Duncans test is to separate groups of means. This test is known to be very liberal and should therefore not be used. A different and less liberal approach for this problem is Tukeys multiple range test. More modern approaches to separate groups of means employ clustering techniques.

Dunnett is a multiple-to-one procedure that controls the family-wise type-I error rate when a several means are compared to the mean of the same "reference" group.

There are no rules.  Usually people use what is common in their field of study, and what is available in the software they use.  Sometimes people have better reasons to choose one test.

Tukey is common in agronomy and related fields.

But if you are just comparing treatments to the control, Dunnett is common too.  It should be more powerful that Tukey in this case.

Thank you for your help 

Dear All

Hi

Would you help me to choose a best Statistical test for a group of patients (same group) with six results of blood sample (same parameter of 2 months interval between each reading ) to follow a progress of management

how to find the significance between readings

Dunnett test is used to compare each of several treatments with a single control. Duncan's multiple range test provides significance levels for the difference between any pair of means, regardless of whether a significant F resulted from an initial analysis of variance.

Hi, Tahreer M. Al-Thuwaini .

I have to point out that your description of Duncan's test is identical to that in SAGE Publishing's Encyclopedia of Research Design, linked below. There was no attribution in your post.

https://methods.sagepub.com/reference/encyc-of-research-design/n124.xml

Yours:

Duncan's multiple range test provides significance levels for the difference between any pair of means, regardless of whether a significant F resulted from an initial analysis of variance.

Original:

... Duncan's new multiple range test, provides significance levels for the difference between any pair of means, regardless of whether a significant F resulted from an initial analysis of variance.