Two-way tables are designed to allow comparisons between one set of data and two others. For example, results for GCSE geography and religious education can be compared with the number of pupils obtaining the same grade in GCSE English language.
Example
Tables were prepared to show the relationship between GCSE English language grades and GCSE geography and religious education grades.
| GCSE geography |
| GCSE grade | A*-A | B-C | D-E | F-G | U-X | Total |
|---|
| GCSE English language |
A*-A |
10 |
6 |
1 |
|
|
17 |
|---|
| B-C |
3 |
30 |
16 |
2 |
|
51 |
| D-E |
|
3 |
19 |
7 |
3 |
32 |
| F-G |
|
|
|
|
|
|
| U-X |
|
|
|
|
|
|
| Total |
13 |
39 |
36 |
9 |
3 |
100 |
| GCSE religious education |
| GCSE grade | A*-A | B-C | D-E | F-G | U-X | Total |
|---|
| GCSE English language |
A*-A |
6 |
5 |
|
|
|
11 |
|---|
| B-C |
5 |
11 |
1 |
|
|
17 |
| D-E |
|
12 |
14 |
1 |
1 |
28 |
| F-G |
|
1 |
1 |
2 |
|
4 |
| U-X |
|
|
|
|
|
|
| Total |
11 |
29 |
16 |
3 |
1 |
60 |
Indicate all the true statements:
- The grade A*-C pass rate for GCSE religious education was exactly 10% higher than the grade A*-C pass rate for geography
- Of the pupils taking GCSE geography, more than half achieved grade C and above in GCSE English language
- Of the pupils taking GCSE religious education, one third did not achieve grade C or above.
Statement one
Looking at the lower table, the religious education results are given in columns. The grades A*-C pass rate for GCSE religious education is 11 + 29 = 40. The total number of pupils taking religious education is 60.
The percentage of pupils who gained grades A*-C was:
x 100% = 66.7%
The grades A*-C pass rate for GCSE geography from the upper table, again shown in the columns, is 13 + 39 = 52. The total number of pupils taking GCSE geography is 100, so the percentage is 52%.
Statement one is therefore false, as 66.7 - 52 is not 10.
Statement two
Looking at the top table, the results for English language are given in rows. Looking across the top rows, 17 pupils gained grades A*-A for English language and 51 pupils gained grades B-C. Therefore 68 pupils gained grade C and above in English language. 100 pupils took geography and English language.
Therefore statement two is true, as 68 is more than half of 100.
Statement three
Looking at the columns in the lower table, the total number of pupils gaining grades A*-A and grades B-C is 11 + 29 = 40. A total of 60 pupils took religious education, so 20 pupils did not achieve a grade C or above. This is the same as 
, so statement three is true.
Avoiding common errors
Most common errors can be avoided by:
- not using the wrong totals
- not using the wrong table, and
- remembering that the totals are always on the opposite side of a table to the category heading.