Test of assumption

In Statistical, a test of assumption is a step consisting in rejecting or accepting a statistical Hypothèse, called null assumption , according to a data file (sample).

Classification

In a diagrammatic way, one generally distinguishes the tests from homogeneity and the tests of conformity .

  • In the case of a test of homogeneity, one wants to compare two samples between them. The null assumption H0 will suppose the homogeneity of the two samples. For example two averages will be compared.

  • Danslecasde a test of conformity, one wants to determine if a sample follows a known statistical law. The null assumption H0 will suppose the adequacy of the sample to this law.

Risk of first and second species

In all the cases, the test follows a succession of definite stages:

  1. Stated null assumption H0 and alternative assumption H1.

  2. Calcul of a variable of decision corresponding to a measurement of the distance enters the two samples the case of the homogeneity, or between the sample and the statistical law in the case of conformity. The larger this distance will be and the less probable the null assumption H0 will be.
  3. Calculus probability to obtain a value of as extreme variable of decision or more extreme as the value obtained, by supposing as H0 is true. This probability, generally called risk of first species and noted α0, corresponds to the risk to reject H0 wrongly if H0 is in fact true.
  4. Conclusion of the test, according to a risk threshold αseuil, in lower part of which one is ready to reject H0. Often, a risk of 5% is regarded as acceptable (i.e. in 5% of the cases when H0 is true, the experimenter will be mistaken and will reject it). But the choice of the threshold to be used will depend on the desired certainty and the probability of the alternatives.

The probability so that H0 is accepted whereas it is false is β, the risk of second species . It is the risk not to reject H0 when one should reject it. Its value depends on the context, and is appraisable with much difficulty (even impossible to evaluate), this is why only the α risk is used as decision criterion.

Traditional tests

There exists many statistical tests traditional among which one can quote:

See also: Test (statistical)

  • the Test of Student, sometimes also called test of Student-Fisher, which is used for the comparison of an average observed with an “awaited” value.

  • the Test of Fisher, sometimes also called test of Fisher-Snedecor, which is used for the comparison of two variances observed.

Not, for that one needs khi 2! -->

  • the Analysis of the variance or ANOVA, which is used to compare several averages observed enters, according to a predetermined experimental plan. It is based on a decomposition of the variance in an “explainable” part and a part “error”, presumedly distributed according to the normal Loi. This test is particularly used in the social sciences (SHS), the cognitive Sciences, medical sciences and sciences of the alive one.

  • the Test of Khi-2, which is used in particular with the comparison of a couple as manpower observed, or with the total comparison several couples of manpower observed, and more generally with the comparison of two distributions observed.

  • the Test of Kolmogorov-Smirnov, which as the test of Khi-2 is a test of adequacy between samples observed and a probability distribution. It compares the Fonction of distribution observed and the function of awaited distribution. It is particularly useful for the random variable continuous.

In methods bayésiennes, one uses much the psi-test (measurement of Distance in the space of possible) which one shows that Khi-2 constitutes a very good asymptotic approximation when exists a great number of observations.

See too

Simple: Statistical hypothesis test

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