When to use a Tukey Quick Test
A Tukey Quick Test is like a t-test, but it can handle nonparametric
(i.e., non-normal) data. It helps determine if the means are the
same or different from each other. The null hypothesis H0
is that the means are the same.
Tukey's Quick Test can be used when:
- There are two unpaired samples of similar size that overlap
each other. Ratio of sizes should not exceed 4:3.
- One sample contains the highest value, the other sample contains
the lowest value. One sample cannot contain both the highest and
the lowest value, nor can both samples have the same high or low
value.
By adding the counts of the number of unmatched points on either
end, one can determine the 5%, 1% and 0.1% critical values as roughly
7, 10, and 13 points. Consider the following example.
Tukey Quick Test Example
Using the data from Tukey's original paper (A Quick, Compact, Two-Sample
Test To Duckworth's Specifications, Technometrics, Vol. 1, No. 1,
February, 1959):
Count the Points
If we combine and sort the points, we can see that there are 5
unmatched points on either end (for a total of 10). And Tukey counts
a tie (14.6 and 15.0) as 0.5. There are two of these for a total
of 11. This means that the two-sided confidence of 99% (>=10)
applies.
Using the QI Macros Tukey Quick Test
Click on the QI Macros Menu and choose Anova-Nonparametric
Click on the Tukey hotlink or the Tukey sheet name:
This brings up the Tukey Quick Test template. Note, that
without data, D1:E1 show "Tukey Not Applicable." If the
data violates any of the rules, the template will not calculate
the Tukey Quick test.
Input your data and confidence level (default = 95):
The Tukey Quick Test template will calculate the results:
Interpreting the Tukey Quick Test results
|
If
|
Then
|
| Total End Count >= 7 |
Reject the null hypothesis at 5% confidence level.
|
| Total End Count >= 10 |
Reject the null hypothesis at 1% confidence level.
|
| Total End Count >= 13 |
Reject the null hypothesis at 0.1% confidence
level. |
| Total End Count < 7 |
Accept the null hypothesis |
The null hypothesis H0 is that the means are the same.
In this example, since the End Count = 11, we reject the null hypothesis
at a 1% confidence level.
Watch Non-parametric tests in Excel Video
The Tukey Quick Test is just one of the tests included in the QI
Macros Statistical Process Control software. Other tests include:
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