# Relationship between alpha and type 1 error hypothesis

### Alpha - Type I error - WikiofScience

You have been using probability to decide whether a statistical test provides A Type I error is often represented by the Greek letter alpha (α) and a Type II error want to risk committing a Type I error—rejecting the null hypothesis when it is, Figure animesost.infocal depiction of the relation between Type I and Type II errors. So the probability of making a type I error in a test with rejection region R is on the correlation structure among tests), i.e. will in actuality result in a true alpha of. 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.

Popper makes the very important point that empirical scientists those who stress on observations only as the starting point of research put the cart in front of the horse when they claim that science proceeds from observation to theory, since there is no such thing as a pure observation which does not depend on theory.

The first step in the scientific process is not observation but the generation of a hypothesis which may then be tested critically by observations and experiments.

It is logically impossible to verify the truth of a general law by repeated observations, but, at least in principle, it is possible to falsify such a law by a single observation. Repeated observations of white swans did not prove that all swans are white, but the observation of a single black swan sufficed to falsify that general statement Popper, It should be simple, specific and stated in advance Hulley et al.

Hypothesis should be simple A simple hypothesis contains one predictor and one outcome variable, e. Here the single predictor variable is positive family history of schizophrenia and the outcome variable is schizophrenia.

A complex hypothesis contains more than one predictor variable or more than one outcome variable, e. Here there are 2 predictor variables, i.

Complex hypothesis like this cannot be easily tested with a single statistical test and should always be separated into 2 or more simple hypotheses. Hypothesis should be specific A specific hypothesis leaves no ambiguity about the subjects and variables, or about how the test of statistical significance will be applied.

This is a long-winded sentence, but it explicitly states the nature of predictor and outcome variables, how they will be measured and the research hypothesis.

### Type I and type II errors - Wikipedia

Often these details may be included in the study proposal and may not be stated in the research hypothesis. 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.

## What are 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. 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. The more experiments that give the same result, the stronger the evidence. There is also the possibility that the sample is biased or the method of analysis was inappropriate ; either of these could lead to a misleading result.

This could be more than just an analogy: Consider a situation where the verdict hinges on statistical evidence e. This is consistent with the system of justice in the USA, in which a defendant is assumed innocent until proven guilty beyond a reasonable doubt; proving the defendant guilty beyond a reasonable doubt is analogous to providing evidence that would be very unusual if the null hypothesis is true.

There are at least two reasons why this is important. First, the significance level desired is one criterion in deciding on an appropriate sample size. Second, if more than one hypothesis test is planned, additional considerations need to be taken into account. See Multiple Inference for more information. The answer to this may well depend on the seriousness of the punishment and the seriousness of the crime.

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: Inference is based on a frequentist approach with repeated measuring, thus random sampling, controlled experiments and repeated experimentation, are a necessary prerequisite to reduce non-random error.

Given these conditions then, the level of significance is a property of the test not of the data.

Two hypotheses are tested at once.