Inferential statistics

Statistical tests are used as a way to quantify if there is an association, a difference or relationship between variables. These tests are performed on sample data, with the aim of inferring beyond the sample data to the wider population. Take a look at the following Minitab pages for an example of inferential statistics compared to descriptive statistics.

The sections below provide a range of resources to help you navigate the steps involved in performing inferential statistics from defining your hypothesis, to performing the statistical test and finally interpreting your or published results. 

Hypothesis testing

Starting with your research question, consider how you might write this in terms of a testable statement or statements (see the null and alternative hypotheses). This will help you think about what type of data to collect and what type of statistical test is appropriate to use to answer your research question.

  • Start with your research question.
  • Define the Null and Alternative Hypotheses.
  • Collect sample data.
  • Set the Significance Level (alpha).
  • Choose and perform an appropriate statistical test.
  • Interpret the results.
  • Reporting the results - linking back to your research question.

The sections below detail the key stages of hypothesis testing.

Additional statistical resources

Statistics uses lots of different terminology and types of tests. Here are some additional resources to help navigate statistical analysis.


A group of UK universities have developed materials for Statstutor, a website with resources for anyone at any level in a range of formats, from 3G mobile to video. Use their coloured menus (or our links below) to take you to materials grouped in different ways – everything is organised A-Z so it's easy to find what you want.

Software training

Recommended books

  • Radcliffe, C. (2020). How to analyze data. London: Red Globe Press: A pocket sized, friendly, practical, beginner's guide to understanding, analyzing and interpreting data. It takes you step-by-step through each stage in the statistical process.
  • Field, A. (2018) Discovering statistics using IBM SPSS statistics. 5th ed. London: Sage: The go-to book on learning statistics using IBM SPSS. Loved by students and cats alike.
  • Navarro, D. & Foxcroft D. (2019). Learning statistics with jamovi: A tutorial for psychology students and other beginners. (Version 0.70). DOI: 10.24384/hgc3-7p15: Covers the content of an introductory statistics class, as typically taught to undergraduate psychology students. Download a free copy of Navarro and Foxcroft.