criterion in mathematical statistics - a strict rule, in accordance with the hypothesis that a certain level of significance is accepted or rejected.To build it, you need to find a specific function.It should depend on the outcome of the experiment, that is, from the empirically determined values.It is this feature will be a tool for evaluating the differences between the samples.
statistical significance.General
statistical significance - is the value of the probability of random occurrence which is very small.Insignificant as more extreme and its performance.The difference is called statistically significant in the case where there are data, the probability of which is negligible if to argue that these differences do not exist.But this does not mean that this difference must necessarily be large and significant.
level of statistical significance test
This term should be understood probability of rejection of the null hypothesis in the case of its truth.This is also called a type I error, or false positive solution.In most cases the process is based on p-value ("PI value").This cumulative probability by observing the level of statistical test.He, in turn, has the sample during the adoption of the null hypothesis.The hypothesis will be rejected if the p-value is less than the level claimed by the analyst.From this index directly depends on the value of the significance of the test: the lower, the respectively, and the more reason to reject the hypothesis.The level of significance usually denoted by the letter S (alpha).Popular among experts figures: 0.1%, 1%, 5% and 10%.If, for example, says that the chances of a match are 1 in 1000, then definitely we are talking about the 0.1% level of statistical significance of a random variable.Different in value of used-levels have their pros and cons.If the index is less then the greater the likelihood that the alternative hypothesis is significant.Although this could be a risk that a false null hypothesis is not rejected.It can be concluded that the choice of the optimal B-level depends on balance "power value" or, respectively, of the probability of compromise false positive and false negative decisions.Synonymous with "statistical significance" in Russian literature is the term "Validation".
Determination of the null hypothesis
in mathematical statistics, this assumption is checked for consistency with existing empirical data in hand.In most cases, the null hypothesis is taken as a hypothesis that the correlation between the studied variables is missing or that there are no differences to study the distribution uniformity.Under standard research mathematician trying to disprove the null hypothesis, that is, to prove that it is not consistent with the experimental findings.And to take place and alternative hypothesis is accepted instead of a zero.
key definitions
criterion U (Mann-Whitney) in mathematical statistics allows you to assess the differences between the two samples.They may be given by the level of a characteristic that is measured quantitatively.This method is ideal for evaluating the differences of small samples.This simple criterion was proposed by Frank Wilcoxon in 1945.And already in 1947, the method has been revised and supplemented by scientists HB Mann and DR Whitney, the names of which he is called to this day.Mann-Whitney test in psychology, mathematics, statistics, and many other sciences is one of the fundamental elements of the mathematical basis of the results of theoretical research.
Description
Mann-Whitney test - a relatively simple method with no parameters.Its capacity is significant.It is much higher than the power of Q-Rosenbaum criterion.The method evaluates how small the area of cross-values between samples, namely, between the rows of the ranked values of the first and second selections.The value of the criterion is less the greater the probability that the difference parameter values are valid.To properly apply the criterion U (Mann-Whitney), do not forget about some restrictions.Each sample should be at least 3 characteristic value.It is possible that in one case the values of the two, but the second time they necessarily must be at least five.In the study sample should be a minimum number of coincident indicators.All the numbers to be different in the ideal case.
use
How to use the Mann-Whitney test?The table, which is made by this method contains certain critical values.First you need to create a single set of two samples mapped, which then ranked.That is, the elements are arranged according to the degree of increase of symptoms, and lower rank is assigned to a smaller value.As a result, we obtain the total number of grades:
N = N1 + N2,
where the quantities N1 and N2 - the number of units contained in the first and second samples, respectively.Further, a single ranked number values is divided into two categories.Units, respectively, the first and second samples.Now considered one by one rank sum values in the first and second rows.Determined most of them (Tx), which corresponds to the sample nx units.To use more Wilcoxon method, its value is computed according to the following procedure.It should be on the table for the selected level of importance to find the critical value of this test for specific commitments N1 and N2.The resulting component can be less than or equal to the value from the table.In this case, it stated a significant difference in levels of trait studied samples.If the resulting value is greater than the table, then the null hypothesis is accepted.When calculated the Mann-Whitney test, it should be noted that if the null hypothesis is true, the criterion will be the expectation and variance.Note that for large volumes of data sampling method is considered almost normal distribution.The significance of differences is higher, the smaller value takes Mann-Whitney test.
