## Definition

Statistical tests work by calculating a **test statistic** – a number that describes how much the relationship between variables in your test differs from the null hypothesis of no relationship.

It then calculates a ** p-value** (probability value). The

*p*-value estimates how likely it is that you would see the difference described by the test statistic if the null hypothesis of no relationship were true.

If the value of the test statistic is more extreme than the statistic calculated from the null hypothesis, then you can infer a **statistically significant relationship** between the predictor and outcome variables.

If the value of the test statistic is less extreme than the one calculated from the null hypothesis, then you can infer **no statistically significant relationship** between the predictor and outcome variables.^{1}

## Who

Being a teaching assistant in statistics for students with diverse backgrounds, I have the chance to see what is globally not well understood by students. **I have realized that it is usually not a problem for students to do a specific statistical test when they are told which one to use (as long as they have good resources and they have been attentive during classes, of course).** However, it appears that the task is much more difficult for them when they need to choose what test to do. This article presents a flowchart to help students in selecting the most appropriate statistical test based on a couple of criteria.^{3}

## What

The choice of statistical test used for analysis of data from a research study is crucial in interpreting the results of the study. What does that entail? Intimate knowledge of the testing process and the resulting data!

## Why

The field of statistics is the science of learning from data. Statistical knowledge helps you use the proper methods to collect the data, employ the correct analyses, and effectively present the results. Statistics is a crucial process behind how we make discoveries in science, make decisions based on data, and make predictions. Statistics allows you to understand a subject much more deeply.

There are two main reasons why studying the field of statistics is crucial in modern society. First, statisticians are guides for learning from data and navigating common problems that can lead you to incorrect conclusions. Second, given the growing importance of decisions and opinions based on data, it’s crucial that you can critically assess the quality of analysis that others present to you.

Statistics is an exciting field about the thrill of discovery, learning, and challenging your assumptions. Statistics facilitates the creation of new knowledge. Bit by bit, we push back the frontier of what is known.^{2}

See Theoretical Knowledge Vs Practical Application.

## How

Statistical tests are used in hypothesis testing. They can be used to:

- determine whether a predictor variable has a statistically significant relationship with an outcome variable.
- estimate the difference between two or more groups.

Statistical tests assume a null hypothesis of no relationship or no difference between groups. Then they determine whether the observed data fall outside of the range of values predicted by the null hypothesis.

If you already know what types of variables you’re dealing with, you can use the flowchart [below] to choose the right statistical test for your data.^{1}

Many of the **References** and **Additional Reading** websites and **Videos** will assist you with determining which statistical test to use.

As some professors say: “It is intuitively obvious to even the most casual observer.“

## References

^{1} ⭐ Bevans, Rebecca. 2020. “Statistical Tests: Which One Should You Use?” *Scribbr*. https://www.scribbr.com/statistics/statistical-tests/.

^{2} “Library Guides: Statistics: Why Study Statistics?” 2022. *libraryguides.centennialcollege.ca*. https://libraryguides.centennialcollege.ca/c.php?g=717168&p=5123066.

^{3} Soetewey, Antoine. “What Statistical Test Should I Do?” 2021. *Medium*. https://towardsdatascience.com/what-statistical-test-should-i-do-612036412147.

## Additional Reading

⭐ Bevans, Rebecca. 2020. “Test Statistics Explained”. *Scribbr*. https://www.scribbr.com/statistics/test-statistic/.

The test statistic is a number calculated from a statistical test of a hypothesis. It shows how closely your observed data match the distribution expected under the null hypothesis of that statistical test. The test statistic is used to calculate the p-value of your results, helping to decide whether to reject your null hypothesis.

Bhandari, Pritha. 2020. “An Introduction To Descriptive Statistics”. *Scribbr*. https://www.scribbr.com/statistics/descriptive-statistics/.

Descriptive statistics summarize and organize characteristics of a data set. A data set is a collection of responses or observations from a sample or entire population. In quantitative research, after collecting data, the first step of statistical analysis is to describe characteristics of the responses, such as the average of one variable (e.g., age), or the relation between two variables (e.g., age and creativity). The next step is inferential statistics, which help you decide whether your data confirms or refutes your hypothesis and whether it is generalizable to a larger population.

“Essential Articles – Statistics”. 2022. *Mathematical Mysteries*. https://mathematicalmysteries.org/essential-articles-statistics/.

“Everything You Need To Know About Hypothesis Testing — Part I”. 2021. *Medium*. https://towardsdatascience.com/everything-you-need-to-know-about-hypothesis-testing-part-i-4de9abebbc8a.

In this post, I’m attempting to clarify the basic concepts of Hypothesis Testing with illustrations. What is Hypothesis Testing? What are we trying to achieve? Why do we need to perform Hypothesis Testing? We must know the answers to all these questions before we proceed.

“Everything You Need To Know About Hypothesis Testing — Part II”. 2019. *Medium*. https://towardsdatascience.com/everything-you-need-to-know-about-hypothesis-testing-part-ii-f0526be27b7d.

In this second part, I will be focusing on the **Statistical Tests**. After we look at the distribution of data and perhaps conducting some descriptive statistics to find the mean, median, or mode, it is time to make inferences about the data. In statistics, we categorize “Hypothesis Testing” under Inferential Statistics. **Statistical Tests **allow us to make inferences because they can show whether an observed pattern is due to intervention or by chance.

