Inferential statistics

Define your null and alternative hypothesis.

Different terminology is used to refer to the Null (Ho or Hn) and Alternative hypothesis (H1 or Ha) . Be sure to use what is expected of you in your subject area.

• H0: A null hypothesis usually assumes no association, no difference or no relationship between variables.
• H1: An alternative hypothesis opposes the null hypothesis, often assuming an association, a difference or a relationship between variables.

Choose either a one-tailed or two-tailed test.

• A two-tailed test looks for differences in either direction.
• A one-tailed test looks for differences in one direction only.

For additional information and examples take a look at the following resources:

• What are the differences between a one-tailed and two-tailed test? by UCLA Statistical Consulting.
• A brief definition of Null and Alternative Hypotheses and the difference between one and two-tailed tests in About the null and alternative hypothesis by Minitab support (2019).
• Practice writing null and alternative hypotheses with the Khan Academy.

Need to know more?

• Take a look at this short guide from Laerd Statistics that outlines the process of hypothesis testing. Starting with your research question, examples are given on how to define a null and alternative hypothesis and the implications these have on the statistical test.
• An example of performing a basic hypothesis test by Minitab support (2019).

Set your Significance Level (α)

Once you have defined your statistical hypotheses, the next step is to select your chosen Significance Level (α, alpha). Many fields of study use α = 0.05 (or 5%) but this isn't always the case, be sure to check which level you should use.

The Significance Level is a value chosen by a researcher chooses as a cut-off to decide if a statistical test result is considered to be significant or not significant. This cut-off value is referred to as the critical value. For more details on this, please refer to What is a critical value? by Minitab support.

Finding a significant result does not guarantee that one really exists, and this 5% indicates the level of risk (or statistical error) that the researcher has chosen to be acceptable. In other words, there is a 5% chance of finding a significant result when one doesn't really exist - you've just found one by chance.

Statistical Errors

Finding a statistically significant result does not guarantee that there really is an association, a difference or a relationship between your variables.

When performing a statistical test, there are four possible outcomes. Two possibilities result in the correct decision and two the incorrect decision.

These incorrect decisions form the basis of Type I and Type II Errors. Each error has a probability of occurring.

• Type I Error has a probability of α, the level of significance.
• Type II Error has a probability of β, the statistical power.

For additional information on the implications of these errors take a look at What are type I and type II errors? a short blog with examples by Minitab support.

Statistical power (β)

What is statistical power (β, beta)? Statistical power is the probability of finding a true significant difference when one exists. For a more detailed explanation, take a look at What is power? by Minitab support.

Which statistical test should I use?

The type of statistical test to choose depends on the type of data that you have, and your research question. One way to choose an appropriate statistical test is to make use of a statistical flowchart. This flow chart for selecting commonly used statistical tests by Gerwien (2014) will help you visualize the steps involved.

Gerwien, R. (2014). Flow chart for selecting commonly used statistical tests. Available at: http://abacus.bates.edu/~ganderso/biology/resources/stats_flow_chart_v2014.pdf (Accessed 17th January 2017).

Choose your statistical test

Click on the links below for examples of commonly used statistical tests. For each test there is a brief description outlining what the test can be used for along with additional links on how to perform this test using different statistical software packages.

• Categorical data
• Continuous data

Test statistic value or P-value

There are two ways to determine if the output from a statistical test can be considered as significant or not significant.

• The first approach compares the test statistic value to the critical value.
• The second approach compares the p-value to the significance level.

The critical value and the p-value approach to hypothesis testing is an excellent resource describing the two approaches (Hartmann, Krois and Waske, 2018).

Need to know more?

• What is a test statistic? by Minitab support (2019).
• Understanding hypothesis tests: Significance levels (alpha) and P values in statistics from Minitab support.
• What the p-value tells you about statistical significance (McLeod, 2019).
• An example of getting and interpreting a p-value from Minitab support.
• For examples of how to interpret your p-value take a look at anatomy of a statistical hypothesis test by Loughborough University Mathematics Learning Support Centres and Coventry University Mathematics Support Centre.
• Practice using P-values to make conclusions with the Khan Academy.

Effect size

A significant result does not necessarily translate to a meaningful effect. Take a look at What does effect size tell you? for details on how to calculate and interpret effect sizes and why it is important to report them (McLeod, 2019).

Using Effect Size - or Why the P Value is Not Enough (Sullivan and Feinn, 2012).

The overall aim of gathering sample data and performing statistical analysis is to substantiate your research findings. Begin by reporting key descriptive statistics - these will help summarise key characteristics of your dataset for the reader.

Reporting and interpreting descriptive statistics

Key measure to report might include:

• Sample size, number of participants - provide full details.
• Demographics.
• Frequencies, percentages and/ or proportions.
• Average values and measures of spread.
• Confidence intervals.

Information can be succinctly summarised using tables and/or graphs. Take a look at your lecture notes and/ or further reading for ideas on how to present these findings.

• Interpret the key results for Descriptive Statistics - a blog designed to support key results from Minitab but can be used to help you think about your data - whatever software you are using. Use the following link to explore other descriptive statistics: Interpret all statistics and graphs for Descriptive Statistics (Minitab, 2019).
• Remember to be critical! Take a look at Descriptive Statistics: Reporting the Answers to the 5 Basic Questions of Who, What, Why, When, Where, and a Sixth, So What? by Thomas Vetter.

Reporting inferential statistics

• Inferential statistics allow you to make inferences (or predictions) about a population based on the results of the sample data. For guidance on how to report your inferential statistics, take a look at your lecture notes. Different subject areas use different conventions, if you are in doubt, ask your module lead for guidance.
• If you are looking for inspiration, worked examples for commonly used statistical tests can be found here. These examples often take you through how to perform the test in addition to how to interpret the output.

Need to know more?

• Reporting results of descriptive and inferential statistics in APA format.