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. Provide constructive, supportive feedback to your classmates’ posts. Purchase the answer to view it
In statistics, hypothesis testing is a crucial tool for drawing conclusions about populations based on sample data. Two commonly used approaches are parametric and non-parametric tests. These tests differ in their assumptions, the types of data they can analyze, and their appropriate use in different situations.
Parametric tests are based on specific assumptions about the underlying distribution of the data. These assumptions include normality, homogeneity of variances, and independence of observations. Examples of parametric tests include the t-test, analysis of variance (ANOVA), and linear regression. These tests are powerful when the assumptions are met, as they can lead to more precise and efficient estimates of population parameters.
For example, let’s consider a study investigating the effects of a new medication on reducing blood pressure. The researcher randomly assigns participants to either the medication or placebo group. The researcher collects data on blood pressure before and after the intervention. To analyze the data, the researcher can use a paired t-test to compare the mean differences in blood pressure between the two groups. In this case, the assumption of normality is crucial, as the t-test assumes that the differences in blood pressure follow a normal distribution.
Non-parametric tests, on the other hand, make fewer assumptions about the data distribution. They are more flexible and can handle a wider range of data types, including ordinal or non-normally distributed data. Examples of non-parametric tests include the Wilcoxon signed-rank test, Kruskal-Wallis test, and Spearman’s rank correlation. These tests are typically used when the assumptions for parametric tests are violated.
Continuing with the previous example, let’s say the blood pressure data in the study exhibited a skewed distribution. In this case, a non-parametric alternative like the Wilcoxon signed-rank test could be used to compare the median differences between the medication and placebo groups. This test makes no assumptions about the distribution of differences and is appropriate for non-normally distributed data.
The assumptions required for parametric tests are important to consider before conducting statistical analyses. If these assumptions are violated, the results of the tests may be biased or unreliable. Violations of normality assumption can lead to incorrect p-values and invalid inferences. Similarly, violating assumptions of homogeneity of variances can result in inaccurate statistical significance and confidence intervals. Lastly, violation of independence assumption can have a significant impact on the validity of statistical tests.
To address the normality assumption, investigators can examine histograms, normal probability plots, or conduct formal tests like the Shapiro-Wilk test. Transformations can also be applied to the data to achieve approximate normality. If the data cannot be transformed, non-parametric tests are recommended.
To assess homogeneity of variances, investigators can use graphical methods like boxplots or formal tests like Levene’s test or Bartlett’s test. If there is evidence of heterogeneity of variances, non-parametric tests are preferred.
Independence assumption can be addressed by randomization or design considerations. For example, in a randomized control trial, participants are assigned to treatment groups using random allocation, ensuring independence of observations.
In terms of data analysis plan, the choice of test will depend on the hypothesis being tested and the nature of the data. For example, if the hypothesis involves comparing means of two groups, a t-test can be used for parametric data, while a Mann-Whitney U-test can be used for non-parametric data.
For reporting measures of central tendency for demographic variables, the mean and standard deviation are commonly reported for parametric data, while the median and interquartile range are reported for non-parametric data. These measures provide a summary of the distribution and aid in the interpretation of the data.
In conclusion, parametric and non-parametric tests differ in their assumptions, the types of data they can handle, and their appropriate use. Parametric tests are more powerful when the assumptions are met, while non-parametric tests are more robust to violations of these assumptions. It is important for investigators to consider the assumptions and select the appropriate test based on the research question and the nature of the data. By carefully selecting the appropriate test and meeting its assumptions, researchers can ensure valid and reliable statistical inference.