In statistic testing of hypotheses an error 2 exists. Kind in considering a null hypothesis true although in truth the alternative hypothesis is correct (being based on wrongly negative results). One calls this error also (beta error).

Examples

• A tester has an urn before itself, into which it cannot look. In it are red and green balls. Only in each case one ball can be taken to test purposes out of the urn.

Alternative hypothesis: "“In the urn are more red than green balls"”.

In order to be able to pass a judgement upon contents of the urn, the tester of the urn will take several times balls to test purposes. Null hypothesis in our example reads the fact that either exactly the same many red as becomes green or however more becomes green than red balls in the urn is (the opposite of the alternative hypothesis). If the tester comes due to its sample thus to the conclusion, null hypothesis is wrong correct and/or the alternative hypothesis, although in truth the alternative hypothesis is correct nevertheless, then would commit it an error 2. Kind.

• We would like to examine the influence of the nutrition on the mental development of children in children's homes. But we compare two groups of children regarding their achievement in cognitive tests: The one sample is nourished after the conventional plan, which receives others a particularly healthy cost cen. we assumes that the healthy food positively affects the cognitive achievements.

Alternative hypothesis: "“Children, who receive a particularly healthy food, exhibit better cognitive achievement as children, who are nourished in the conventional way."”

If we compare now the cognitive achievement of our two samples, then we do not determine a difference in the cognitive achievement. Therefore we consider the alternative hypothesis wrong and confirm null hypothesis. If however in truth the population of the healthy nourished ones exhibits a better achievement nevertheless, then we commit an error 2.Art.

But we determined no difference nevertheless in our In addition, this Gleicheit can be to due to the coincidental dispersion of the results of measurement or to the unfavorable composition of our samples.

Committing of an error 2.Art is usually less `schlimm"´, than an error 1.Art. This depends however individually on the investigation article. In our example the error 2.Art has very negative consequences: Although the healthy nutrition improves the achievement, we decide to maintain the conventional nutrition. An error 1.Art, thus the introduction of the healthy nutrition for all children, although this no achievement improvement brings, seems to have here less fatal consequences.

Note: With the computation with beta (and also alpha) it concerns conditioned probabilities.

See also

• Evaluation of a Klassifikators
• Error 1. Kind

Articles in category "Error 2. Kind"

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