# 5 Tips for Choosing the Right Statistical Test

One of the most important and potentially challenging parts of statistical analysis is ensuring that the statistical test used aligns with the research question and available data. Common statistical tests include t-tests, Chi-squared, ANOVA, regression analysis, and more, and each is suited to different types of data and research questions. Using the wrong statistical test can lead to misleading conclusions, compromised data integrity, and invalid results. It can result in either Type I errors, where you incorrectly reject a true null hypothesis, or Type II errors, where you fail to detect a true effect. By carefully considering factors such as the nature of your data, your research question, and the assumptions underlying each test, you can ensure that your statistical analysis is robust and reliable. This article provides five essential tips to guide you in selecting the right statistical test for your research.

The foundation of any statistical analysis begins with a thorough understanding of the available data. First, it is important to recognize the types of data available. Categorical data, for example, includes variables that can be grouped into categories but have no inherent order, such as preferred color. Ordinal data, on the other hand, has categories in a clear order, but no consistent difference between those categories, such as levels of satisfaction. Interval and ratio data are both numeric with interval data lacking a true zero and ratio data having a meaningful zero point.

Besides the type of data, understanding the available data also includes knowing the distribution and variability. Visualizations like bar graphs and scatterplots can be utilized based on the variable types. Descriptive statistics of central tendency and variability can also describe the main features of the dataset. Finally, verifying whether numerical data is normally distributed can be essential for certain types of statistical tests.

## 2. Develop a Research Question

Before selecting and running any statistical test, a research question must be in place to guide the analysis. This involves identifying the primary aim of the sturdy and specifying what exactly you seek to uncover from the data. A good research question will be highly specific and testable. For example, “what impacts customer satisfaction with the notebook” is not a good research question upon which to build a statistical test as it is too vague. On the other hand, “what notebook color do customers prefer” is specific and testable as satisfaction scores for different colored notebooks can be specifically compared.

## 3. Consider the Comparison You are Making

Once you have a specific and testable research question, consider what type of comparison that research question is making. Different statistical tests can make different types of comparisons based on what types of variables are present and what comparison is being made.

One class of statistical tests, including t-tests and ANOVAs, can compare a numerical variables between two or more groups. For example, an ANOVA can test if the mean satisfaction score is different between red, blue, and green notebooks to see if there is a statistically significant difference.

Another class can compare two numerical variables with each other. In these cases, correlation and regression analyses are commonly used. Correlations measure the strength and direction of the relationship between two variables while regressions go a step further and model the relationship, allowing for predictions to be made based on the data.

Finally, there are tests that can compare two categorical variables and determine if there is an association, such as the relationship between gender and preferred color.

## 4. Consult Statistical References

Once all of these factors impacting the selection of a statistical test are understood, a statistical reference can be consulted to finalize the test decision. The most commonly used references are flow charts that start by asking what type of data is being compared, numerical or categorical. Then, you select the type of comparison you are running. Additional questions and branches of the flow chart ultimately lead you to a statistical test that matches the analysis you are running.

One such flow chart is available from Colorado State University. Taking the example research question “what notebook color do customers prefer”, and assuming that the preference score is continuous and normally distributed and that you are comparing more than two colors, this would lead to selecting an ANOVA test.

## 5. Check the Assumptions of Your Test

Finally, before carrying out the statistical test, it is essential to verify that the data meets the assumptions required by that test. Some of these assumptions, such as requiring continuous data across more than two categories for an ANOVA analysis, have already been validated by this point. However, each test will also have its own set of assumptions that need to be verified to ensure that the conclusions are correct and reliable.

For example, many tests require that the continuous variables be normally distributed and that all the variables included be independent from each other. Most tests also require all the data points to be independent of each other, so including the same person more than once is usually not permitted.

If the assumptions of a statistical test are not met, alternative methods like non-parametric tests can be considered. Alternatively, the existing data can be transformed, more data can be collected, or outliers can be removed where justified.

## Conclusion

Choosing the right statistical test is a pivotal aspect of conducting robust and reliable research. By understanding your data, developing a clear research question, considering the comparisons you are making, performing exploratory data analysis, and checking the assumptions of your chosen test, you can significantly enhance the accuracy and credibility of your findings. When assumptions are not met, adapting your approach through data transformation, non-parametric tests, or other robust methods ensures the integrity of your analysis. With these five essential, you are well-equipped to make informed decisions in your statistical testing, leading to more meaningful and valid conclusions.