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¶ … statistical analysis as well as ensuring the data used is accurate, it is also essential that the appropriate statistical tools are used to undertaken in the analysis. Two similar tests are the t-test and the z-test. In both cases the test is usually applied in a situation where there is a desire to test the means of two samples, or the mean of one sample against a known mean to determine of there is a statistical difference. However, despite the similarities of the purpose of the t-test and the z-test, there are also some differences which mean that the tests are suitable for different types of situation. To appreciate when the different tests should be used, the paper will start buy looking at the z-test, and when it should be used, as well as consider the use of a t-test, which will lead to an understanding of when the less popular z-test should be used in preference to a t-test.
The z-test can be used to determine if there is a statistical difference between the means of two samples, or a single sample z-test may be used where there is a known measure against which the mean can be assessed (Curwin and Slater,...
However, for the z-test to give a reliable result there are some specific requirements of the data. Firstly, it should only be used where there are sample sizes of 30 or more (Curwin and Slater, 2007). The z-test is also most suitable for data that is normally distributed. Normal distribution is seen when data for a particular phenomena being studied appears to be a bell shape on a distribution curve, as shown below. This is where the majority of the data points are towards the mean, with outliers and an equal distribution of the data towards the edges of the distribution line (Curwin and Slater, 2007). The x axis will be the measurements for the phenomena, whereas the Y axis will be the number of data points at that level, the mid point of the curve in a perfect curve will be both the mean and the median.
Figure 1; Normal distribution curve
An assessment of the normal distribution may be undertaken by examining the variants, and the application of the central limit theorem (Kahn Academy, 2014). For larger sample is there is a greater capacity for the test to be used if there is a non-normal…
References
Curwin J, Slater R, (2003), Quantitative Methods for Business Decisions, London, Thompson Business Press
Kahn Academy, (2014), Z-statistics vs. T-statistics, retrieved from http://www.khanacademy.org/math/probability/statistics-inferential/hypothesis-testing/v/z-statistics-vs. -- t-statistics
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