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.

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Introduction:

In statistics, parametric and non-parametric tests are two types of statistical tests that are used to analyze data in different scenarios. As a medical professor responsible for designing and conducting lectures, evaluating student performance, and providing feedback through examinations and assignments, it is important to understand the differences between non-parametric and parametric tests, when to use them, and the assumptions that must be met by the investigator to run the test. In this answer, we will discuss these aspects and also touch on the data analysis plan that can be used to address the study hypothesis.

Answer:

Parametric tests are used when data follow a normal distribution and have a known variance. These tests assume that the data is normally distributed and the variances are equal in the different groups being compared. Examples of parametric tests include t-tests and ANOVA. For instance, a t-test can be used to compare the mean scores of two groups on a continuous variable such as a blood pressure reading.

Non-parametric tests, on the other hand, are used when the data do not follow a normal distribution or have unknown variances. These tests do not make any assumptions about the underlying population distribution and are thus useful when the normality assumption is violated or the data is ordinal or nominal. Examples of non-parametric tests include the Mann-Whitney U test and Kruskal-Wallis test. For instance, the Mann-Whitney U test can be used to compare the difference in pain scores between two groups where the data is skewed.

Assumptions that must be met by the investigator vary depending on whether we use a parametric or non-parametric test. For parametric tests, the following assumptions must be met: normality, homoscedasticity, linearity, and independence. Violation of any of these assumptions may lead to incorrect conclusions. For non-parametric tests, there are no strict assumptions about the normality of the data or the variances between groups. Non-parametric tests are robust to violations of assumptions.

In terms of the data analysis plan, it is important to choose a test that is most appropriate for the research question. The choice of statistical tests will depend on the type of data collected, the study design, and the research question. For instance, if the research question is to compare the differences in blood pressure between two groups, a two-sample t-test could be used. However, if the data is not normally distributed, a non-parametric alternative like the Mann-Whitney U test can be used.

Finally, measures of central tendency such as the mean, median, and mode can be used to report demographic variables like age, gender, and ethnicity. These measures can help describe the sample being studied and provide a baseline for comparisons between groups.