Statistics · Data representation
Chapter 1 · 4
The idea
Two-way tables
Why every person in a two-way table is counted exactly once, so the rows, the columns and the grand total all have to agree — and why completing a table is never guesswork: you find the row or column with a single gap and work outwards.
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Statistics · Data representation
Two-way tables
Why every person in a two-way table is counted exactly once, so the rows, the columns and the grand total all have to agree — and why completing a table is never guesswork: you find the row or column with a single gap and work outwards.
Why it works
Everyone lands in exactly one cell
An ordinary frequency table sorts a group by one question. A two-way table sorts the same group by two questions at once: each row heading answers the first, each column heading the second, and every member of the group lands in exactly one cell — never two, never none. That one sentence is the whole subject; everything else falls out of it.Why the totals have to agree
Each person sits in exactly one cell, so adding a row's cells counts everybody in that row exactly once — the row total must be its cells added up, and the same runs down a column. The grand total can then be reached by two different routes — add the row totals, or add the column totals — and both count every person once, so both must give the same number. That is why a two-way table checks itself: row totals summing to on a survey of people is the table announcing a mistake.Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
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