Studentized range

In <a href="/facts/Statistics/DNPsKGYU">statistics</a>, the studentized range, denoted q, is the difference between the largest and smallest data in a <a href="/facts/Sample_(statistics)/URCwKNge">sample</a> <a href="/facts/Normalization_(statistics)/734U3VFY">normalized</a> by the <a href="/facts/Standard_deviation/qSug9BRl">sample standard deviation</a>.
It is named after <a href="/facts/William_Sealy_Gosset/5v21pjTh">William Sealy Gosset</a> (who wrote under the pseudonym "Student"), and was introduced by him in 1927. 
The concept was later discussed by Newman (1939), Keuls (1952), and <a href="/facts/John_Tukey/2a5FbPWb">John Tukey</a> in some unpublished notes.
Its statistical distribution is the <a href="/facts/Studentized_range_distribution/SU7PMqgJ">studentized range distribution</a>, which is used for <a href="/facts/Multiple_comparisons_problem/lAItaL18">multiple comparison</a> procedures, such as the single step procedure <a href="/facts/Tukey%27s_range_test/RV7mFmgP">Tukey's range test</a>, the <a href="/facts/Newman%E2%80%93Keuls_method/QuL5JvdQ">Newman–Keuls method</a>, and the Duncan's step down procedure, and establishing <a href="/facts/Confidence_interval/NS8mG5UE">confidence intervals</a> that are still valid after <a href="/facts/Data_snooping/X11G2jBn">data snooping</a> has occurred.

Studentized range open-in-new

Studentized range