Power analysis

4. Power analysis#

In previous weeks we focussed on testing how likely a given result was to occur due to chance, if the null hypothesis were true (chance of a Type 1 error).

This week we are thinking about the other type of error, Type 2.

Type 2 errors occur when the alternative hypothesis is actually true (eg, there is a difference in means between groups) but we fail to detect it.

Power is the probability of not making a Type 2 error, that is the probability of detecting an effect, if there is one present.

We saw in the lecture that whilst the probability of a Type 1 error is generally fixed at 5% (or whatever alpha value we use) for any sample size, the probability of a Type 2 error is much larger in small samples

In other words, sometimes our sample is just too small to reliably detect an effect even if there is one

To assess the sample size needed to detect an effect of a certain size, we conduct a power analysis

We will cover two examples:

  • power of a correlation (Pearson’s r) analysis

  • power of a t-test (independent and paired samples)

We will see how power analyses can be constructed using ‘home made’ code, and also learn to run them for \(t\)-test and correlation using a built in function in the Python library statsmodels.

4.1. Tasks for this week#

Conceptual material is covered in the lecture. In addition to the live lecture, you can find lecture videos on Canvas.

Please work through the guided exercises in this section (everything except the page labelled “Tutorial Exercises”) in advance of the computer-based tutorial session.

To complete the guided exercises you will need to either:

  • open the pages in Google Colab (simply click the Colab button on each page), or

  • download them as Jupyter Notbooks to your own computer and work with them locally (eg in JupyterLab)

If you find something difficult or have questions, you can discuss with your tutor in the computer-based tutoral session.

This week is particularly heavy on conceptual material, so please do discuss the guided exercises and tutorial exercises with your tutor to make sure you understand

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