Search results
Results from the WOW.Com Content Network
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
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.
This probability of making an incorrect decision is not the probability that the null hypothesis is true, nor whether any specific alternative hypothesis is true. This contrasts with other possible techniques of decision theory in which the null and alternative hypothesis are treated on a more equal basis.
Suppose we have an independent and identically distributed sample X 1, ..., X n each of which is normally distributed with mean θ and variance σ 2, and we are interested in testing the null hypothesis θ = 0 vs. the alternative hypothesis θ ≠ 0. We can perform a one sample t-test using the test statistic
The null hypothesis corresponds to the position of the defendant: just as he is presumed to be innocent until proven guilty, so is the null hypothesis presumed to be true until the data provide convincing evidence against it. The alternative hypothesis corresponds to the position against the defendant.
When statistical tests are studied for their power to distinguish against the alternatives that are close to the null hypothesis, it is done within the so-called "local alternatives" framework: the null hypothesis is H 0: θ = θ 0 and the alternative is H 1: θ = θ 0 + h/ √ n. This approach is especially popular for the unit root tests.
If there is interest in the marginal probability of obtaining a tail, only the number T out of the 100 flips that produced a tail needs to be recorded. But T can also be used as a test statistic in one of two ways: the exact sampling distribution of T under the null hypothesis is the binomial distribution with parameters 0.5 and 100.
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).