Set 13 — correspondence analysis
After lecture 15 · 17 November · about 35 minutes
Data: brands.csv — 2 356 respondent × brand × attribute associations. Build the contingency table with table(brands$brand, brands$attribute).
Nothing here is random: no seed needed, and the Blackboard test checks your numbers as they come.
1 · Is there anything to analyse
Run chisq.test on the table. Report the statistic, the degrees of freedom and the p-value.
Correspondence analysis decomposes exactly this statistic. What would it mean to run CA on a table where the test came back at p = 0.4 — would the plot be empty, or would it be misleading? Answer carefully: this is the trap.
2 · Inertia is chi-square in disguise
Fit ca::ca(tab). Report total inertia and the percentage on the first two dimensions.
Verify numerically that total inertia equals \(\chi^2 / n\). Then say, in one sentence, what “explaining 98% of the inertia” is explaining.
3 · Read the map, with discipline
Plot the symmetric map.
- Name the contrast each axis captures, in the language of the attributes
- Identify one brand that sits near the origin. What does that position mean, and why is “average” a better word than “unremarkable”?
4 · The distance you are not allowed to read In class
We discuss this one in lecture 16, on 23 Nov — bring your answer.
A student points at brand B and attribute Reliable, close together, and says “B is reliable”.
Explain what is wrong with that reading on a symmetric map, and what you can legitimately say about B and Reliable. Then state what you would have to plot instead to make the student’s sentence defensible.
5 · One slide for the client In class
We discuss this one in lecture 16, on 23 Nov — bring your answer.
Produce a single figure with a one-line title that a brand manager could act on. Nothing else — no table, no second panel.
Write the sentence you would say while showing it.
Check yourself on Blackboard
Open the test Set 13 on Blackboard, enter your numbers, and read the feedback as soon as you submit. Not graded; as many attempts as you like.
This set checks: that CA is a decomposition of a test you already know, and that reading a symmetric map row-to-column is the standard mistake.