# Type i error and ii relationship problems

### Type I, II, and III statistical errors: A brief overview Kaur P, Stoltzfus J - Int J Acad Med

Year: | Volume: 3 | Issue: 2 | Page: To decrease Type II error, one should increase the sample size in order to detect an. So, if we assume Type II error constant, then yes with increasing sample size Type I disease or an endangered species, then we often loosen the Type I error. Specifically, they can make either Type I or Type II errors. So if you're testing a hypothesis about a safety or quality issue that could affect.

The probability of a difference of The probability is known as the p value and may be written p It is worth recapping this procedure, which is at the heart of statistical inference. Suppose that we have samples from two groups of subjects, and we wish to see if they could plausibly come from the same population. Hence, if the confidence interval excludes zero, we suspect that they are from a different population.

The other approach is to compute the probability of getting the observed value, or one that is more extreme, if the null hypothesis were correct.

This is the p value.

These two approaches, the estimation and hypothesis testing approaches, are complementary. What would be the p value? A moment's thought should convince us that it is 2.

## Understanding Type I and Type II Errors

This is known as a one sided p value, because it is the probability of getting the observed result or one bigger than it. To support the complementarity of the confidence interval approach and the null hypothesis testing approach, most authorities double the one sided p value to obtain a two sided p value. Alternative hypothesis and type II error It is important to realise that when we are comparing two groups, a non-significant result does not mean that we have proved the two samples come from the same population - it simply means that we have failed to prove that they do not come from the population.

When planning studies, it is useful to think of what differences are likely to arise between the two groups, or what would be clinically worthwhile. For example, what do we expect to be the improved benefit from a new treatment in a clinical trial?

To reduce Type I error, one should decrease the pre-determined level of statistical significance. To decrease Type II error, one should increase the sample size in order to detect an effect size of interest with adequate statistical power. Type III error, although rare, occurs when one correctly rejects the null hypothesis of no difference, but does so for the wrong reason.

### Type I and II Errors

The following core competencies are addressed in this article: Practice-based learning and improvement, Medical knowledge. Kaur P, Stoltzfus J. Int J Acad Med ;3: The null hypothesis symbolized by H0 states that there is no difference in the population parameter s. For example, when examining the effectiveness of an experimental antibiotic, the null hypothesis would be that the drug has no effect on a disease in the larger population.

## Significance testing and type I and II errors

In contrast, the alternative hypothesis symbolized by HA or H1 is assumed to be true when the null hypothesis is false.

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.