In statistics, various tests are used to make inferences about data collected. There is a wide range of statistical tests, and the choice of a test is based on the study design, data distribution, and the types of variables. Below are three common tests in statistics;
Pearson’s Correlation
Pearson's correlation coefficient is a statistical test often used to measure the relationship between two variables that are continuous. It is the best method to measure the relationship between variables that are of interest since it is based on covariance. This method often provides the researcher with information about the magnitude of a correlation between variables and the direction taken by the relationships. For a Pearson correlation test to be used in a survey, the data must be continuous (Oktavia et al., 2018). In order to determine the validity of a survey, the Pearson's correlation coefficient must be calculated. Pearson's correlation coefficient is used to identify the score of the respondents’ responses to items with total scores (Karras, 1997) . The coefficient is calculated as follows:
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? = ? ∑ ?? −∑ ? ∑ ? /√[ ? ∑ ? 2−(∑ ? ) 2][ ? ∑ ? 2−(∑ ? ) 2]
In this equation, ? o is the coefficient, and n is the total of valid responses. X and y represent an item's score and the score of each respondent, respectively. The assumption in this test is that both variables ( x and y ) are both distributed normally. The validity of the survey is determined using the validity coefficient values. These values are then interpreted to determine if they are beneficial (strongly beneficial) or least beneficial. Very beneficial values have strong validity and can, therefore, be used, while the least beneficial values have less validity and cannot or are unlikely to be used.
Mann-Whitney U Test
The Mann-Whitney U test often compares the difference existing between two groups, normally independent when the dependent variable is continuous or ordinal and not distributed (Murphy & Morrison, 2007) . Therefore, this tests the independent samples’ equality means. For example, the test could be used to understand whether attitudes towards job discrimina tion, where an ordinal scale is used to measure attitudes, vary with age or gender. In this case, the independent variable is "attitude towards job discrimination," while "age or gender" becomes the independent variable; the independent variable has two groups "young" or "old" or "male" or "female."
Ultimately, this test could be used to determine whether data measured using a continuous scale differs based on certain parameters, such as age, education level, or any other perspective. For this reason, this test is often referred to as the non-parametric alternative to the t-test. Unlike the t-test, this test allows the researcher to draw various conclusions about collected data based on their assumptions regarding the data distribution (Salkind, 2010). The conclusions made can vary from determining whether the samples differ to identifying whether there are median, mean, or other differences between the groups. The conclusions vary depending on the data distribution.
There are various assumptions made when applying this statistical test. First, the dependent variable is often measured at the continuous level; an example of a continuous level is time, weight, or IQ measured in hours, kilograms, and IQ scores, respectively. Another assumption is that the independent variable must have two categories in the independent groups; an example is gender, which has male and female.
Kruskal Wallis Test
The Kruskal Wallis test is a statistical test that serves as an alternative to the ANOVA test. This test is non-parametric, meaning that it does not assume that the data used does not necessarily come from a certain distribution (Hoffman, 2019) . This test is often applied when the ANOVA test assumptions have not been met. This test is used by researchers to determine whether the medians of groups (two or more) differ. Like other statistical tests, a test statistic is calculated and then compared to a cut-off point of the distribution. In this test, the test statistic is known as the H-statistic and often has two hypotheses. The null hypothesis assumes that the medians of a population in research are equal, while the alternative hypothesis assumes that the medians of the populations in the research are unequal. Often, this test helps the researcher identify whether there exists a significant difference between the population groups. The only problem with this test is that it never tells the researcher the different groups; this is determined using the Post Hoc test.
There are various assumptions in the Kruskal Wallis tests. The first assumption is that one independent variable has one or more independent groups (Ramachandran & Tsokos, 2015) . This test is best suited for three or more levels. Also, there should be no connection between members between or within the groups. Additionally, all the groups should have a similar distribution.
References
Hoffman, J., 2019. Basic Biostatistics for Medical and Biomedical Practitioners. Second ed. Academic Press.
Karras, D., 1997. Statistical Methodology: 11. Reliability and Validity Assessment in Study Design, Part A. Academic Emergency Medicine, 4(1), pp. 64-71.
Murphy, B. & Morrison, R., 2007. Introduction to Environmental Forensics. Second ed. Academic Press.
Oktavia, R., Mentari, M. & Mulia, I. S., 2018. Assessing the validity and reliability of questionnaires on the implementation of. Journal of Physics: Conference Series, Volume 1088.
Ramachandran, K. & Tsokos, C., 2015. Mathematical Statistics with Applications in R. Second ed. Academic Press.
Salkind, N.J 2010, Encyclopedia of research design , vol. 0, SAGE Publications, Inc., Thousand Oaks, CA, [Accessed 27 October 2020], doi: 10.4135/9781412961288.
