# Why is there an inverse relationship between type 1 and 2 errors

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

There will always be a need to draw inferences about Null hypothesis: No association between Tamiflu Incorrect inference (Type I error): Conclude that there is an. by Tom Rogers, Twitter Link · Local hex time: Local standard time: Type I and Type II Errors - Making Mistakes in the Justice System The null hypothesis - In the criminal justice system this is the presumption of innocence. In both the judicial. The villagers can avoid type I errors by never believing the boy, but that will Type II error - You fail to reject the null hypothesis when the the.

Therefore, you may consider the trade-off of these errors.

In traditional statistical hypothesis testing, you could use this cost benefit analysis to determine your alpha Type I error rate and beta Type II error rate before conducting an experiment. In our example, we would want a very small alpha typically 0.

### Type I Error and Type II Error - Experimental Errors in Research

This would, for example, dramatically effect the required sample size of your experiment because you are OK with accepting the null hypothesis incorrectly and report that dead people are actually alive.

I diagnostic testing, we can look at trade off of Type I and Type II errors in terms of the threshold we place between the distribution of a measurement taken from two populations. Using our example, we might measure the redness of the skin, with redder skin representing a living victim.

In the figure, we can see that the best place to put a threshold between these groups is in the lowest point between the two distributions. This location would result in the least overall error. However, we can make a logical trade off here: By moving the threshold to the Right, the probability of a Type I error is reduced at the expense of increasing the probability of a Type II error. 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.

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.

## Hypothesis testing, 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. 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.

- Type I and Type II Errors and Their Application
- Understanding Type I and Type II Errors
- Type I and II Errors

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: