# Relationship between alpha and type 1 error null

### What are type I and type II errors? - Minitab

The probability of a type I error is denoted by the Greek letter alpha, and Hypothesis testing involves the statement of a null hypothesis and the selection of a. When you loose the Type I error rate to alpha = or higher, you are choosing to reject your null hypotesis on your own risk, but you can not say that it is with a. In statistical hypothesis testing, a type I error is the rejection of a true null hypothesis while a A test's probability of making a type I error is denoted by α. Tabularised relations between truth/falseness of the null hypothesis and outcomes of.

That would be undesirable from the patient's perspective, so a small significance level is warranted.

If the consequences of a Type I error are not very serious and especially if a Type II error has serious consequencesthen a larger significance level is appropriate. Two drugs are known to be equally effective for a certain condition. They are also each equally affordable. However, there is some suspicion that Drug 2 causes a serious side-effect in some patients, whereas Drug 1 has been used for decades with no reports of the side effect.

The null hypothesis is "the incidence of the side effect in both drugs is the same", and the alternate is "the incidence of the side effect in Drug 2 is greater than that in Drug 1. So setting a large significance level is appropriate. See Sample size calculations to plan an experiment, GraphPad. Sometimes there may be serious consequences of each alternative, so some compromises or weighing priorities may be necessary. The trial analogy illustrates this well: Which is better or worse, imprisoning an innocent person or letting a guilty person go free?

Trying to avoid the issue by always choosing the same significance level is itself a value judgment.

Sometimes different stakeholders have different interests that compete e. Similar considerations hold for setting confidence levels for confidence intervals. Claiming that an alternate hypothesis has been "proved" because it has been rejected in a hypothesis test. This is an instance of the common mistake of expecting too much certainty.

There is always a possibility of a Type I error; the sample in the study might have been one of the small percentage of samples giving an unusually extreme test statistic. This is why replicating experiments i.

## Type I and type II errors

The alternative hypothesis cannot be tested directly; it is accepted by exclusion if the test of statistical significance rejects the null hypothesis. One- and two-tailed alternative hypotheses A one-tailed or one-sided hypothesis specifies the direction of the association between the predictor and outcome variables. The prediction that patients of attempted suicides will have a higher rate of use of tranquilizers than control patients is a one-tailed hypothesis.

A two-tailed hypothesis states only that an association exists; it does not specify the direction. The prediction that patients with attempted suicides will have a different rate of tranquilizer use — either higher or lower than control patients — is a two-tailed hypothesis.

The word tails refers to the tail ends of the statistical distribution such as the familiar bell-shaped normal curve that is used to test a hypothesis. One tail represents a positive effect or association; the other, a negative effect.

### Type I and II Errors

A one-tailed hypothesis has the statistical advantage of permitting a smaller sample size as compared to that permissible by a two-tailed hypothesis. Unfortunately, one-tailed hypotheses are not always appropriate; in fact, some investigators believe that they should never be used.

However, they are appropriate when only one direction for the association is important or biologically meaningful. An example is the one-sided hypothesis that a drug has a greater frequency of side effects than a placebo; the possibility that the drug has fewer side effects than the placebo is not worth testing.

Whatever strategy is used, it should be stated in advance; otherwise, it would lack statistical rigor. Data dredging after it has been collected and post hoc deciding to change over to one-tailed hypothesis testing to reduce the sample size and P value are indicative of lack of scientific integrity. Because the investigator cannot study all people who are at risk, he must test the hypothesis in a sample of that target population.

### Hypothesis testing, type I and type II errors

No matter how many data a researcher collects, he can never absolutely prove or disprove his hypothesis. There will always be a need to draw inferences about phenomena in the population from events observed in the sample Hulley et al. The absolute truth whether the defendant committed the crime cannot be determined. Instead, the judge begins by presuming innocence — the defendant did not commit the crime.

The judge must decide whether there is sufficient evidence to reject the presumed innocence of the defendant; the standard is known as beyond a reasonable doubt. A judge can err, however, by convicting a defendant who is innocent, or by failing to convict one who is actually guilty. In similar fashion, the investigator starts by presuming the null hypothesis, or no association between the predictor and outcome variables in the population.

Based on the data collected in his sample, the investigator uses statistical tests to determine whether there is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis that there is an association in the population.

The standard for these tests is shown as the level of statistical significance. The defendant did not commit crime Null hypothesis: No association between Tamiflu and psychotic manifestations Guilt: The defendant did commit the crime Alternative hypothesis: There is association between Tamiflu and psychosis Standard for rejecting innocence: Beyond a reasonable doubt Standard for rejecting null hypothesis: Convict a criminal Correct inference: Conclude that there is an association when one does exist in the population Correct judgment: Acquit an innocent person Correct inference: Conclude that there is no association between Tamiflu and psychosis when one does not exist Incorrect judgment: Convict an innocent person.

Incorrect inference Type I error: Conclude that there is an association when there actually is none Incorrect judgment: Acquit a criminal Incorrect inference Type II error: Sometimes, by chance alone, a sample is not representative of the population. Thus the results in the sample do not reflect reality in the population, and the random error leads to an erroneous inference.

A type I error false-positive occurs if an investigator rejects a null hypothesis that is actually true in the population; a type II error false-negative occurs if the investigator fails to reject a null hypothesis that is actually false in the population.

Although type I and type II errors can never be avoided entirely, the investigator can reduce their likelihood by increasing the sample size the larger the sample, the lesser is the likelihood that it will differ substantially from the population.

False-positive and false-negative results can also occur because of bias observer, instrument, recall, etc.