⭐ “First steps with DATAtab”. 2022. *Datatab.Net*. https://datatab.net/tutorial/get-started.

DATAtab is a web-based statistics software that runs right here in your browser window. Since it is a web application, it does not need to be downloaded or installed. You can start analyzing your data online in the statistics calculator on DATAtab at any time.

Ingram, Owen. 2021. “Which Statistical Test You Should Use?” *Research Prospect*. https://www.researchprospect.com/which-statistical-test-you-should-use/.

Statistical tests are used for testing the hypothesis to statistically determine the relationship between the independent and dependent variables, along with statistically estimating the difference between two or more groups. A null hypothesis is a statement for no link and relationship or difference between different groups that are assumed in the statistical testing. The null hypothesis test determines if the data’s values fall outside the range predicted through the null hypothesis. In this article, we will discuss the different aspects of statistical tests, including the selection of parametric and nonparametric tests to understand the statistical testing in detail.

Nayak, BarunK, and Avijit Hazra. 2011. “How To Choose The Right Statistical Test?” *Indian Journal Of Ophthalmology* 59 (2): 85. doi:10.4103/0301-4738.77005. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3116565/.

Today statistics provides the basis for inference in most medical research. Yet, for want of exposure to statistical theory and practice, it continues to be regarded as the Achilles heel by all concerned in the loop of research and publication – the researchers (authors), reviewers, editors and readers.

Sivarajah, Sivakar. “Statistical Testing: Understanding How To Select The Best Test For Your Data!” 2020. *Medium*. https://towardsdatascience.com/statistical-testing-understanding-how-to-select-the-best-test-for-your-data-52141c305168.

This post is not meant for seasoned statisticians. This is geared towards data scientists and machine learning (ML) learners & practitioners, who like me, do not come from a statistical background. For a person being from a non-statistical background the most confusing aspect of statistics, are the fundamental statistical tests, and when to use which test. This post is an attempt to mark out the difference between the most common tests and the relevant key assumptions.

“Statistical Testing – Understanding Which Testing Methods To Use”. 2022. *datascience.foundation*. https://datascience.foundation/sciencewhitepaper/statistical-testing-understanding-which-testing-methods-to-use.

Data Science, Machine Learning, Artificial Intelligence, Deep Learning – You need to learn the basics before you become a good Data Scientist. Math and Statistics are the building blocks of Algorithms for Machine Learning. Knowing the techniques behind different Machine Learning Algorithms is fundamental to knowing how and when to use them. In this paper, we will look at statistics as a concept. What are the different tests and most important, ‘When to use Which? ’

“⭐ The Beginner’s Guide to Statistical Analysis | 5 Steps & Examples.” 2022. *Scribbr*. https://www.scribbr.com/category/statistics/.

Statistical analysis means investigating trends, patterns, and relationships using quantitative data. It is an important research tool used by scientists, governments, businesses, and other organizations. To draw valid conclusions, statistical analysis requires careful planning from the very start of the research process. You need to specify your hypotheses and make decisions about your research design, sample size, and sampling procedure. After collecting data from your sample, you can organize and summarize the data using descriptive statistics. Then, you can use inferential statistics to formally test hypotheses and make estimates about the population. Finally, you can interpret and generalize your findings. This article is a practical introduction to statistical analysis for students and researchers. We’ll walk you through the steps using two research examples. The first investigates a potential cause-and-effect relationship, while the second investigates a potential correlation between variables.

“The Statistics Tutor’s Quick Guide to Commonly Used Statistical Tests”. 2022. *statstutor.ac.uk*. https://www.statstutor.ac.uk/resources/uploaded/tutorsquickguidetostatistics.pdf.

This PDF guide is designed to help you quickly find the information you need about a particular statistical test.**Section 1** contains general information about statistics including key definitions and which summary statistics and tests to choose. Use the “Which test should I use?” table to allow the student to choose the test they think is most appropriate, talking them through any assumptions or vocabulary they are unfamiliar with.**Section 2** takes you through the most common tests used and those that are usually as complex as the students require. As a statistics tutor, you should be familiar with all these techniques.**Section 3** contains tests and techniques that are more complex or are used less frequently. This section is aimed at tutors who have studied statistics in detail before.

“Types Of Statistical Tests | CYFAR”. 2022. *cyfar.org*. https://cyfar.org/types-statistical-tests-0.

After looking at the distribution of data and perhaps conducting some descriptive statistics to find out the mean, median, or mode, it is time to make some inferences about the data. As mentioned previously, inferential statistics are the set of statistical tests researchers use to make inferences about data. These statistical tests allow researchers to make inferences because they can show whether an observed pattern is due to intervention or chance. There is a wide range of statistical tests. The decision of which statistical test to use depends on the research design, the distribution of the data, and the type of variable. In general, if the data is normally distributed, parametric tests should be used. If the data is non-normal, non-parametric tests should be used. Below is a list of just a few common statistical tests and their uses.

## Videos

⭐ I suggest that you read the entire reference. Other references can be read in their entirety but I leave that up to you.