# Type 1 error and 2 relationship test

### Significance testing and type I and II errors | Health Knowledge Keywords: Effect size, Hypothesis testing, Type I error, Type II error Here there are 2 predictor variables, i.e., positive family history and stressful life Complex hypothesis like this cannot be easily tested with a single statistical test and. In statistical test theory, the notion of statistical error is an integral part of hypothesis stats testing A type I error occurs when the null hypothesis is true, but is rejected. A tabular relationship between truthfulness/falseness of the null . “Fail to Reject” or “Reject” the null hypothesis (H0) are the 2 decisions. When you do a hypothesis test, two types of errors are possible: type I and type II. The risks of these two errors are inversely related and determined by the level.

But what do we mean by "no difference"? Chance alone will almost certainly ensure that there is some difference between the sample means, for they are most unlikely to be identical. Consequently we set limits within which we shall regard the samples as not having any significant difference. If we set the limits at twice the standard error of the difference, and regard a mean outside this range as coming from another population, we shall on average be wrong about one time in 20 if the null hypothesis is in fact true.

If we do obtain a mean difference bigger than two standard errors, we are faced with two choices: Imagine tossing a coin five times and getting the same face each time. This has nearly the same probability 6. Do we regard it as a lucky event or suspect a biased coin? If we are unwilling to believe in unlucky events, we reject the null hypothesis, in this case that the coin is a fair one.

### Type I and II Errors

To reject the null hypothesis when it is true is to make what is known as a type I error. We try to show that a null hypothesis is unlikely, not its converse that it is likelyso a difference which is greater than the limits we have set, and which we therefore regard as "significant", makes the null hypothesis unlikely.

However, a difference within the limits we have set, and which we therefore regard as "non-significant", does not make the hypothesis likely.

To repeat an old adage, 'absence of evidence is not evidence of absence'. A range of not more than two standard errors is often taken as implying "no difference", but there is nothing to stop investigators choosing a range of three standard errors or more if they want to reduce the chances of a type I error. Testing for differences of two means To find out whether the difference in blood pressure of printers and farmers could have arisen by chance, the general practitioner puts forward the null hypothesis that there is no significant difference between them.

The question is, how many multiples of its standard error does the difference in means represent? Since the difference in means is 9 mmHg and its standard error is 0. Reference to normal distribution tables shows that z is far beyond the figure of 3.

Type I and Type II Errors

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.

The null hypothesis is "the incidence of the side effect in both drugs is the same", and the alternate is "the incidence of the side effect in Drug 2 is greater than that in Drug 1.

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• Significance testing and type I and II errors
• Hypothesis testing, type I and type II errors

So setting a large significance level is appropriate. See Sample size calculations to plan an experiment, GraphPad. 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.

## What are type I and type II errors?

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.