Hypothesis Testing – 4 Steps to the Correct Test

It can take years of learning and practice before you get comfortable with hypothesis testing, and knowing when and how to choose the right statistical hypothesis test is no mean feat.

Fortunately, there are ways to shortcut this by having a process, a strategy and a nice, big diagram!

Here I'm going to give you all three!

​Hypothesis Testing - Getting Started

​I think everyone responds well to a good visualisation, so ​that's where we're going to start.

To help you make better hypothesis testing decisions I've created what I call The Hypothesis Wheel. To be honest, I don't ​expect the name to catch on, but I do expect it to be really useful and help you make some ​solid ​hypothesis testing decisions!

​So without further ado, here it is - The Hypothesis Wheel - making its debut in the world:

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Hypothesis Testing - Spinning The Wheel

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Now, there's a HUGE amount of information in there, and I don't expect anyone to absorb it all with just a quick glance, so it will take you quite a bit of study time to get to grips with it all. This is why most people get confused when they dip their toes into the hypothesis testing world!

We have an exclusive video course dedicated to teaching all of this in The Hive, but for now, let's have a look at the wheel to see how to 'read' it.

Hypothesis Testing - Spinning The wheel

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​Hypothesis Testing - a 4 Step Strategy

​When making decisions about hypothesis testing and deciding which test to select, you need a plan of action, and here's my 4 step strategy:

  1. 1
    ​Deduce the properties of your outcome variable (aka dependent ​or hypothesis variable)
  2. 2
    ​Deduce the properties of your input variable (aka independent or predictor variable)
  3. 3
    ​Deduce the parameters of the relationship
  4. 4
    Look up the statistic on the Hypothesis Wheel

Steps 1 & 2: Your Variable Properties


​As steps 1 and 2 ​are the same thing, ​you can do them together. The properties you need to check for your input and outcome variables are:

  1. 1
    ​Data Type
  2. 2
    ​Distribution
  3. 3
    ​Number of Classes

​I've previously written an in-depth post about data types, but it's worth briefly going over them again.

There are 4 distinct data types that you'll come across in your research, and they are Ratio (R), Interval (I), Ordinal (O) and Nominal (N), like this:

Data Types

In terms of the distribution you need to check whether your data (Ratio or Interval data only) are normally-distributed (ND) or non-normally distributed (NND). Actually, all you really need to know is whether they are symmetrical or not - they don't actually need to be ​full-blown Gaussian distributions to qualify here.

Data Distributions

Finally, you need to check (Ordinal or Nominal only) how many classes (categories) there are in your data. It's easier to explain what that means by example - the variable Gender has 2 classes; Male and Female, whereas My Favourite Colour Of The Rainbow has 7 (ROYGBIV). What you really need to know is whether your variable has 2 classes or more than 2.

Number of Classes

​Step 3: Hypothesis Testing Relationship Parameters

​The relationship parameter you need to know for the Hypothesis Wheel ​is which type of analysis are you conducting, univariate or multivariate, like this:

Types of Analysis

Hypothesis Wheel Colour Codes

To help you navigate around the hypothesis wheel I've colour coded various parts of it, like this:

Hypothesis Wheel Colour Codes

Step 4: Look up Your Statistic on the Hypothesis Wheel

We always start in the centre with the properties of the hypothesis variable, coloured in purple. There are 3 concentric circles corresponding to Data Type, Distribution and Number of Classes.

Spinning further out, in red we have the properties of the predictor variable - again, there are 3 circles for Data Type, Distribution and Number of Classes.

Then we have a blue circle for the relationship parameters, which denotes whether our analysis is univariate (UV) or multivariate (MV). When you look closely you'll see that there are 2 hypothesis wheels, and the larger one contains only univariate hypothesis tests while the smaller one has only the multivariate hypothesis tests.

Finally, the outer orange circle tells us which hypothesis test we should choose in any given circumstance.

​Statistical Hypothesis Testing - Spinning The Wheel #statistics #datascience @eelrekab @chi2innovations

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Hypothesis Testing - an Example on The Wheel

Let's zoom in on a particular example to see how you would use the hypothesis wheel to tell you which univariate test you should use.

Let's say that your hypothesis variable has the following properties:

  • ​Ordinal
  • ​>2 classes

And your predictor variable has these properties:

  • ​Nominal
  • ​>2 classes

Now let's see what that looks like on the hypothesis wheel:

Hypothesis Wheel Example

​Starting from the centre, locate the data type of ​your hypothesis variable (Ordinal). It has more than 2 classes, so ​we locate that too. Spinning out to the red segment, locate the data type of your predictor variable (Nominal). In this case, since the hypothesis variable has more than 2 classes it doesn't matter how many classes the predictor variable has - the correct statistic is the Chi-Squared Test.

​Hypothesis Testing - Summary

​The Hypothesis Wheel is more than just another flow chart that ​helps you choose which statistical hypothesis test you should use. The world doesn't need ​another ​flow chart, it needs a better one - and I believe this is it.

The Hypothesis Wheel is a framework for helping you to ask the right questions of your data so you can get the correct answers. All you need to do is ask 3 questions to correctly select your hypothesis test:

  1. 1
    ​What are my data types (RION)?
  2. 2
    ​What are their distributions (ND, NND), and/or how many categories do they have (2, >2)?
  3. 3
    ​What types of ​analysis am I looking to perform (UV, MV)?

​Once you've answered these questions - and they are right there on the chart to help you decide - the Hypothesis Wheel will help you choose the correct statistical tool to use.

But this isn't why it is a framework. It is a framework because if there is a statistical test that is not present on the chart (I've only included the most used in hypothesis testing), it is really easy to see exactly where it ​should fit on the Hypothesis Wheel​, like this:

Paired t-test

Hypothesis Wheel - Free Download

If you want your very own hypothesis wheel to download and keep, you can get a high definition pdf right here:

Hypothesis Wheel Poster

If you'd quite like to have it stuck on your wall so you can refer to it whenever you need to (and add your favourite hypothesis tests to it), you can get a high definition poster of hypothesis testing here:

Hypothesis Testing - Spinning The Wheel
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