One Cell, Four Answers, and Only the Denominator Moved

You'll learnto find the total a question puts underneath a count, and to read association off a display that rescales every group instead of off the raw cells.

200 students, cross-classified by grade and by whether they hold a part-time job. The senior-with-a-job cell holds 30 students, and that one count answers four different questions: 15.0% of all students, 50.0% of the seniors, 41.7% of the workers, and — reading the margin instead — 36.0% of all students hold a job at all. The numerator never changed. Then the harder half: juniors supply more working students than seniors, 42 against 30, and work at a far lower rate, 30.0% against 50.0%. Both sentences describe the same grid. Only one of them is about employment, and only a display that puts both grades on the same scale can show you which.

8 STEPS · 6 QUICK CHECKS · MARGINAL · JOINT · CONDITIONAL · SEGMENTED BARS · MOSAIC · v1

30 of 200 = 15.0% · 30 of 60 = 50.0% · 30 of 72 = 41.7% · 72 of 200 = 36.0%

Before you start

What you're looking at

A two-way table of 200 students. Rows are grades, columns are whether the student holds a part-time job, and the edges carry the totals.

The question

The senior-with-a-job cell holds 30 students. What percentage is that — and why does the question have four answers?

Watch for

The violet block. It is never the numerator; it is always the total the sentence put underneath, and it is the only thing moving.

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