# Discussion Question Discuss the differences between non-parametric and parametric tests. Provide an example of each and discuss when it is appropriate to use the test. Next, discuss the assumptions that must be met by the investigator to run the test. Conclude with a brief discussion of your data analysis plan. Discuss the test you will use to address the study hypothesis and which measures of central tendency you will report for demographic variables. Purchase the answer to view it

Non-Parametric and Parametric Tests in Data Analysis

In the field of statistics, researchers commonly employ two types of tests to analyze data: non-parametric tests and parametric tests. These tests serve different purposes and have distinct assumptions, making them suitable for different research scenarios. In this discussion, we will explore the differences between these two types of tests, provide examples for each, discuss their appropriate use, and examine the assumptions needed for accurate results. Additionally, we will touch upon the data analysis plan, focusing on the test that will address the study hypothesis and the measures of central tendency that will be reported for demographic variables.

Non-parametric tests, also known as distribution-free tests, are used when the underlying data does not conform to specific distribution assumptions. These tests make fewer assumptions about the population and can be applied to nominal or ordinal data. The Mann-Whitney U test is an example of a non-parametric test. It is used to compare two independent samples when the data are ranked or when the assumption of normality is violated. For instance, if a researcher wants to compare the salaries of employees in two different companies without knowing the salary distribution, the Mann-Whitney U test would be appropriate.

On the other hand, parametric tests are used when certain distributional assumptions can be made about the data. They are more powerful than non-parametric tests when the data satisfies the assumptions. One of the most well-known parametric tests is the t-test. The independent samples t-test, for example, compares the means of two independent groups. It assumes that the data are approximately normally distributed and that the variances of the two groups are equal. Suppose a researcher wishes to compare the effectiveness of two teaching methods on student performance, using a normally-distributed test score as the outcome variable. In this case, the independent samples t-test would be appropriate.

When it comes to determining the appropriate test to use, researchers should consider the nature of the data, any underlying assumptions, and the research question. If the data do not meet the assumptions of normality or the presence of outliers makes parametric tests inappropriate, non-parametric tests offer a valid alternative. Non-parametric tests are also useful for small sample sizes or when the data are measured on an ordinal scale. However, it is important to note that parametric tests are generally more powerful when the assumptions are met, making them preferable when the conditions allow.

For accurate results, both non-parametric and parametric tests require certain assumptions to be met by the investigator. In non-parametric tests, the primary assumption is that the data are independent and identically distributed from a population with the same distribution. Additionally, the level of measurement should be nominal or ordinal. In contrast, parametric tests assume that the data are independent, identically distributed, and come from populations that follow a specific distribution (e.g., normal). Furthermore, parametric tests also assume that the variables have equal variances and that the observations within each group are independent. Failing to meet these assumptions can lead to biased or misleading results.

Turning to the data analysis plan, it is important to consider the appropriate test to address the study hypothesis accurately. In some cases, demographic variables can be compared between groups using appropriate statistical tests. For example, if the researcher wants to compare the mean age of two groups, an independent samples t-test can be used. Alternatively, if the data are not normally distributed or the assumptions of the t-test are not met, a non-parametric test like the Mann-Whitney U test can be employed. In addition to reporting measures of central tendency, such as means or medians, it is important to include measures of variability, such as standard deviations or interquartile ranges, depending on the nature of the data.

In conclusion, non-parametric and parametric tests serve different purposes and have distinct requirements. Non-parametric tests are suitable when data do not meet specific distribution assumptions, while parametric tests are appropriate when these assumptions are met. Researchers must be attentive to the assumptions necessary for each test to ensure accurate results. In data analysis plans, the selection of the appropriate test depends on the research question and the nature of the data. Measures of central tendency, such as means or medians, and measures of variability should be reported to comprehensively describe the data for demographic variables.