According to Chesemore (2011), statistics is concerned with methods based on mathematics theory and probability, which allows the user to summarize many observations concisely. The first recorded use of statistics was in the 16th century; it was used by gamblers and life insurance companies. The use and development of statistical methods has greatly expanded in the 20th century. The invention of the computer simplified calculations (Chesemore, 2011). In addition to learning that statistics is used more often than I thought, I have learned the methods, calculations, the theories behind the formulas, and the requirements for each testing method.
Descriptive statistics is a system which is used to understand large sets of data. Tools include graphs, charts, and histograms. Data is plotted to determine the distribution, but descriptive statistics is limited to measures of central tendency, mean, mode, median, and standard deviation (Weinclaw, 2009). Descriptive statistics is very basic; there is no testing or predicting based on testing the data. It can be used to determine if a sample is normally distributed. The next level of statistics is inferential statistics.
Inferential statistics is much more complex than descriptive statistics and is used for analysis and making inferences based on hypothesis testing to determine statistical significance of calculated values. Inferential statistics uses a vast array of testing procedures. The tests which are used depend on how the test is set up and what the user wants to discover (Weinclaw, 2009).
A simple test to determine if a sample is representative of a population is the z-test. The z-test is heavily used to determine if the sample is representative of a population. After z has been calculated, the value is compared with a table to determine whether or not the sample is representative of a population. The sample needs to be relatively large and distributed normally. A company can use a z-test to determine if a measure, such as income, is equivalent with its competitors. The null hypothesis is that the sample mean is equal to the population mean; the alternate hypothesis is that they are not equal. (Tanner & Youssef-Morgan, 2013).
The one sample t-test accomplishes the same thing as the z-test, except it can be used on small samples. The calculated t from the sample is compared to a t value which is determined by degrees of freedom and alpha. The t-test can be one-tailed or two-tailed, based on what is being tested. The null hypothesis is that the sample mean and population mean are statistically equal. The alternate hypothesis is that they are not equal. A t-test could be used to determine if departmental overtime is greater than corporate policy dictates.
If there are two independent samples to be tested, an independent samples t-test can be used. In this test, two samples of the same size are repeatedly drawn. The data are subtracted, and the result will be a distribution of difference scores....