Value (+/) Conclusion  Random 50.0% 2.1213 0.6744 REJECT Random 75.0% 2.1213 1.1503 REJECT Random 90.0% 2.1213 1.6448 REJECT Random 95.0% 2.1213 1.9599 REJECT Random 97.5% 2.1213 2.2414 ACCEPT Random 99.0% 2.1213 2.5758 ACCEPT Random 99.9% 2.1213 3.2905 ACCEPT Frequency Test for Randomness Response Variable: Y3 H0: The Data Are Random Ha: The Data Are Not Random Summary Statistics: Number of Observations: 200 Sum of +1 and 1 Values: 58.0000 Frequency Test Statistic: 4.1012 CDF Value: 0.9999 PValue: 0.0000 Conclusions  Null Null Confidence Test Critical Hypothesis Hypothesis Level Statistic Value (+/) Conclusion  Random 50.0% 4.1012 0.6744 REJECT Random 75.0% 4.1012 1.1503 REJECT Random 90.0% 4.1012 1.6448 REJECT Random 95.0% 4.1012 1.9599 REJECT Random 97.5% 4.1012 2.2414 REJECT Random 99.0% 4.1012 2.5758 REJECT Random 99.9% 4.1012 3.2905 REJECT ******************************* ** FREQUENCY BLOCK TEST Y1 ** ******************************* Frequency Within a Block Test for Randomness Response Variable: Y1 H0: The Data Are Random Ha: The Data Are Not Random Summary Statistics: Number of Observations: 200 Block Size: 20 Number of Observations Within a Block: 10 Frequency Within A Block Test Statistic: 8.5999 PValue: 0.5704 Conclusions  Null Null Confidence Hypothesis Hypothesis Level PValue Conclusion  Random 50.0% 0.5704 ACCEPT Random 75.0% 0.5704 ACCEPT Random 90.0% 0.5704 ACCEPT Random 95.0% 0.5704 ACCEPT Random 97.5% 0.5704 ACCEPT Random 99.0% 0.5704 ACCEPT Random 99.9% 0.5704 ACCEPT  
Date created: 02/03/2004 Last updated: 12/11/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 