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Hi guys, welcome to the 28th lecture of the course Biological Diversity Theories,

Measures and Data Sampling Techniques.

Today I will talk to you about the fifth part of the statistic applied to

biological diversity.

Last time we saw parametric tests and how to use them.

This time we see how to use non-parametric tests and comparison between medians.

Non-parametric or independent from the distribution tests

are those tests that did not require special conditions to be applied, do not

need normal distributional data, should not be scaled or be in relationship.

Anyway, when distribution is similar to the normal distribution,

parametric meters are more efficient estimators.

These tests are particularly suited to compare various more samples.

One of the most used non-parametric tests is Mann-Whitney U test.

This test allows the analysis of ordinal data

to compare the medians of two independent samples.

To calculate the test, you need to proceed as follows.

First, establish the null hypothesis,

that the two samples come from the same population.

Then list all values your observation of both samples together, in ascending order

assigning each a rank from one to n, that is the total of the observation.

Then highlight only the values and

the ranks of the one of the two samples in the list.

Then add up separately the ranks of the values highlighted and

those of non highlighted values.

So the ranks of the first sample R1 and those of the second sample R2.

And then you need to calculate the U statistics for

both samples that is shown with the formula in this picture.

So you need then to verify that U1 plus U2 is equal to n1 multiplied by n2.

Then you need to choose the smallest of the two values of U and

compare it to the value in the table for the corresponding values of n1 and n2.

If the U value calculated is less than the critical value in the table,

you can reject the null hypothesis and

conclude that there is a significant difference between the medians.

Please pay attention to the fact that this is the only test [INAUDIBLE] for

paired data that to reject the null hypothesis must have good calculated

value lower than the critical one in table and not higher.

When there are samples with more than 20 sample units,

it is necessary to covert the smallest value of that in U.

Let us bring back the statistical task of the normal curve.

To do this, we add up the following formula.

If the calculated value of zed after the conversion of U exceed

the critical value of 1.96, the null hypothesis H0 Can be

rejected at P=0.05 that there is a significant difference.

If it also exceed the value at 2.58 the null hypothesis may be rejected at P=0.01,

and the difference between the medians of the two samples is highly significant.

Another useful non-parametric test when you want to compare two samples

is the Kolmogorov-Smirnov test.

The Kolmogorov-Smirnov test allows you the comparison of quantitative data, and

to calculate it you need to proceed as follows.

First of all,

you divide the data of each sample in frequency categories of equal width.

In the example that I show you in this table,

you can divide the heights in five meter, in five.

So it means that one category is 1, 5, the second one is 6, 10,

the third one is 11, 15 and the fourth one is 16, 20.