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The following table defines the possible outcomes when testing multiple null hypotheses. Suppose we have a number m of null hypotheses, denoted by: H 1, H 2, ..., H m. Using a statistical test, we reject the null hypothesis if the test is declared significant. We do not reject the null hypothesis if the test is non-significant.
Null distribution is a tool scientists often use when conducting experiments. The null distribution is the distribution of two sets of data under a null hypothesis. If the results of the two sets of data are not outside the parameters of the expected results, then the null hypothesis is said to be true. Null and alternative distribution
Thus the counternull is an alternative hypothesis that, when used to replace the null hypothesis, generates the same p-value as had the original null hypothesis of “no difference.” [3] Some researchers contend that reporting the counternull, in addition to the p -value, serves to counter two common errors of judgment: [ 4 ]
The null hypothesis is that it does. Chi-squared tests of independence are used for deciding whether two variables are associated or are independent. The variables are categorical rather than numeric. It can be used to decide whether left-handedness is correlated with height (or not). The null hypothesis is that the variables are independent.
Thus, the null hypothesis is rejected if >, (where , is the upper tail critical value for the distribution). Bartlett's test is a modification of the corresponding likelihood ratio test designed to make the approximation to the χ k − 1 2 {\displaystyle \chi _{k-1}^{2}} distribution better (Bartlett, 1937).
Where the null hypothesis represents a special case of the alternative hypothesis, the probability distribution of the test statistic is approximately a chi-squared distribution with degrees of freedom equal to , [2] respectively the number of free parameters of models alternative and null.
A portmanteau test is a type of statistical hypothesis test in which the null hypothesis is well specified, but the alternative hypothesis is more loosely specified. Tests constructed in this context can have the property of being at least moderately powerful against a wide range of departures from the null hypothesis.
The null hypothesis and the alternative hypothesis are types of conjectures used in statistical tests to make statistical inferences, which are formal methods of reaching conclusions and separating scientific claims from statistical noise. The statement being tested in a test of statistical significance is called the null hypothesis.