Homogeneity of variance is the equal variances across different samples (Mishra & Pandey, 2019). The assumption of the homogeneity of variance assumes the independent sample t-test stating that all comparison groups have the same variance. When using the test for homogeneity of variance, four outcomes are considered. One is since violation of homogeneity of variance assumption occurred; the independent t-test may not be the appropriate statistical procedure for data analysis. Therefore, it may opt for a lower order nonparametric statistical test; this type or this alternative is beneficial because it is free of parametric analyses’ assumptions. That is, they are generally considered less potent than the parametric analyses.
The nonparametric test is also known as the distribution-free test. It is based on fewer assumptions; for instance, do not assume that the outcome is approximately normally distributed (Lenart & Pipień, 2017). It involves specific probability distributions. Another benefit for opting to use the nonparametricnonparametric method is that it can be simple to conduct for the outcomes that are ordinal or require ranking. Another advantage is that it is easy to understand. It has short calculations, and it applies to all types of data. On the other side, it has some shortcomings as compared to parametric tests. It is less efficient compared to parametric. The results are not individual in providing the right or accurate answers because they are distribution free.
The second possible outcome as a result of homogenous variance violation is abandoning the test altogether. By abandoning the test, it won’t be easy in things to do with generalization. The results of a t-test are essential in that when it comes to conclusions, they are usually accurate and correct compared to other methods. by abandoning the test, it will be challenging to deal with such issues. The t-test is easy to interpret. By abandoning it; means that the interpretation of the output will be challenging. The output tells the different means from each group, which will be a challenge when abandoned. Abandoning the whole test will mean having no results, which could be easy to calculate by working to the end using the available data. The available data using the t-test would make it easy to calculate since that is one of its benefits. Again abandoning the test will mean that there will be no source data; this is because the t-test enables us to compare the average value of two sets of data and determine whether the samples come from the same population. T-test saves on time. This will not be the case if we abandon the test. It saves on time in that since small sample size is needed for calculations, it is not only time saving but also saves on money while on duration taken to collect and analyze large amounts of data.
On the other side, when we abandon the whole process, it has some benefits such as avoiding the carry-over effects; when relying on paired sample t-test, some problems such as repetition are experienced, so we avoid such by leaving the process problems. The difficulty of finding the subject is also dealt with when we leave the entire process. It means that finding the subject is for the same data it is sometimes .very tricky and expensive to get the subject. The T-test cannot be used for multiple comparisons since it results in some errors; leaving the process can greatly benefit since the output could be affected by some environmental changes affecting the entire results. Unreliability of some collected data could be avoided by abandoning the whole process, which could produce unreliable output.
The third possible outcome will be to use the parametric measure because of the test’s robust nature. The parametric test, is that which assumes that sample data comes from a population that can be modeled by a probability distribution that has a fixed set of parameters. Its advantages are; don’t require data; this is an advantage in that much data is not needed that could be converted into some order or format. This process of conversion is what appears in ranks format. Another benefit of this method is that it is quite easy to calculate them, everything in this method can be calculated with ease. Another benefit is that it provides all necessary information. The information from this method is usually real information that is provided regarding the population. When spread in groups it can perform well even when the groups are different and this again makes to be its benefit.
Some disadvantages are; one this method is not valid; the parametric tests are not valid when it comes to small data sets. Another disadvantage is that the size of the sample is always very big. This can be a challenge because of handling big sizes of samples. The last disadvantage is that parametric tests are only able to assess data that is continuous, and the results will be affected sometimes.
Resampling with a large sample size and reset will be the fourth option (Dwivedi & Alvarado, 2017). Resampling from its definition, which means drawing repeated samples from the original it means that it will increase or improve the accuracy. One of its benefits is that it is less bias and it is less of errors, or in case of errors, they are minimal. The disadvantage of this method is that it has higher variance. The second option will be more effective since it has more alternatives to choose from.
References
Dwivedi, A. K., Mallawaarachchi, I., & Alvarado, L. A. (2017). Analysis of small sample size studies using nonparametricnonparametric bootstrap test with pooled resampling method. Statistics in medicine, 36(14), 2187-2205.
Mishra, P., Singh, U., Pandey, C. M., Mishra, P., & Pandey, G. (2019). Application of student’s t-test, analysis of variance, and covariance. Annals of cardiac anaesthesia, 22(4), 407.
Lenart, Ł., & Pipień, M. (2017). NonparametricNonparametric test for the existence of the common deterministic cycle: the case of the selected European countries. Central European Journal of Economic Modelling and Econometrics, 201-241.