In the statistics an error 1 exists when testing hypotheses. Kind in rejecting a null hypothesis although it is true (being based on wrongpositive results). One calls this error also a-errors.

With a test and/or an investigation accepted the probability, with a decision an error 1. To commit, one calls kind also level of significance. Usually one accepts an alpha level of 5% (significantly) or 1% (very significantly).

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. If it thereupon to decision arrives that alternative hypothesis applicable to be can, thus it opinion represents that more red than green balls in urn are, although in reality null hypothesis applies, i.e. that equivalent red as green or less red than green balls is in the urn, then commits it an error 1. Kind.

• We want to examine whether a new Lernmethode increases the intelligence quotient of pupils. But we compare a group from pupils, those after the new Lernmethode were informed with a sample of pupils, who were informed according to the old method.

Alternative hypothesis: "“Pupils, who were informed after the new Lernmethode, were informed to have a higher intelligence quotient than pupil, those according to the old method."”

Assumed in our investigation the sample of pupils, who were informed after the new Lernmethode, exhibits actually a higher IQ. Perhaps this difference is based in addition, only on coincidence or other influences. If thus in truth between the two populations at all no difference exists and we falsely reject null hypothesis - regard it thus as secured that the new method improves the IQ - then commit we an error 1.Art. This can have naturally fatal consequences, if we change entire instruction over e.g. at high costs and much expenditure to the new Lernmethode, although this causes no better results in truth at all.

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

See also

• Evaluation of a Klassifikators
• Error 2. Kind
• Operation characteristic

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