Jump to navigation Jump to search For the significance of hypothesis in research, see Null Hypothesis: The Journal of Unlikely Science.

In inferential statistics, the null hypothesis is a general statement or default position that there is no relationship between two measured phenomena, or no association among groups. The null hypothesis is generally assumed to be true until evidence indicates otherwise. 0, never the upper-case letter of the alphabet O. The concept of a null hypothesis is used differently in two approaches to statistical inference. In the significance testing approach of Ronald Fisher, a null hypothesis is rejected if the observed data are significantly unlikely to have occurred if the null hypothesis were true.

In the hypothesis testing approach of Jerzy Neyman and Egon Pearson, a null hypothesis is contrasted with an alternative hypothesis and the two hypotheses are distinguished on the basis of data, with certain error rates. Statistical inference can be done without a null hypothesis, by specifying a statistical model corresponding to each candidate hypothesis and using model selection techniques to choose the most appropriate model. Hypothesis testing requires constructing a statistical model of what the data would look like, given that chance or random processes alone were responsible for the results. The hypothesis that chance alone is responsible for the results is called the null hypothesis. The model of the result of the random process is called the distribution under the null hypothesis. Hypothesis testing works by collecting data and measuring how likely the particular set of data is, assuming the null hypothesis is true, when the study is on a randomly selected representative sample.

If the data do not contradict the null hypothesis, then only a weak conclusion can be made: namely, that the observed data set provides no strong evidence against the null hypothesis. For instance, a certain drug may reduce the chance of having a heart attack. Possible null hypotheses are «this drug does not reduce the chances of having a heart attack» or «this drug has no effect on the chances of having a heart attack». The test of the hypothesis consists of administering the drug to half of the people in a study group as a controlled experiment. The null hypothesis and the alternative hypothesis are types of conjectures used in statistical tests, which are formal methods of reaching conclusions or making decisions on the basis of data.

The statement being tested in a test of statistical significance is called the null hypothesis. The test of significance is designed to assess the strength of the evidence against the null hypothesis. Usually, the null hypothesis is a statement of ‘no effect’ or ‘no difference’. The statement that is being tested against the null hypothesis is the alternative hypothesis. Statistical significance test: «Very roughly, the procedure for deciding goes like this: Take a random sample from the population. The following sections add context and nuance to the basic definitions.

Given the test scores of two random samples, one of men and one of women, does one group differ from the other? A stronger null hypothesis is that the two samples are drawn from **significance of hypothesis in research** same population, such that the variances and shapes of the distributions are also equal. 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.

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Example: A hypothesis specifying a normal distribution with a specified mean and an unspecified variance. Exact hypothesis Any hypothesis that specifies an exact parameter value. Inexact hypothesis Those specifying a parameter range or interval. A one-tailed hypothesis is said to have directionality. 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. See the quotations below about his reasoning.

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 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. 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. 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.

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