Factor analysis: surveys and NPS drivers

You

The NPS follow-up survey has 20 questions. I was about to report 20 separate averages to the board.

Alex Tutor

Please don't. Many of those questions are probably just echoing the same few underlying attitudes. We can find those attitudes with factor analysis.

You

Underlying attitudes? Like reading minds?

Alex Tutor

Almost as good. If 'I trust this brand' and 'I'd recommend it' always move together, there's probably one hidden trait — say, brand loyalty — driving both.

Alex Tutor

Factor analysis starts by computing the correlation matrix between every pair of your 20 questions.

Alex Tutor

Correlations between four survey itemsQ1 'recommend' and Q2 'trust the brand' correlate strongly with each other; Q3 'delivery speed' and Q4 'packaging' correlate strongly with each other. The cross-pairs barely correlate at all — two clear blocks.

Chart data

Question pair	Correlation
Q1-Q2	0.8
Q3-Q4	0.75
Q1-Q3	0.2
Q1-Q4	0.15
Q2-Q3	0.25

Show 1 more row

Q2-Q4

0.2

You

So Q1 and Q2 are basically the same question in disguise?

Alex Tutor

Not identical, but driven by the same hidden factor. Q3 and Q4 form a second block — probably an 'operations' factor, unrelated to loyalty.

Alex Tutor

Question 1

Q1 'recommend to a friend' and Q2 'trust the brand' correlate at 0.8; both correlate under 0.25 with Q3 'delivery speed' and Q4 'packaging'. What does this pattern suggest?

Choose one answerQ1 and Q2 are likely driven by one hidden factor that Q3 and Q4 do not shareAll four questions measure exactly the same thingThe survey has no useful structure at allQ1 causes Q2's answer

Alex Tutor

Once factors are extracted, each item gets a factor loading per factor — the correlation between that item and the factor.

You

So a loading close to 1 means the item basically is the factor?

Alex Tutor

Right. Sum the squared loadings of a factor across all items, and you get its eigenvalue — how much total variance that factor explains.

Alex Tutor

\lambda_j = \sum_i a_{ij}^2

Eigenvalue of factor j: the sum of its squared loadings a across all items i.

You

Give me real numbers, not letters with subscripts.

Alex Tutor

Say Factor 1's loadings on our four items are 0.8, 0.8, 0.1, 0.1. Square and sum them, and you have the eigenvalue.

Alex Tutor

Question 2

Factor 1's loadings on four survey items are 0.8, 0.8, 0.1 and 0.1. What is this factor's eigenvalue (the sum of its squared loadings)?

Your answer

Units: eigenvalue (e.g. 1.30)

Alex Tutor

Raw factors are often messy — every item loads a little on every factor. Rotation sharpens the picture: big loadings grow, small ones shrink.

You

Doesn't that just make the numbers prettier without changing anything real?

Alex Tutor

It changes the axes, not the data. Orthogonal rotation keeps the new factors uncorrelated; oblique rotation allows them to correlate, if that fits reality better.

After rotation, we drop weak factors. The Kaiser criterion keeps only factors with eigenvalue ≥ 1.

Alex Tutor

Scree plot: four factors, four eigenvaluesEigenvalues 2.1, 1.3, 0.5 and 0.1 sum to 4.0 — the total variance of 4 standardised items. The elbow after factor 2 marks where real signal ends.

Chart data

Factor number	Eigenvalue
1	2.1
2	1.3
3	0.5
4	0.1

You

So the scree plot and the Kaiser rule are two ways to answer the same question?

Alex Tutor

Exactly — 'how many factors are real'. They usually agree; when they don't, that's worth investigating rather than picking whichever gives more factors.

Alex Tutor

Question 3

Four factors have eigenvalues 2.1, 1.3, 0.5 and 0.1. Under the Kaiser criterion (keep eigenvalue ≥ 1), how many factors are retained?

Your answer

Units: factors (e.g. 2)

Alex Tutor

Last step: naming the surviving factors. Look at which items load heavily on each, and describe the theme they share.

You

That sounds like the part where I make something up.

Alex Tutor

It's informed naming, not guessing — grounded in exactly which items loaded highly. It just isn't purely mechanical like the earlier steps.

You

Fair enough. Let's see if I can name one correctly.

Alex Tutor

Question 4

After rotation, Q1 'recommend' and Q2 'trust the brand' load heavily on Factor 1, while Q3 'delivery speed' and Q4 'packaging' load heavily on Factor 2. What would you name Factor 1?

Choose one answerBrand loyaltyDelivery operationsPackaging qualityPrice sensitivity

Factor analysis earns its keep in two more places besides surveys: cutting down a huge variable list, and fixing multicollinearity before a regression.

You

Multicollinearity — that's when predictors correlate with each other and break the regression, right?

Alex Tutor

Right. Replace the correlated predictors with one factor score, and the regression becomes stable again.

You

So it's a fixer for other analyses, not just an end in itself.

Alex Tutor

Question 5

Factor analysis can help fix multicollinearity in a regression by replacing several correlated predictors with one factor.

TrueFalse

Alex Tutor

So: correlation matrix, extract factors, rotate, drop the weak ones, name what's left. Same recipe every time.

You

Feels mechanical enough that I could almost script it.

Alex Tutor

Good — because the order matters. Try laying the steps out yourself.

You

Challenge accepted.

Alex Tutor

Question 6

Put the steps of a factor analysis in the right order.

Tap an item, then tap where it should go. You can also drag or use the arrows.

Beyond surveys, remember factor analysis has two other jobs: shrinking a huge variable list, and rescuing a regression from multicollinearity.

You

So it's not just a survey tool — people misuse it for that all the time, right?

Alex Tutor

Sometimes the opposite: people run it correctly but for the wrong reason, like hoping it'll force disagreeing respondents to agree.

You

That would be nice, honestly.

Alex Tutor

Question 7

Which of these are legitimate reasons to run factor analysis on CatChow's 20-question NPS follow-up survey? Select all that apply.

Choose all that applyReduce 20 correlated questions to a handful of underlying themesRemove multicollinearity before feeding survey scores into a regressionGuarantee that every respondent gives the same answerMake the raw data table shorter without losing much information

Alex Tutor

Good instinct on the legitimate reasons. Now put it in your own words — imagine explaining this to someone who'd rather just average all 20 questions.

You

Ah, the 'why can't we just take the average' question. I get that one a lot.

Alex Tutor

Perfect practice, then.

You

Give me a second to word this properly.

Alex Tutor

Question 8Short answer · AI-checked task

In 2–3 sentences, explain why CatChow should run factor analysis on a 20-item NPS follow-up survey instead of just reporting each question's average score separately.

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Nicely put. One more, trickier situation: a team got 5 factors instead of 2 and wants to present all of them.

You

Five drivers of loyalty sounds impressive on a slide, though.

Alex Tutor

Impressive and correct aren't the same thing. Let's see why.

You

Okay, lay out the numbers for me.

Alex Tutor

Question 9Case · AI-checked task

Write your recommendation for the survey team below.

CatChow's survey team ran factor analysis on 15 NPS driver questions. The Kaiser criterion (eigenvalue ≥ 1) keeps 5 factors, but the scree plot shows a clear elbow after factor 2. The team wants to name and present all 5 factors to leadership as '5 key drivers of loyalty.'

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That's factor analysis. Last lesson of the module: tying every method in the course together into one decision guide.

Alex Tutor

That’s the lesson. You answered every task — nicely done.

Next lesson: Course recap: choosing the right test