# Type 1 error and 2 relationship quotes

### Type I and type II errors - Wikipedia

Power is directly proportional to the sample size and type I error; but if we omit the power from the sentence what will be the relation of two? .. There is only a relationship between Type I error rate and sample size if 3 2 Recommendations. Type I and Type II errors, β, α, p-values, power and effect sizes – the ritual of null hypothesis significance testing contains many strange concepts. Much has. study power, types I and II statistical errors, the pitfalls of multiple comparisons, and one and the corresponding P-value of the relationship between data pairs. Many published statistical analyses quote P-values as ≥ (not However, the clinical advantage of an additional 2 mm Hg reduction in.

These terms are also used in a more general way by social scientists and others to refer to flaws in reasoning.

### P – VALUE, A TRUE TEST OF STATISTICAL SIGNIFICANCE? A CAUTIONARY NOTE

Statistical test theory[ edit ] In statistical test theory, the notion of statistical error is an integral part of hypothesis testing. The test requires an unambiguous statement of a null hypothesis, which usually corresponds to a default "state of nature", for example "this person is healthy", "this accused is not guilty" or "this product is not broken".

An alternative hypothesis is the negation of null hypothesis, for example, "this person is not healthy", "this accused is guilty" or "this product is broken". The result of the test may be negative, relative to the null hypothesis not healthy, guilty, broken or positive healthy, not guilty, not broken. If the result of the test corresponds with reality, then a correct decision has been made.

However, if the result of the test does not correspond with reality, then an error has occurred. Due to the statistical nature of a test, the result is never, except in very rare cases, free of error.

### Two error types

Two types of error are distinguished: It is asserting something that is absent, a false hit. In terms of folk talesan investigator may see the wolf when there is none "raising a false alarm".

Where the null hypothesis, H0, is: Often, the significance level is set to 0. It is failing to assert what is present, a miss.

## Understanding Statistical Power and Significance Testing

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. 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.

Statistics 101: Visualizing Type I and Type II Error