Editing Null hypothesis (section)

==Terminology==
{{main|Statistical hypothesis testing#Definition of terms}}

; Simple hypothesis : Any hypothesis which specifies the population distribution completely. For such a hypothesis the sampling distribution of any statistic is a function of the sample size alone.
; Composite hypothesis : Any hypothesis which does ''not'' specify the population distribution completely.<ref name="Rossi2018">{{citation | last= Rossi | first= R. J. | year= 2018 | title= Mathematical Statistics | publisher= [[Wiley (publisher)|Wiley]] | page= 281 }}.</ref> Example: A hypothesis specifying a normal distribution with a specified mean and an unspecified variance.

The simple/composite distinction was made by Neyman and Pearson.<ref name="Neyman 289–337"/>

; Exact hypothesis: Any hypothesis that specifies an exact parameter value.<ref>{{cite book | last1 = Winkler | first1 = Robert L | last2 = Hays | first2 = William L | title = Statistics : probability, inference, and decision | publisher = Holt, Rinehart and Winston | location = New York | year = 1975 | isbn = 978-0-03-014011-2 | page = [https://archive.org/details/statisticsprobab0000wink/page/403 403] | url = https://archive.org/details/statisticsprobab0000wink/page/403 }}</ref> Example: μ = 100. Synonym: '''point hypothesis'''.
; Inexact hypothesis : Those specifying a parameter range or interval. Examples: μ ≤ 100; 95 ≤ μ ≤ 105.

Fisher required an exact null hypothesis for testing (see the quotations below).

A [[One-tailed test|one-tailed hypothesis]] (tested using a one-sided test)<ref name=moore/> is an inexact hypothesis in which the value of a parameter is specified as being either:
* above or equal to a certain value, or
* below or equal to a certain value.
A one-tailed hypothesis is said to have '''directionality'''.

Fisher's original ([[lady tasting tea]]) example was a one-tailed test. The null hypothesis was asymmetric. The probability of guessing all cups correctly was the same as guessing all cups incorrectly, but Fisher noted that only guessing correctly was compatible with the lady's claim.