# Relationship between power and type 1 error probability

### Type 1 errors (video) | Khan Academy

Differences between means: type I and type II errors and power in sample 2, the formula denoting the standard error of the difference between two means is. The probability of a type I error is called the significance level. In Statistical Power, the effect size or the strength of association is basically the. The probability of making a type I error is α, which is the level of significance you value for alpha means that you will be less likely to detect a true difference if your risk of committing a type II error by ensuring your test has enough power.

Sometimes different stakeholders have different interests that compete e. Similar considerations hold for setting confidence levels for confidence intervals.

### Hypothesis Testing

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.

So in this case we will-- so actually let's think of it this way. We say look, we're going to assume that the null hypothesis is true. So let's say we're looking at sample means.

## Type 1 errors

We get a sample mean that is way out here. So we are going to reject the null hypothesis. So we will reject the null hypothesis. Now what does that mean though? Let's say that this area, the probability of getting a result like that or that much more extreme is just this area right here.

So let's say that's 0. Statistical information and the fictitious results are shown for each study A—F in Figure 2, with the key information shown in bold italics.

Although these six examples are of the same study design, do not compare the made-up results across studies. Six fictitious example studies that each examine whether a new app called StatMaster can help students learn statistical concepts better than traditional methods click to view larger.

In Study A, the key element is the p-value of 0. Since this is less than alpha of 0. While the study is still at risk of making a Type I error, this result does not leave open the possibility of a Type II error. Said another way, the power is adequate to detect a difference because they did detect a difference that was statistically significant.

## What Is Power?

It does not matter that there is no power or sample size calculation when the p-value is less than alpha. In Study B, the summaries are the same except for the p-value of 0. Since this is greater than the alpha of 0. In this case, the criteria of the upper left box are met that there is no sample size or power calculation and therefore the lack of a statistically significant difference may be due to inadequate power or a true lack of difference, but we cannot exclude inadequate power.

We hit the upper left red STOP. Since inadequate power—or excessive risk of Type II error—is a possibility, drawing a conclusion as to the effectiveness of StatMaster is not statistically possible.

Type I and II Errors, Power, Effect Size, Significance and Power Analysis in Quantitative Research

In Study C, again the p-value is greater than alpha, taking us back to the second main box. The ability to draw a statistical conclusion regarding StatMaster is hampered by the potential of unacceptably high risk of Type II error. That is a good thing. In Study E, the challenges are more complex. With a p-value greater than alpha, we once again move to the middle large box to examine the potential of excessive or indeterminate Type II error.

Second, a sample size will provide adequate power to detect an effect size that is at least as big as the desired effect size or bigger, but not smaller.