Placement tests the placement testing process

Recommended Course	N	%	Mean Score
Standard Deviation
Basic Math I	499	71.1	151.8	5.06
Basic Math II	179	25.5	167.2	5.28
College Math	24	3.4	179.7	4.71

Placement was nominally mandatory. However, some students followed recommendations; others appealed placements and enrolled in higher courses; others still opted to take a lower than recommended course, while some did not enroll in any math course. In fact, about 29% of the students originally tested never enrolled in any math course over the six terms of the study. Most of these students had discontinued studies at the institution.
What happened to the students who did enroll? Table 4 shows that success rates in math were good for those who followed recommendations, but slightly lower for those who took a course higher than originally assigned.

Table 4: Recommendations, enrollments, and success* rates
RECOMMENDED COURSE	ENROLLMENT LEVEL
	LOWER			RECOMMENDED				HIGHER
	N	% Succ	MEAN	N	% Succ	MEAN	N		% Succ	MEAN
Basic Math I				322	63	151.7	35		60	153.2
Basic Math II	24	92	161.4	82	78	167.2	15		67	170.6
College Math	0	n/a		19	84	179.7

( * Success = Grade A, B, or C.)
What exactly does this mean in terms of the assignments by the placement tests? Considering the group of students recommended for Basic Math I we see that 63% of 322, or 203 were successful. But, 60% of 35, or 21 students that appealed and took Basic Math II were also successful at the higher level. Thus, it might be argued that the cut scores alone had misplaced these 21 students out of 357 in the Basic Math I group for an error rate of about 6%. A similar review of the Basic Math II group shows that 67% of 15, or 10 students were successful at a higher course. Again, based on cut scores alone, 10 out of 121 or about 8% of the students were misplaced. Would such error rates be acceptable in a mandatory assignment process?
Sturtz and McCarroll suggest another way to assess the success of the process. The underprepared students who followed recommendations were compared to those who did not in terms of persistence (mean number of terms attended) and quality point average (similar to GPA) over the six terms of the study.

Table 5: Following recommendations: Did it help?
CATEGORY (Basic Math Courses Only)	MATHEMATICS STUDENTS
	N	Mean QPA	Mean No. of Terms
Recommended and Successful	268	2.71	4.15
Recommended and Not successful	136	1.45	3.63
Higher Course and Successful	31	2.92	4.74
Higher Course and Not Successful	19	2.33	3.58
No Math Course	224	2.07	2.47

They conclude: "Students who were successful in their recommended basic-level courses tended to continue enrollment ... for a slightly greater number of terms (Sturtz and McCarroll, 1993, p17)." This conclusion really does not say much as it is probable that those who failed in the remedial math courses would be more likely to withdraw from college and would obviously have a lower mean attendance as a group. With regard to QPA, it also seems obvious that the successful groups must show the higher QPA's whether or not they followed recommendations. In fact, it is the students who challenged assignments and took higher level courses who show the highest QPA and persistence. Does this show that self-selecting a higher than recommended course is the best route to success?
Finally, the study looked at how the remedial cohort fared with college-level math. While asserting that overall the evidence supports the placement process, they note: "Data for completion of college-level math courses are inconclusive (Sturtz and McCarroll, p17)." Only 28% of students who enrolled in Basic Math I, and 55 % of students who enrolled in Basic Math II eventually completed a college-level math course.
This study reveals a number of the difficulties in evaluating a mathematics course placement process. It is relatively straightforward to collect data on test scores, grades, and attendance; it is not so straightforward to interpret the data and determine if it is reasonable to say that the placement process is significantly beneficial to underprepared students.