
KLOTZ TESTName:
A Klotz test is a nonparametric alternative to the F test. It is based on the squares of normal scores. Normal scores are computed as
where R_{i} is the rank of the ith observation, N is the sample size, and \( \Phi^{1} \) is the percent point function of the standard normal distribution. The advantage of many tests based on normal scores is that they perform well when the assumptions of the standard parametric test are satisfied while still providing protection when the assumptions are not satisfied. The Klotz test is defined as
The critical values based on the normal test are only approximate. Dataplot does not currently compute exact critical values.
<SUBSET/EXCEPT/FOR qualification> where <LOWER TAILED/UPPER TAILED> is an optional keyword for the two sample case; <y1> is the first response variable; <y2> is the second variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional. The LOWER TAILED and UPPER TAILED keywords are optional Only one can be specified and if neither is entered a twotailed test will be performed.
<SUBSET/EXCEPT/FOR qualification> where <LOWER TAILED/UPPER TAILED> is an optional keyword for the two sample case; <y1> ... <yk> is a list of 2 to 30 response variables; and where the <SUBSET/EXCEPT/FOR qualification> is optional. The LOWER TAILED and UPPER TAILED keywords are optional Only one can be specified and if neither is entered a twotailed test will be performed. This syntax will generate all the pairwise Klotz tests for the list of variables.
LOWER TAILED KLOTZ TEST Y1 Y2 UPPER TAILED KLOTZ TEST Y1 Y2 KLOTZ TEST Y1 TO Y10
The TO syntax is supported for this command.
LET A = KLOTZ TEST CDF Y1 Y2 LET A = KLOTZ TEST PVALUE Y1 Y2 LET A = KLOTZ TEST LOWER TAILED PVALUE Y1 Y2 LET A = KLOTZ TEST UPPER TAILED PVALUE Y1 Y2 Enter HELP STATISTICS to see what commands can use these statistics.
. Step 1: Read Data (from p. 402 of Conover) . let y1 = data 10.8 11.1 10.4 10.1 11.3 let y2 = data 10.8 10.5 11.0 10.9 10.8 10.7 10.8 set write decimals 4 . . Step 2: Check the statistic . let stat = klotz test y1 y2 let cdf = klotz test cdf y1 y2 let pval = klotz test pvalue y1 y2 print stat pval cdf . . Step 3: Perform Klotz test . klotz test y1 y2The following output is generated. PARAMETERS AND CONSTANTS STAT  2.3447 PVAL  0.0190 CDF  0.9905 Two Sample TwoSided Klotz Test First Response Variable: Y1 Second Response Variable: Y2 H0: Var(Y1) = Var(Y2) Ha: Var(Y1) <> Var(Y2) Summary Statistics: Number of Observations for Sample 1: 5 Mean for Sample 1: 10.7400 Variance for Sample 0.2430 Number of Observations for Sample 2: 7 Mean for Sample 2: 10.7857 Variance for Sample 0.0247 Test (Normal Approximation): Test Statistic Value: 2.3447 CDF Value: 0.9904 PValue (2tailed test): 0.0190 PValue (lowertailed test): 0.9904 PValue (uppertailed test): 0.0095 TwoTailed Test: Normal Approximation H0: Var(Y1) = Var(Y2); Ha: Var(Y1) <> Var(Y2)  Null Significance Test Critical Hypothesis Level Statistic Value (+/) Conclusion  80.0% 2.3447 1.2815 REJECT 90.0% 2.3447 1.6448 REJECT 95.0% 2.3447 1.9599 REJECT 99.0% 2.3447 2.5758 ACCEPT  
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Date created: 09/15/2011 