Respond to two or more of your colleagues
Discussion: Data Assumptions and Parametric Statistical Tests
The accuracy of parametric statistical tests is largely based on the data distribution of the collected data. Parametric tests are based on distribution assumptions, such as normality, linearity, equality of variances, etc. These assumptions and others vary based on the statistical test; therefore, it is critical for quantitative researchers to evaluate the assumptions pertaining to their statistical analyses and identify actions taken if assumptions are grossly violated.
To prepare for this Discussion, review the Lumley et al. (2002) article, as well as Lessons 19–21 and 24 in the Green and Salkind (2017) text. Use the Walden Library databases to identify a research example using your doctoral research proposal and consider the role and importance of the assumptions underlying each parametric test.
Mohammed,
There are few studies that apply the t-test analysis to examine the relationship between variables and almost no peer-reviewed articles that used the t-test analysis in the field of occupational fraud where my study focus. The available research in this topic was to examine the relationship between the employee strain and occupational fraud in which the researcher defines the employee strain as the independent variable while the occupational fraud as the dependent variable, however, the researcher used Pearson Correlation test to address the hypothesis.
The one-sample t-test is commonly used when the data distribution is normal, and when the population mean is known (Rochon & Kieser, 2011).
The paired-samples t-test applied for the studies where there are two variables and the purpose of the test to compare the mean of the two variables in the same group and determine whether the mean of the difference between the two variables is different from zero (Green & Salkind, 2017).
The independent-samples t-tests or sometimes called the two samples t-test is used to compare the difference between the means of two variables where they are in independent groups (Manfei XU et al., 2017).
In summary, the assumption for using any one of the three t-test is that the data is normally distributed. In case the assumption violated it is either to use another statistics test such as ANOVA or Wilcoxon rank sum test. The other option is to increase the sample size sufficiently. In this case, the condition of the normal distribution to the outcome will not be necessary with sufficient sample size (Lumley, Diehr, Emerson, & Chen, 2002).
References
Green, S. B., & Salkind, N. J. (2017). Using SPSS for Windows and Macintosh: Analyzing and understanding data (8th ed.). Upper Saddle River, NJ: Pearson.
Lumley, T., Diehr, P., Emerson, S., & Chen, L. (2002). The Importance of the normality assumption in large public health data sets. Annual Review of Public Health, 23(1), 151. doi:10.1146/annurev.publhealth.23.100901.140546
Manfei XU, Fralick, D., Zheng, J. Z., Bokai Wang, Tu, X. M., & Changyong FENG. (2017). The differences and similarities between two-sample t-test and paired t-test. 双样本t 检验和配对检验的异同性., 29(3), 184–188. doi:10.11919/j.issn.1002-0829.217070
Rochon, J., & Kieser, M. (2011). A closer look at the effect of preliminary goodness-of-fit testing for normality for the one-sample t-test. British Journal of Mathematical & Statistical Psychology, 64(3), 410–426. doi:10.1348/0007-1102.002003
Mythily
Data Assumptions and Parametric Statistical Tests
One-sample t-tests evaluates whether the population mean on a variable is different from a constant which can be a midpoint, average value, or chance level of performance (Green & Salkind, 2017). In my research study example, I can use a variable to determine whether the users have a positive or negative view toward disruptive technologies like artificial intelligence (AI) and robotics.
Paired-samples t-tests evaluates whether the mean of the difference between two variables is different from zero in the population and is applicable for repeated-measures and matched-subjects (Green & Salkind, 2017). In my research study example, I can determine whether the users are more willing to adopt AI solutions after they are made aware of the benefits of AI. The participants will be surveyed twice-once before and once after a demonstration of AT solutions. The paired-sample t-test can then statistically determine the likelihood of any difference between the two measures (Saunders, Lewis, & Thornhill, 2015)
Independent-samples t-test is to compare group means for two groups (Laureate Education, 2016a) using a measure of spread of scores (Saunders et al., 2015). In my research study example, I can determine whether users with certain job roles like managers are more likely to adopt AI solutions than the users who are individual contributors.
There are multiple assumptions underlying the independent-samples t-test: (a) the test variable is normally distributed, (b) the variances of the test variable are equal, and (c) the cases are a random sample with independent scores on the test variable (Green & Salkind, 2017). The size of the sample impacts valid p values with normal or nonnormal population distribution. The power of the test may be reduced considerably for nonnormal populations (Green & Salkind, 2017). If the assumptions are violated the p value cannot be trusted. Green and Salkind (2017) recommend using parametric test when the assumptions are met and non-parametric alternatives when normality assumptions of the independent-samples t-test are not met.
References
Green, S. B., & Salkind, N. J. (2017). Using SPSS for Windows and Macintosh: Analyzing and understanding data (8th ed.). Upper Saddle River, NJ: Pearson.
Laureate Education (Producer). (2016a). Independent samples t-test, Part 1 [Video file]. Baltimore, MD: Author.
Saunders, M. N. K., Lewis, P., & Thornhill, A. (2015). Research methods for business students (7th ed.). Essex, England: Pearson Education Unlimited.