Due date Thursday 1/12 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
Introduction
In the field of statistical analysis, there are two main types of tests used: parametric tests and non-parametric tests. These tests differ in terms of their assumptions and the type of data they can analyze. This discussion will explore the differences between these two types of tests, provide examples of each, and discuss when it is appropriate to use them. Furthermore, the assumptions that must be met by the investigator to run each test will be examined. Finally, a data analysis plan will be discussed, including the test that will be used to address the study hypothesis and the measures of central tendency that will be reported for demographic variables.
Differences between Non-parametric and Parametric tests
Non-parametric tests, also known as distribution-free tests, make fewer assumptions about the population distribution. These tests are used when the data does not meet the assumptions required by parametric tests. Non-parametric tests do not require the data to be normally distributed or have equal variances. They work by rank-ordering the data and comparing the ranks instead of the actual values. Some common non-parametric tests include the Mann-Whitney U test and the Wilcoxon signed-rank test.
On the other hand, parametric tests make certain assumptions about the population distribution. These tests are used when the data meets specific assumptions, such as normal distribution and equal variances. Parametric tests calculate test statistics based on the actual values of the data. Examples of parametric tests include the t-test and the analysis of variance (ANOVA).
Example and Appropriateness of Non-parametric and Parametric tests
To illustrate the differences between these two types of tests, let’s consider a hypothetical study comparing the effectiveness of two different pain medications. Suppose the study aims to assess the difference in pain relief between Medication A and Medication B in patients with chronic back pain.
If the data collected for this study is ordinal or non-normally distributed, a non-parametric test such as the Mann-Whitney U test would be appropriate. The Mann-Whitney U test compares the distribution of ranks between two groups, in this case, the patients receiving Medication A and Medication B. This test is appropriate when the assumption of equal variances is violated and can handle skewed or non-normal data distributions. The research question can be framed as “Is there a difference in pain relief between patients receiving Medication A and Medication B?”
Conversely, if the data collected for this study is normally distributed and the assumption of equal variances holds, a parametric test like the independent samples t-test would be more appropriate. The t-test compares the means of two groups, in this case, the mean pain relief scores of patients receiving Medication A and Medication B. This test assumes that the data is normally distributed and has equal variances. The research question can be framed as “Is there a significant difference in mean pain relief between patients receiving Medication A and Medication B?”
Assumptions for Non-parametric and Parametric tests
Non-parametric tests have fewer assumptions compared to parametric tests. The Mann-Whitney U test, for example, assumes independent observations, a continuous dependent variable, and ordinal or continuous independent variables. This test does not assume normality or equal variances. The Wilcoxon signed-rank test, another non-parametric test, assumes paired continuous data that are at least ordinal. It does not assume normality or equal variances.
Parametric tests, on the other hand, have more stringent assumptions. The independent samples t-test assumes independent observations, a continuous dependent variable, and categorical independent variables with two groups. It assumes that the data is normally distributed and has equal variances. The ANOVA assumes independent observations, a continuous dependent variable, and categorical independent variables with more than two groups. It also assumes normality and equal variances.
Data Analysis Plan
In this hypothetical study, the data analysis plan will involve comparing the pain relief scores between patients receiving Medication A and Medication B. Given that the data collected for this study is ordinal or non-normally distributed, the Mann-Whitney U test will be used to address the study hypothesis. The test will compare the distribution of ranks between the two groups, indicating whether there is a significant difference in pain relief.
For the demographic variables, measures of central tendency such as the mean, median, and mode may be reported. These measures provide information about the typical value or the most common value for each variable. It is important to report multiple measures of central tendency to capture the different aspects and characteristics of the data. For example, reporting both the mean and median can help identify any potential outliers that may affect the interpretation of the results.
In conclusion, the differences between non-parametric and parametric tests lie in their assumptions and the types of data they can analyze. Non-parametric tests are suitable for data that does not meet the assumptions of parametric tests, such as non-normality and unequal variances. On the other hand, parametric tests are appropriate when these assumptions are met. The appropriate test to use depends on the type of data collected and the research question being addressed. In this hypothetical study, the Mann-Whitney U test is appropriate for comparing pain relief scores between two groups, while measures of central tendency such as the mean, median, and mode will be reported for demographic variables.