The theoretical curve of normal distribution.
If the arithmetic mean to add and subtract from it one sigma (M ± 15), a normal distribution within these limits will be not less than 68.3% of the variation (observations), which is considered the norm for the phenomenon. If a ± 28 2, then these will be within 95.5% of all cases, and if k ± 38 M, then these will be within 99.7% of all observations. Thus, the standard deviation is the standard deviation, which allows to predict the probability of occurrence of such values of the studied trait, which is within the prescribed limits.
Evaluation of the reliability of arithmetic means and the relative values
In the study of solid (general) population for its numerical characteristics are calculated M and δ.
In practice, as a rule, we do not deal with the general, and on the sample.
For sampling method is very important method of selection from the whole, as the selected portion, as mentioned previously, should be representative.
In sampling errors are possible bias, that there are such events, the occurrence of which can not be accurately predicted. . However, they are legitimate, objective and appropriate. In determining the degree of accuracy of sampling error estimated value that can occur during sampling. Such errors are called random errors of representativeness (t) is the actual difference between the means or the relative values obtained by selective research, and similar values that would be obtained in the study of the whole population.
The average error of the arithmetic mean of the number is determined by the formula:
The average error of the arithmetic mean value can be calculated as the sigma, the amplitude variation series:
S – the coefficient to determine the error corresponding to the number of observations (see tab. 5.10). In this example (from Table. 5.8) the average error was ± 0,16 days.
And when calculating the amplitude variation series:
Days, which is close enough to the average errors calculated in the usual formula.
In assessing the result on the size of the average error are the confidence factor (t), which makes it possible to determine the probability of a correct answer, that is, it points to the fact that the obtained value of the sampling error is not more than the actual error made due to the continuous observation. So, if we take t = 2,6, then the probability of a correct answer will be 99.0%, which means that out of 100 sample observations once the sample mean may be beyond the general average. At t = 1 the probability of a correct answer will be only 68.3%, and 31.7% of medium can be calculated out of bounds. Consequently, with increasing confidence increases the width of the confidence interval, which in turn increases the reliability of judgments, the controversial results (Table 5.11).