Duncan's new multiple range test
Encyclopedia
In statistics
, Duncan's new multiple range test (MRT) is a multiple comparison
procedure developed by David B. Duncan in 1955. Duncan's MRT belongs to the general class of multiple comparison procedures that use the studentized range statistic qr to compare sets of means.
Duncan's new multiple range test (MRT) is a variant of the Student–Newman–Keuls method
that uses increasing alpha levels to calculate the critical values in each step of the Newman–Keuls procedure. Duncan's MRT attempts to control family wise error rate (FWE) at αew = 1 − (1 − αpc)k−1 when comparing k, where k is the number of groups. This results in higher FWE than unmodified Newman–Keuls procedure which has FWE of αew = 1 − (1 − αpc)k/2.
David B. Duncan developed this test as a modification of the Student–Newman–Keuls method that would have greater power. Duncan's MRT is especially protective against false negative (Type II) error
at the expense of having a greater risk of making false positive (Type I) errors
. Duncan's test is commonly used in agronomy
and other agricultural research.
Duncan's test has been criticised as being too liberal by many statisticians including Henry Scheffé
, and John W. Tukey. Duncan argued that a more liberal procedure was appropriate because in real world practice the global null hypothesis H0= "All means are equal" is often false and thus traditional statisticians overprotect a probably false null hypothesis against type I errors. Duncan later developed the Duncan–Waller test which is based on Bayesian principles. It uses the obtained value of F to estimate the prior probability of the null hypothesis being true.
The main criticisms raised against Duncan's procedure are:
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, Duncan's new multiple range test (MRT) is a multiple comparison
Multiple comparisons
In statistics, the multiple comparisons or multiple testing problem occurs when one considers a set of statistical inferences simultaneously. Errors in inference, including confidence intervals that fail to include their corresponding population parameters or hypothesis tests that incorrectly...
procedure developed by David B. Duncan in 1955. Duncan's MRT belongs to the general class of multiple comparison procedures that use the studentized range statistic qr to compare sets of means.
Duncan's new multiple range test (MRT) is a variant of the Student–Newman–Keuls method
Newman–Keuls method
In statistics, the Newman–Keuls method is a post-hoc test used for comparisons after the performed F-test is found to be significant...
that uses increasing alpha levels to calculate the critical values in each step of the Newman–Keuls procedure. Duncan's MRT attempts to control family wise error rate (FWE) at αew = 1 − (1 − αpc)k−1 when comparing k, where k is the number of groups. This results in higher FWE than unmodified Newman–Keuls procedure which has FWE of αew = 1 − (1 − αpc)k/2.
David B. Duncan developed this test as a modification of the Student–Newman–Keuls method that would have greater power. Duncan's MRT is especially protective against false negative (Type II) error
Type I and type II errors
In statistical test theory the notion of statistical error is an integral part of hypothesis testing. The test requires an unambiguous statement of a null hypothesis, which usually corresponds to a default "state of nature", for example "this person is healthy", "this accused is not guilty" or...
at the expense of having a greater risk of making false positive (Type I) errors
Type I and type II errors
In statistical test theory the notion of statistical error is an integral part of hypothesis testing. The test requires an unambiguous statement of a null hypothesis, which usually corresponds to a default "state of nature", for example "this person is healthy", "this accused is not guilty" or...
. Duncan's test is commonly used in agronomy
Agronomy
Agronomy is the science and technology of producing and using plants for food, fuel, feed, fiber, and reclamation. Agronomy encompasses work in the areas of plant genetics, plant physiology, meteorology, and soil science. Agronomy is the application of a combination of sciences like biology,...
and other agricultural research.
Duncan's test has been criticised as being too liberal by many statisticians including Henry Scheffé
Henry Scheffé
Henry Scheffé was an American statistician. He is known for the Lehmann–Scheffé theorem and Scheffé's method.- External links :...
, and John W. Tukey. Duncan argued that a more liberal procedure was appropriate because in real world practice the global null hypothesis H0= "All means are equal" is often false and thus traditional statisticians overprotect a probably false null hypothesis against type I errors. Duncan later developed the Duncan–Waller test which is based on Bayesian principles. It uses the obtained value of F to estimate the prior probability of the null hypothesis being true.
The main criticisms raised against Duncan's procedure are:
- Duncan's MRT does not control family wise error rate at the nominal alpha level, a problem it inherits from Student–Newman–Keuls method.
- The increased power of Duncan's MRT over Newman–Keuls comes from intentionally raising the alpha levels (Type I errorType I and type II errorsIn statistical test theory the notion of statistical error is an integral part of hypothesis testing. The test requires an unambiguous statement of a null hypothesis, which usually corresponds to a default "state of nature", for example "this person is healthy", "this accused is not guilty" or...
rate) in each step of the Newman–Keuls procedure and not from any real improvement on the SNK method.