People can make mistakes when they test a hypothesis with statistical analysis. Specifically, they can make either Type I or Type II errors. A type II error is a statistical term used within the context of hypothesis testing that describes the error that occurs when one fails to reject a null. Example: A large clinical trial is carried out to compare a new medical treatment with a standard one. The statistical analysis shows a.
Type I and II Errors
This should be done before analyzing the data -- preferably before gathering the data. If the consequences of a type I error are serious or expensive, then a very small significance level is appropriate.
Example 1 Two drugs are being compared for effectiveness in treating the same condition. Drug 1 is very affordable, but Drug 2 is extremely expensive. The null hypothesis is "both drugs are equally effective," and the alternate is "Drug 2 is more effective than Drug 1. That would be undesirable from the patient's perspective, so a small significance level is warranted. If the consequences of a Type I error are not very serious and especially if a Type II error has serious consequencesthen a larger significance level is appropriate.
Two drugs are known to be equally effective for a certain condition. They are also each equally affordable. However, there is some suspicion that Drug 2 causes a serious side-effect in some patients, whereas Drug 1 has been used for decades with no reports of the side effect.
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. So setting a large significance level is appropriate. See Sample size calculations to plan an experiment, GraphPad.
What are type I and type II errors? - Minitab
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.
What type of test you plan to use e. See Step 6 if you are not familiar with these tests. See the next section of this page for more information. If the power is less than 0.
Power Analysis, Statistical Significance, & Effect Size
What is statistical significance? Testing for statistical significance helps you learn how likely it is that these changes occurred randomly and do not represent differences due to the program.
To learn whether the difference is statistically significant, you will have to compare the probability number you get from your test the p-value to the critical probability value you determined ahead of time the alpha level.
If the p-value is less than the alpha value, you can conclude that the difference you observed is statistically significant. P-values range from 0 to 1. The lower the p-value, the more likely it is that a difference occurred as a result of your program.
Alpha is often set at. The alpha level is also known as the Type I error rate.
What alpha value should I use to calculate power? An alpha level of less than. The following resources provide more information on statistical significance: Creative Research Systems, Beginner This page provides an introduction to what statistical significance means in easy-to-understand language, including descriptions and examples of p-values and alpha values, and several common errors in statistical significance testing. Part 2 provides a more advanced discussion of the meaning of statistical significance numbers.
Beginner This page introduces statistical significance and explains the difference between one-tailed and two-tailed significance tests. The site also describes the procedure used to test for significance including the p value What is effect size?
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When a difference is statistically significant, it does not necessarily mean that it is big, important, or helpful in decision-making. It simply means you can be confident that there is a difference.
The mean score on the pretest was 83 out of while the mean score on the posttest was Although you find that the difference in scores is statistically significant because of a large sample sizethe difference is very slight, suggesting that the program did not lead to a meaningful increase in student knowledge. To know if an observed difference is not only statistically significant but also important or meaningful, you will need to calculate its effect size. Rather than reporting the difference in terms of, for example, the number of points earned on a test or the number of pounds of recycling collected, effect size is standardized.