Editing Null hypothesis (section)

==Goals of null hypothesis tests==
There are many types of [[Statistical hypothesis testing#Common test statistics|significance tests]] for one, two or more samples, for means, variances and proportions, paired or unpaired data, for different distributions, for large and small samples; all have null hypotheses. There are also at least four goals of null hypotheses for significance tests:<ref>{{cite journal
 | author-link = David Cox (statistician)
 | title = Statistical Significance Tests
 | journal = Br. J. Clin. Pharmacol.
 | volume = 14 | issue = 3
 | pages = 325–331 | year = 1982 | doi = 10.1111/j.1365-2125.1982.tb01987.x
 | pmid = 6751362
 | pmc = 1427620
 | last1 = Cox
 | first1 = DR
 }}</ref>
* Technical null hypotheses are used to verify statistical assumptions. For example, the residuals between the data and a statistical model cannot be distinguished from random noise. If true, there is no justification for complicating the model.
* Scientific null assumptions are used to directly advance a theory. For example, the angular momentum of the universe is zero. If not true, the theory of the early universe may need revision.
* Null hypotheses of [[Homogeneity (statistics)|homogeneity]] are used to verify that multiple experiments are producing consistent results. For example, the effect of a medication on the elderly is consistent with that of the general adult population. If true, this strengthens the general effectiveness conclusion and simplifies recommendations for use.
* Null hypotheses that assert the equality of effect of two or more alternative treatments, for example, a drug and a placebo, are used to reduce scientific claims based on statistical noise. This is the most popular null hypothesis; It is so popular that many statements about significant testing assume such null hypotheses.

Rejection of the null hypothesis is ''not necessarily'' the real goal of a significance tester. An adequate statistical model may be associated with a failure to reject the null; the model is adjusted until the null is not rejected. The numerous uses of significance testing were well known to Fisher who discussed many in his book written a decade before defining the null hypothesis.<ref>Statistical Methods for Research Workers (11th Ed): Chapter IV: Tests of Goodness of Fit, Independence and Homogeneity; With Table of χ<sup>2</sup>.  Regarding a significance test supporting goodness of fit: If the calculated probability is high then "there is certainly no reason to suspect that the [null] hypothesis is tested.  If it is [low] it is strongly indicated that the [null] hypothesis fails to account for the whole of the facts."</ref>

A statistical significance test shares much mathematics with a [[confidence interval]]. They are [[Confidence interval#Statistical hypothesis testing|mutually illuminating]]. A result is often significant when there is confidence in the sign of a relationship (the interval does not include 0). Whenever the sign of a relationship is important, statistical significance is a worthy goal. This also reveals weaknesses of significance testing: A result can be significant without a good estimate of the strength of a relationship; significance can be a modest goal. A weak relationship can also achieve significance with enough data. Reporting both significance and confidence intervals is commonly recommended.

The varied uses of significance tests reduce the number of generalizations that can be made about all applications.