# Statistical Work in Manager Practice

The work of a statistician is closely connected with possible risks of sampling error; therefore, it is always important to approach the study of statistical data wholly and objectively. Thanks to the theory, which includes several analytical tools of sample assessment, specialists can check whether the data obtained during the collection are given a fair description and whether a statistical error has been made. In general, a specialist’s critical task is to check the hypotheses set; they are ordinary text notes using mathematical analysis of sample data.

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For example, in the course of the task, it is necessary to establish whether there is a difference in salaries between men and women in the company. Such examinations respond to questions about pay equity, therefore, they are particularly relevant for managers. Typically, the test starts with a null hypothesis and an alternative hypothesis postulating contradictory statements about the question posed. Immediately after the hypothesis, the expert should establish the acceptable level of significance α required for statistical analysis. It is important to note that α may be interpreted as a probability of error in the compilation of the sample — in the statistical analysis, α tends to decrease when the accuracy of the study increases. One of the most important steps is to choose a statistical test: either a t-test or an f-test. While the first one is suitable for comparing the average values of two samples (average wages), the second one meets the request to compare two dispersions (whether the differences in wages are equal) (Surbhi, 2018). The fourth step is the decision rule, and it is worth clarifying that it is constant for almost all tests. In the case of p values less than α, the null hypothesis is rejected. The steps described above are the pre-working stage when direct access to data is not necessary. The statistical processing of the results starts with the fifth step, which is implemented in the processing of the sample with the help of tests, either by themselves or using Excel. Finally, drawing a line is the sixth step in which a specialist interprets the results by consistently answering three questions.

In the effective practice of managers, it is essential to admit that statistical work is not performed with a specific number, but with the distribution of data that does not always fit the normal function. Naturally, sample distributions will differ a bit, but the hypothesis assumes that these differences are insignificant. In practice, managers often use compa-ratio, which shows an employee’s position in the salary range. In particular, the coefficient fluctuates slightly in both directions near the value of 1.0 because it reflects the ratio of the real wage of an employee to the average one for a given position in the labor market.

F-test shows how close the deviation values of two samples are to each other: it is evident that the closer the calculated value of the f coefficient to 1.0 is, the more reason to conclude that the given null hypothesis is fair. It should be remembered that the critical value F from which the null hypothesis is rejected is determined by the level of significance (α = 0.05) and the number of degrees of freedom for each of the compared dispersions. In Excel, there are two versions of this test: F-Test Two-Sample for Variances and F-TEST. When using the F-Test Two-Sample for Variances, only the one-tail criterion corresponding to the first hypothesis test case is calculated. When a two-way criterion is to be used, the significance level α must be halved and the resulting value for the two-way criterion. F-TEST gives fewer output data, but immediately shows a two-way probability that the difference between the dispersions of the arguments is insignificant. The two-sample t-test checks the equality of the general population means values for each sample. This function allows determining the probability that two samples are taken from general sets that have the same average.

## References

Surbhi, S. (2018). Difference between t-test and f-test. Key Differences. Web.

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