Chapter 11. Looking at relationships — from univariate to multivariate, with AI

Key points

• Analysis climbs: look at one variable → look at two together → look at many at once
• The combination of variable types decides which method to use
• AI proposes, executes and helps interpret — but validity is confirmed with a specialist

Analysis climbs a staircase

Once the data is clean, analysis begins. There is no need to make it complicated: analysis is just climbing three steps in order.

Step 1: univariate analysis (one variable at a time). First, learn the character of each variable.

• Continuous → mean, median, standard deviation (centre and spread); a histogram (the shape of the distribution)
• Nominal → proportions, bar charts This is where you grasp the whole. The iron rule is look at them one at a time before looking at relationships.

Step 2: bivariate analysis (the relationship between two variables). Next, "is there a relationship between A and B?" Here the combination of variable types from Chapter 6 comes into play.

Step 3: multivariate analysis (many factors at once). Reality is complex, and many factors act on an outcome at the same time. Multivariate analysis untangles that.

The multivariate toolbox

The main methods, with what they are for. You do not need to memorise names. Knowing that such tools exist, and being able to pull them out with AI when needed, is enough.

• Multiple regression — predict one continuous outcome from several factors (e.g. evaluating several influences on memory at once)
• Logistic regression — when the outcome is yes/no (e.g. the risk factors separating those who kept going from those who did not)
• Cluster analysis — automatically group cases with similar characteristics (e.g. sorting users into types to design an approach)
• Factor analysis — extract the common elements behind many items (e.g. the structure behind cognitive function)
• Multilevel analysis — handle individual and group structure (facility by facility, say) together
• ROC analysis — examine the balance of sensitivity and specificity, and assess a cut-off value

Hypothesis, variables and method must line up

The most important thing in analysis is that hypothesis, variables and method form a straight line. An example:

Hypothesis: exercising three or more times a week prevents memory decline Variables needed: memory (continuous), exercise habit present or absent (nominal) Method: t-test, or logistic regression adjusting for age, sex and so on

Does the line from hypothesis to variables to method hold? If it is out of true, no amount of sophisticated calculation will hit the target.

AI runs alongside the analysis, but does not guarantee it

AI accompanies the whole process. Ask "what method suits this data and hypothesis?", hand it "write the code and run it", ask "interpret this result for a beginner". The idea of entrusting work, learned in the previous part, applies fully.

But here is the point this guide wants to press hardest.

AI can be confidently wrong about statistics. It chooses inappropriate methods, invites misreadings of p-values, and calculates on assumptions that do not hold.

As Chapter 11 of Foundations said, for simple aggregation and getting a sense of tendency, AI is a powerful ally. But at the level of research, conference presentations, papers and important business decisions, always verify with a statistician, a supervisor and the original sources. AI runs alongside the analysis; it does not guarantee its correctness. Do not step over that line.

A prompt to try

You are a data scientist who knows biostatistics well. Where you are uncertain, say honestly that a specialist should confirm it. My hypothesis and the variables I hold are as follows.

[Hypothesis] (e.g. people with an exercise habit have higher life satisfaction) [Variables] (e.g. exercise habit = nominal; life satisfaction = continuous; age and sex also collected)

1. List candidate methods for testing this hypothesis, with your reasons.
2. Give the assumptions each method requires, and how to check them.
3. Point out any variables that should be adjusted for as confounders.
4. List the points I should confirm with a specialist if this analysis is to be presented at a conference or in a paper.

Chapter 11 summary

• Analysis climbs from univariate to bivariate to multivariate
• The combination of variable types decides the method; hypothesis, variables and method must line up
• AI runs alongside but does not guarantee; where responsibility is involved, verify with a specialist