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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. The obtained results are compared with the distribution under the null hypothesis, and the likelihood of finding the obtained results is thereby ...
Thus the null hypothesis is that a population is described by some distribution predicted by theory. He uses as an example the numbers of five and sixes in the Weldon dice throw data. [6] 1904: Karl Pearson develops the concept of "contingency" in order to determine whether outcomes are independent of a given categorical factor.
The purpose of the test is to evaluate how likely the observed frequencies would be assuming the null hypothesis is true. Test statistics that follow a χ 2 distribution occur when the observations are independent. There are also χ 2 tests for testing the null hypothesis of independence of a pair of random variables based on observations of ...
For example, if one test is performed at the 5% level and the corresponding null hypothesis is true, there is only a 5% risk of incorrectly rejecting the null hypothesis. However, if 100 tests are each conducted at the 5% level and all corresponding null hypotheses are true, the expected number of incorrect rejections (also known as false ...
Normally, there are n − 1 degrees of freedom (with n being the total number of observations). [17] A paired samples t-test based on a "matched-pairs sample" results from an unpaired sample that is subsequently used to form a paired sample, by using additional variables that were measured along with the variable of interest. [18]
The hypothesis of Andreas Cellarius, showing the planetary motions in eccentric and epicyclical orbits. A hypothesis (pl.: hypotheses) is a proposed explanation for a phenomenon. A scientific hypothesis must be based on observations and make a testable and reproducible prediction about reality, in a process beginning with an educated guess or ...
Let the null hypothesis be given as a set of distributions for data .Usually = (, …,) with each a single outcome and a fixed sample size or some stopping time. We shall refer to such , which represent the full sequence of outcomes of a statistical experiment, as a sample or batch of outcomes.
In coin flipping, the null hypothesis is a sequence of Bernoulli trials with probability 0.5, yielding a random variable X which is 1 for heads and 0 for tails, and a common test statistic is the sample mean (of the number of heads) ¯.