Historically there has been moderate correlations between scores in English and mathematics on the college entrance test. This correlation has never been strong enough to use to predict mathematics placements from an English score, but they support a non-causal link between English skills and mathematics skills on the entrance test.

The following is a table of correlations for 230 regular freshmen who entered in the fall of 2005. This number is less than the actual number, the data I have is not complete for every student and the correlation analysis can only be run for students with complete data.


y Structure Reading Writing Placement Group Math M Sum
Structure 1 0.25 0.48 0.46
0.36 0.39 0.46
Reading 0.25 1 0.17 0.18
0.34 0.34 0.38
Writing 0.48 0.17 1 0.48
0.26 0.25 0.32
Placement 0.46 0.18 0.48 1
0.17 0.18 0.22
Math 0.36 0.34 0.26 0.17
1 0.98 0.87
M 0.39 0.34 0.25 0.18
0.98 1 0.87
Sum 0.46 0.38 0.32 0.22
0.87 0.87 1

In the original data the Math column contains either 90, 95, 98, or 100. This is a non-linear scale. The M column contains a 1, 2, 3, or 4 for 90, 95, 98, or 100 respectively. This provides a linear scale to run the English data against. The Sum column in the original data contains the sum of the four math columns, in other words, the total number correct. This can vary from 0 to 40. The sum is useless for placement purposes, but correlates very strongly to placement. Thus the sum is as good a single value as is available for correlation studies against the English data.

Each row shows the correlation of the x-values in purple along the top against the y-values on the left in pink. Thus the strongest correlations can be seen for math placement, math level, and math sum for the structure section of the test in the first row, and for reading against the sum in the second row.

Only the numbers in red bold exceed the critical value for significance at an alpha of 0.05 (5%) on a two-tailed test for significance. Thus only the structure and reading tests are significantly correlated with the math sum. The essay is not significantly correlated. The following x-y scatter graph shows the distribution of the structure versus the math sum:

english structure versus math linear correlation

Again, these correlations are not strong enough to place students in mathematics. This study must be viewed with considerable caution - it is only a study of 230 students, a subset of those admitted to associate degree programs. This is a large subset, but still potentially problematic. This said, I would note with caution that the data supports the contention I made at the mathematics meeting that students who achieve admission to associate's degree program are already above the weakest level of performance in mathematics.

Put another way, the national site might not see many students who could not achieve success at MS 090 in its new PreAlgebra format if they worked hard. The state sites, however, are likely to see weaker students and may find a need for a re-purposed and re-developed MS 065.

Post-Script of interest only to those working on the admission's cut-off

One of the site directors asked that students below "MS 090 PreAlgebra" level in mathematics not be admitted. This generates the obvious question, "What are the lowest scores on the math entrance test?" Given that the test is multiple choice with five options on 40 questions, students should theoretically randomly get eight correct. Yet there are admitted students performing well below this number. The following is the data for three students below a sum of seven:
1 Pohnpei
PICS 47 14 24 29 1b 90 1 2 Chuukese Y
2 Pohnpei
OCHS 51 20 25 33 2c 90 1 4 PNI Y
3 Pohnpei
PSDA 47 17 33 24 2d 90 1 6 Kaping Y

Why they scored so poorly is left a mystery. I would note that all three were on the deficiency list at midterm - that is the "Y" on the far right side (thanks JG!).

This is why when I designed the limbo (non-admitted) group I avoided making the cut-off dependent on a single score - a student might wipe out mysteriously on a single test. By using a sum of z-scores only students who have done poorly on all of the tests collectively wind up in the non-admitted category. This removes the risk that one single test could knock off your chance at attending college, but it also means that we would not be building a system that ensured every student was above some particular level in mathematics.