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In a classic significance test, based on a random sample with size

In this day and age testing for significance has become a ritual which, if it leads to a significant result, still opens the doors to many well-known journals in nearly every scientific field. This is the case even though for a long time the application of null hypothesis significance testing has been criticized and even rejected [

In the significance test as defined by Fisher [

Even though the randomness of the sample is a premise for a test of significance, it is seldom certified. Additionally, the ‘‘iid’’ assumption requires that the order of drawings from the population is known and this allows the split of a random sample into a series of smaller subsamples. The sample size

A series of examples with randomly drawn samples should illustrate the typical situations. In a first example, the null hypothesis

In this specific case we know however that the true value is 0.55, hence the null hypothesis does not apply, but the rejection of the null hypothesis based on the given sample is not possible. This would nevertheless be possible if one would, for example, only take the first 28 units into consideration. As a result the

In a second example random values for the “true” value

What is striking here is that the

A final example should clarify the situation further: the “true” value that the binomially distributed random value creates is

From a sample size of

Consequently, we can draw the following conclusions. If as in usual practice only a

One method to include the additional information given in the partial sample’s

In the first example given here the “true” value was

The null hypothesis can be rejected as the sample was taken from a population with

In the second example the “true” value was

The null hypothesis cannot be rejected as the sample was taken from a population with

In the last example the “true” value was

The probability of this sample result if the null hypothesis is valid equals 0.0448. The mean and standard deviation of the bootstrap distribution of

In contrast to our examples, one usually does not know the “true” value of

Consequently, should the classic significance test lead to a result that is “not significant”, then this does not necessarily mean our analysis has come to an end (it does however also not necessarily indicate a “significant” result). The

Our idea to extend the classical significance testing does not describe a sequential analysis in the sense of Wald’s sequential probability ratio test [

In summary, in this paper, we propose a significance test that takes into account information from

Sample:

Sample:

Sample: