
QUADE TESTName:
The Quade test assumes that there are k experimental treatments (k ≥ 2). The observations are arranged in b blocks, that is
Let R(X_{ij}) be the rank assigned to X_{ij} within block i (i.e., ranks within a given row). Average ranks are used in the case of ties. Compute the range in each block (the maximum value  the minimum value for the original data) and then rank these:
Then let
and
Then the Quade test is
If the hypothesis of identical treatment effects is rejected, it is often desirable to determine which treatments are different (i.e., multiple comparisons). Treatments i and j are considered different if
This is equivalent to the Fisher least significant difference computed on the S_{ij} rather than the data.
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <block> is a variable that identifies the block; <treat> is a variable that identifies the treatment; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
QUADE TEST Y X1 X2 QUADE TEST Y BLOCK TREATMENT SUBSET BLOCK > 2
If your data are in a format similar to that given in the DESCRIPTION section (i.e., you have colums Y_{1} to Y_{k}, each with b rows), you can convert it to the format required by Dataplot with the commands:
LET BLOCKID = SEQUENCE 1 1 NBLOCK LET Y BLOCK TREAT = REPLICATED STACK Y1 Y2 Y3 Y4 Y5 BLOCKID QUADE TEST Y BLOCK TREAT
The treatment ranks and multiple comparisons are written to the file dpst2f.dat in the current directory. Comparisons that are statistically significant at the 95% level are flagged with a single asterisk while comparisons that are statistically significant at the 99% level are flagged with two asterisks.
LET A = QUADE TEST CDF Y X1 X2 LET A = QUADE TEST PVALUE Y X1 X2 Enter HELP STATISTICS to see what commands can use these statistics.
SKIP 25 READ QUADE2.DAT Y X1 X2 SET WRITE DECIMALS 5 . LET A1 = QUADE TEST Y X1 X2 LET A1 = QUADE TEST CDF Y X1 X2 LET A1 = QUADE TEST PVALUE Y X1 X2 PRINT A1 A2 A3 . QUADE TEST Y X1 X2The following output is generated for the Quade test Quade Two Factor Test Response Variable: Y First GroupID Variable: X1 Second GroupID Variable: X2 H0: Treatments Have Identical Effects Ha: Treatments Do Not Have Identical Effects Summary Statistics: Total Number of Observations: 35 Number of Blocks: 7 Number of Treatments: 5 Test: Quade Test Statistic: 3.82925 Total Sum of Squares (A2): 1366.50000 Treatment Sum of Squares (B): 532.35714 CDF of Test Statistic: 0.98481 PValue: 0.01518 Percent Points of the F Reference Distribution  Percent Point Value  0.0 = 0.000 50.0 = 0.863 75.0 = 1.445 90.0 = 2.194 95.0 = 2.775 97.5 = 3.379 99.0 = 4.217 99.9 = 6.589 Conclusions (Upper 1Tailed Test)  Alpha CDF Critical Value Conclusion  10% 90% 2.194 Reject H0 5% 95% 2.775 Reject H0 2.5% 97.5% 3.379 Reject H0 1% 99% 4.217 Accept H0  
Date created: 08/31/2011 Last updated: 12/11/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 