# What does significantly different mean in statistics

## Definition of significance

If a statistical result is designated as significant, this expresses that the probability of error that an assumed hypothesis also applies to the population is not above a specified level. To put it simply: a measured relationship between two variables does not just happen randomly in the sample, but also applies to the population. Only hypotheses can be checked for significance, not the result of individual features. The result of the individual question “How much do you weigh?” Cannot be checked for significance - the characteristic must be related to at least one other characteristic.

An example: If you compare the variables body weight and height, you will probably identify a statistical relationship, here probably a positive correlation. The expression positive correlation stands for the hypothesis that the increase in value for one of the two characteristics is associated with the increase in value for the other characteristic (more body size equals more weight - and vice versa). The decisive question: Does this relationship, which applies to the sample, also occur in the population or does the sample reflect a random result?

In order to determine this, it must be determined how high the probability of error (p-value) for the hypothesis (here the positive correlation) may be as a maximum. The upper limit for the probability of error is given with the significance level (α). In general, a maximum of 5 percent probability of error is recognized as permissible, i.e. α = 5%.

This is followed by a test of our hypothesis with a hypothesis test that can be applied to the present characteristics (there are several). The result of the test gives the p-value, the probability of error. If this p-value is below α = 5%, the result is considered significant.

If a statistical relationship such as our hypothesis on the relationship between height and weight is listed as “significant”, this means that the measured relationship of a sample also applies to the population with a probability of 95%. This means that there is still a 5% chance that the checked connection is due to chance. After all, this applies to one in 20 cases.

The significance should not be confused with the error limit, which indicates the percentage deviations of the individual results from an actual opinion of the population.

Please note that the individual definitions in our statistics lexicon are simplified explanations. The aim here is to bring the individual terms closer to the broadest possible user group. In this respect, it is possible that individual definitions do not fully correspond to scientific standards.

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