[MUSIC] Hi guys, welcome to the 25th lecture of the course Biological Diversity Theories, Measures and Data sampling techniques. Today we will talk about statistic applied to biodiversity on the second part. As already explained in the previous lecture, the standard deviation, is a measure of variation around the mean of the sample, and it can be calculated in the following way. In this formula, you see that x is the value of an observation, mu is the mean of the sample, and N is the numbers of sampling units. The numerator of the radical is defined of deviance. When the data are grouped by frequency values, it is needed to multiply the frequency f to the numerator of the radical. The variance, however, is simply the square value of the standard deviation, as indicated by a sigma square or s square. The standard error from the mean indicates how much the mean of the sample is close to the population mean. The standard error is simply the sigma or the s o the sample divided by the square root of n, where n represents the number of sampling units. It makes no sense to report a mean without providing an indication of the associated standard deviation, or standard error. So it is important, therefore, to always write that the sample as a mean of x plus or minus an sd, or plus or minus a standard error. When the variance of a sample is considerably higher than the mean, we have a case of aggregate data. In nature, aggregate random or uniform distribution of data can be observed. Because vary measured varies in ecology and in particular in the study of the biodiversity are asymmetrical as in normal the distribution, it is necessary to process the data. With this operation we obtain a compression of the asymmetric days. In other words, we squeeze the distribution to get a normalization of values. Distribution in this way acquires the same properties of a normal distribution and the same narrow limits can be used for the statistical analysis, as described in the previous lecture, to 95% or to 99%. So, the probability of 0.05 or 001. The most useful transformation, when there are aggregates valued with greater variance from the mean, and no uniform, or symmetric distribution, is the logarithm transformation. That is to recalculate all the sample values transforming them with the log ten or the natural logarithm. If the variance is approximately equal to the mean, the distribution is defined random or Pearsonian. In these cases, the transformation with the square root is the most adequate. Sometimes it can be useful to adopt the arcsine transformation when the data are expressed as relative or percentage frequencies. In this way, the values will be scattered and included in a range between zero and one. Some statistical tests in particular, non parametric required to use of ranks. These latter are nothing more than an alternative system for classifying data. To assign ranks, all the data are listed in ascending order, ascending order depending on the test requirements. And to each one an integral value from 1 to N, the total number of sample units is assigned. Thank you guys for your attention, and see you in the third part of the statistical analysis applied to biological diversity.