# Relationship between alpha level and type 1 error rate

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

significant difference). So the probability of making a type I error in a test with rejection region R is enough so significance levels need to be chosen carefully . When the "null hypothesis" includes more than one state of nature, the actual .. and contrasting, p-values, significance levels and type I error. Alpha (α) is the probability of making a Type I error while testing two The alpha level also informs us of the specificity (= 1 - α) of a test (ie, the.

Alpha represents an area were two population distributions may coincide. Data that fall within this area may pertain either to one or the other population. Thus, deciding whether the data are representative of one or the other is subjected to two types of error: A Type I error is made when we decide that the data is representative of one population typically phrased as the alternative hypothesis and not the other typically phrased as the null hypothesis when the data is, indeed, representative of the latter.

Said otherwise, we make a Type I error when we reject the null hypothesis in favor of the alternative one when the null hypothesis is correct.

### statistical significance - Stats: Relationship between Alpha and Beta - Cross Validated

A Type II error is made when we decide that the data is representative of one population typically phrased as the null hypothesis and not the other typically phrased as the alternative hypothesis when the data is, indeed, representative of the latter. Said otherwise, we make a Type II error when we fail to reject the null hypothesis in favor of the alternative one when the alternative hypothesis is correct.

Neyman and Pearson used the concept of level of significance as a proxy for the alpha level. This level of significance, always set beforehand, represents the probability of making a Type I error in the long run, ie after repeated experimentation under control conditions. In any case, the alpha level is better understood within Neyman-Pearson's theoretical positioning within statistics: However, they should be clear in the mind of the investigator while conceptualizing the study. Hypothesis should be stated in advance The hypothesis must be stated in writing during the proposal state.

The habit of post hoc hypothesis testing common among researchers is nothing but using third-degree methods on the data data dredgingto yield at least something significant. This leads to overrating the occasional chance associations in the study. The null hypothesis is the formal basis for testing statistical significance. By starting with the proposition that there is no association, statistical tests can estimate the probability that an observed association could be due to chance.

The proposition that there is an association — that patients with attempted suicides will report different tranquilizer habits from those of the controls — is called the alternative hypothesis.

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.

## Type I and type II errors

One tail represents a positive effect or association; the other, a negative effect. 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.

## What are type I and type II errors?

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. 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.

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

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.

Type 1 errors - Inferential statistics - Probability and Statistics - Khan Academy

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: