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The statement that is being tested against the null hypothesis is the alternative hypothesis. [2] Alternative hypothesis is often denoted as H a or H 1. In statistical hypothesis testing, to prove the alternative hypothesis is true, it should be shown that the data is contradictory to the null hypothesis. Namely, there is sufficient evidence ...
This is why the hypothesis under test is often called the null hypothesis (most likely, coined by Fisher (1935, p. 19)), because it is this hypothesis that is to be either nullified or not nullified by the test. When the null hypothesis is nullified, it is possible to conclude that data support the "alternative hypothesis" (which is the ...
In this situation, if the estimated value exists in one of the one-sided critical areas, depending on the direction of interest (greater than or less than), the alternative hypothesis is accepted over the null hypothesis. Alternative names are one-sided and two-sided tests; the terminology "tail" is used because the extreme portions of ...
In this case, the null hypothesis is rejected and an alternative hypothesis is accepted in its place. If the data are consistent with the null hypothesis statistically possibly true, then the null hypothesis is not rejected. In neither case is the null hypothesis or its alternative proven; with better or more data, the null may still be rejected.
Statistical hypothesis tests define a procedure that controls (fixes) the probability of incorrectly deciding that a default position (null hypothesis) is incorrect. The procedure is based on how likely it would be for a set of observations to occur if the null hypothesis were true.
The alternative hypothesis, as the name suggests, is the alternative to the null hypothesis: it states that there is some kind of relation. The alternative hypothesis may take several forms, depending on the nature of the hypothesized relation; in particular, it can be two-sided (for example: there is some effect, in a yet unknown direction) or ...
We define two hypotheses the null hypothesis, and the alternative hypothesis. If we design the test such that α is the significance level - being the probability of rejecting H 0 {\displaystyle H_{0}} when H 0 {\displaystyle H_{0}} is in fact true, then the power of the test is 1 - β where β is the probability of failing to reject H 0 ...
The alternative hypothesis depends on which version of the test is used, but is usually stationarity or trend-stationarity. It is an augmented version of the Dickey–Fuller test for a larger and more complicated set of time series models.