Assumptions and Post-Hoc Tests

Too often, researchers rely heavily on whether a p value is less than .05 or whether an “r” is close to +/- 1. But both assumptions and post-hoc tests ensure that all factors have been adequately considered.

Develop an original response proposing a scenario where either:

assumptions tests were not properly performed, and the wrong statistical procedure was applied, giving inaccurate results;

or

post-hoc procedures were not applied to contextualize the results and, although the null hypothesis was rejected, power and effect were not considered.

Describe the scenario hypothetically and propose ways you could avoid such situations in your own application of statistics in research in the future.

Using the information provided, respond in one paragraph, for each of the three posts below.

Post 1

When conducting research, researchers often develop hypotheses or assumptions about the expected outcomes based on existing theories or prior knowledge. These assumptions guide the study design, data collection, and analysis. However, it is important to acknowledge that research findings can be influenced by various factors, and there may be unexpected or unplanned effects that emerge during data analysis. Post-hoc tests, also known as post hoc analyses or follow-up analyses, are conducted after the initial analysis to further explore the data and investigate additional research questions. These tests are not pre-planned or hypothesized before data collection but are conducted based on observed patterns or significant results in the data. It is important to consider that post-hoc tests should be interpreted with caution, as they are exploratory in nature and can be susceptible to false positives. The results of post-hoc tests should be considered as preliminary and hypothesis-generating, rather than definitive conclusions. Even if a researcher makes assumptions about the results ahead of time, post-hoc tests can still be valuable in exploring unexpected findings, controlling for Type I error rate, enhancing interpretation, and informing future research. Thoughts?

Post 2

In order to utilize applied statistics for a data set, statisticians must correctly apply assumption tests to the dataset to confirm the characteristics. These assumptions are the characteristics of the data that must be verified prior to utilizing a particular test when analyzing the data. Once certain characteristics are revealed, it will determine if we should use parametric or nonparametric procedures to analyze the data in which to describe the population. One way to complete the assumptions test is to conduct the homogeneity of variance test. This test will determine the variability of differences and similarities between the two groups analyzed. If the variance is not confirmed, we will not know how to proceed between a parametric or nonparametric procedure of data analysis. An example of this is when the data set is not normally distributed but the statistician proceeded to conduct a pearsons’r test on the data set. This will result in an incorrect conclusion of the data analysis and the results between its correlation. We will not be able to state that the samples represent the population nor draw inferences from the analysis. This can often occur when analyzing the final grades of a course where outliers are present in the distribution of scores. This will present a false pretense regarding the distribution of scores across the classroom.

Post 3

A study that looked at the association between exercise intensity and stress reduction in individuals. The researchers intended to use a linear regression model to investigate this association. They did not, however, test for critical assumptions for linear regression such as multicollinearity, residual normality, and homoscedasticity.

They proceeded with the linear regression analysis without addressing these assumptions due to an oversight. As a result, the findings revealed a link between exercise intensity and stress reduction. However, the model was poorly fitted due to multicollinearity difficulties and violated normality and homoscedasticity requirements, resulting in erroneous coefficient values and untrustworthy results.

Implementing adequate checks and balances is critical to avoiding such scenarios in future studies. Consider the following steps:

Pre-Analysis tests: Perform assumption tests specific to the chosen method before beginning any statistical analysis. In regression analysis, for example, quantifying multicollinearity, residual normality, and homoscedasticity is crucial. These checks can be aided by tools like as scatterplots, residual plots, and variance inflation factor (VIF) computations (Field, 2013).

Use Appropriate Statistical Procedures: Ensure that the statistical method used is appropriate for the nature of the data and the research issue. When in doubt, consulting statistical guidelines or specialists can assist in selecting the best appropriate analysis technique (APA, 2020).

Post-hoc Analysis and Interpretation: Once the data have been obtained, undertake detailed post-hoc analysis to interpret the findings in context. To comprehend the extent and relevance of the observed effects, consider effect sizes, confidence intervals, and practical significance in addition to p-values (Cohen, 1994).

Transparency and documentation: Document all processes taken throughout the analysis phase, including assumption checks, reasoning for chosen procedures, and post-hoc analyses. This transparency improves the study's reproducibility and allows for peer evaluation and verification (APA, 2019).

By carefully following these steps and ensuring thorough checks and balances throughout the statistical analysis process, researchers can reduce the likelihood of selecting inappropriate procedures or overlooking critical assumptions, resulting in more accurate and reliable results in their research endeavors.