¶ … 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, 2007). 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 distribution, but in cases of large variance, it is likely that the t-test may be preferable. Where there is a two sample test, the z test is most appropriate when the sample sizes are similar (Curwin and Slater, 2007). Standard deviation should also be known for the application of a Z test. However, this may be problematic in some circumstances where there is a large population and the standard deviation may remain unknown (Curwin and Slater, 2007).
It is possible to apply the z-test to smaller population sizes, but for those under 30 it becomes essential to ensure that there is a normal distribution. By comparison it maybe argued that t-tests provide a greater level of flexibility, utilizing a key distribution (Kahn Academy, 2014). The t-test may be utilized on a much broader range of data, including samples under the size of 30 (Kahn Academy, 2014). The flexibility also facilitates an examination of data where there is not a normal distribution and in two sample assessments where the sizes of the samples are different.
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