# Learn About Null Hypothesis and Alternative Hypothesis

For example, consider a clinical trial of a drug which is thought to reduce the risk of death. However, it may be found that the drug actually the risk of death. If H0 was defined as 'there is no difference in risk of death according to treatment status', then H1 would be 'there is a difference in risk of death according to treatment status', and a two-tailed test would be performed. This hypothesis test would be expected to find evidence against the null hypothesis (the direction of which would be quantified through a measure of effect such as the risk ratio). However, if the investigators were convinced that the drug would not increase the risk of death, then H0 may be stated as 'the risk of death is not reduced amongst treated animals', in which case H1 would be 'the risk of death is reduced amongst treated animals'. In this case, a one-tailed hypothesis test would be performed, which would fail to find evidence against the null hypothesis (since the null is in fact correct). For this reason, two-tailed tests are used in the vast majority of cases.

### Hypothesis - Simple English Wikipedia, the free encyclopedia

In a related but distinguishable usage, the term hypothesis is used for the of a ; thus in proposition "If P, then Q", P denotes the hypothesis (or antecedent); Q can be called a . P is the in a (possibly ) question.

### What is the null hypothesis? Why is it important? - Quora

Recall the compact model definition from (Eq 3.2): . Here we can regard the VAR[] model coefficients as a filter which transforms innovations (random white noise), , into observed, structured data . Consequently, for coefficient estimates , we can obtain the residuals . If we have adequately modeled the data, the residuals should be small and uncorrelated (white). Correlation structure in the residuals means there is still some correlation structure in the data that has not been described by our model. Checking the whiteness of residuals typically involves testing whether the residual autocorrelation coefficients up to some desired lag are sufficiently small to ensure that we cannot reject the null hypothesis of white residuals at some desired significance level.

## Second, for a moment forget the null hypothesis.

This type of error refers to the situation where it is concluded that a difference between the two groups exists, when in fact it does not. The probability of a type I error is often denoted with the symbol α. As this type of error is based on a situation in which the 'null hypothesis' is correct, it is associated with the p-value given in a hypothesis test, which is often set at 0.05 to indicate 'significance'. This means that there is a 5% chance of a type I error (which in the case of hypothesis testing, is interpreted as 'if the null hypothesis was correct, we would expect to see this difference or greater only 5% of the time - meaning that there is [weak] evidence against the null hypothesis being correct).

### Hypothesis Testing | Brilliant Math & Science Wiki

In the previous section, we noted that the simple asymptotic ACF test may yield misleading results when the coefficients are considered independently rather than as a group, derived from a multivariate process. In contrast, tests are a powerful class of test statistics explicitly derived to test up to some lag . SIFT implements three portmanteau test statistics: . Under the null hypothesis, for large sample size and , each of these test statistics approximately follow a -distribution with degrees of freedom. A -value can thus be obtained by comparing the test statistic with the c.d.f. of this distribution. If 1- is greater than some value (e.g., 0.05 for a 5% significance level), we cannot reject the null hypothesis and we accept that the residuals are white.

### The Good, the Bad and the Null Hypothesis | Watts Up …

SUGGESTED READING: Wikipedia also has a discussion of the concept of the null hypothesis which is somewhat readable. The discussion can be found at >.

### Null hypothesis and alternative hypothesis - …

For example, consider a clinical trial of a drug which is thought to reduce the risk of death. However, it may be found that the drug actually the risk of death. If H0 was defined as 'there is no difference in risk of death according to treatment status', then H1 would be 'there is a difference in risk of death according to treatment status', and a two-tailed test would be performed. This hypothesis test would be expected to find evidence against the null hypothesis (the direction of which would be quantified through a measure of effect such as the risk ratio). However, if the investigators were convinced that the drug would not increase the risk of death, then H0 may be stated as 'the risk of death is not reduced amongst treated animals', in which case H1 would be 'the risk of death is reduced amongst treated animals'. In this case, a one-tailed hypothesis test would be performed, which would fail to find evidence against the null hypothesis (since the null is in fact correct). For this reason, two-tailed tests are used in the vast majority of cases.