Change Prerequisite and its Impact on Nursing
Statistics Course

Shawn X Liu
Department of Mathematics and Computing
Mount Royal University
Calgary, Alberta, Canada

May, 2019

Change Prerequisite and its Impact on Nursing Statistics Course
Shawn X Liu
Department of Mathematics and Computing
Mount Royal University
Calgary, Alberta, Canada

Abstract
In 2008 Alberta Education proposed a change of high school mathematics curriculum
from the previous Pure Math-10, 20, 30 and Applied Math-10, 20, 30 to Math 10-C, Math
20-1, Math 30-1, Math 20-2, Math 30-2, Math 10-3 Math 20-3 and Math 30-3. The new
high school mathematics curriculum was implemented in 2010 and the first group of high
school graduates with this new mathematics curriculum got into the post-secondary
institutions in 2013.
With the old mathematics curriculum, the prerequisite was Pure Math 30 for the students
taking mathematics or statistics courses in science and engineering (including nursing) in
any post-secondary institutions in Alberta. With the new mathematics curriculum, the
prerequisite is Math 30-1 for the students taking mathematics or statistics courses in
science and engineering. A question was raised: “Do we allow the students with Math
30-2 to take introductory statistics for nursing degree program?” By comparing the
contents of Math 20-1, Math 30-1 and Math 20-2, Math 30-2, the answer was yes from
all the post-secondary institutions in Alberta. As a result, the prerequisite for nursing
statistics course has been Math 30-1 or Math 30-2 (changed from the previous Pure Math
30) since 2013. What is the impact with this change of the prerequisite? Is there any
difference in statistics course performance between the students with prerequisite Math
30-1 and Math 30-2?
In the past five years, there were about 1000 students taking the nursing statistics course
at Mount Royal University. A sample of 279 students regarding their performance in
statistics course and prerequisites was gathered. Statistical analyses indicate significant
difference between two groups. Some explanations and suggestions are given in this
study.

Background

In 2008 Alberta Education proposed a change of high school mathematics curriculum from the
previous Pure Math-10, 20, 30 and Applied Math-10, 20, 30 to Math 10-C, Math 20-1, Math 301, Math 20-2, Math 30-2, Math 10-3 Math 20-3 and Math 30-3. The new high school
mathematics curriculum was implemented in 2010 and the first group of high school graduates
with this new mathematics curriculum got into the post-secondary institutions in 2013.

Alberta Mathematics Curriculum
Math 10, Math 20, Math 30
→
Pure Math 10, Pure Math 20, Pure Math 30
Applied Math 10, Applied Math 20, Applied Math 30
→
Math 10-C, Math 20-1, Math 30-1
Math 10-C, Math 20-2, Math 30-2
Math 10-C, Math 20-3, Math 30-3

With the old mathematics curriculum, the prerequisite was Pure Math 30 for the students taking
mathematics or statistics courses in science and engineering (including nursing) in any postsecondary institutions in Alberta. With the new mathematics curriculum, the prerequisite is
Math 30-1 for the students taking mathematics or statistics courses in science and engineering.
A question was raised: “Do we allow the students with Math 30-2 to take introductory statistics
for nursing degree program?” By comparing the contents of Math 20-1, Math 30-1 and Math 202, Math 30-2, the answer was yes from all the post-secondary institutions in Alberta. As a result,
the prerequisite for nursing statistics course has been Math 30-1 or Math 30-2 (changing from
the previous Pure Math 30) since 2013.

Prerequisite for Nursing Statistics Course in Alberta Post-Secondary Institutions
Math 30 → Pure Math 30 → Math 30-1 → Math 30-1 or Math 30-2

Questions

What is the impact with this change of the prerequisite?
Is there any difference in statistics course performance between the students with prerequisite
Math 30-1 or Math 30-2?

Data Collection

In the past five years, there have been about 1000 students taking the nursing statistics course at
Mount Royal University. A sample data of 279 students regarding their performance in statistics
course and prerequisites was collected. The variables of consideration are listed below:

Variables:

Prerequisite (Math 30-1 or Math 30-2)
High school Mark (Math 30-1 or Math 30-2)
Test 1 Mark (Nursing Statistics Course)
Test 2 Mark (Nursing Statistics Course)
Test 3 Mark (Nursing Statistics Course)
Minitab Mark (Nursing Statistics Course)
Final Exam Mark (Nursing Statistics Course)
Overall Mark (Nursing Statistics Course)

What are the Populations of Study?

There are two populations of study to be considered here. One is all the nursing students taking
statistics course at Mount Royal University with prerequisite Math30-1. The other is all the
nursing students taking statistics course at Mount Royal University with prerequisite Math30-2.
Over the past five years, the sample proportions (by the year) for the students with prerequisite
Math30-1 and Math30-2 are summarized in Table I. In the academic year of 2013-2014, about
3/4 of the students had Math30-1 and 1/4 of the students had Math30-2. There was a notable
change for 2014-2015 and 2015-2016. For these two years, we had 2/3 of the students with
Math30-1 and 1/3 of the students with Math30-2. For the years of 2016-2017 and 2017-2018,
the ratio reversed back to 3/4 for Math30-1 and 1/4 for Math30-2. Therefore, our analysis is
conducted for the periods of 2013-2016, 2016-2018 and 2013-2018.

Table I: Two Sample Proportions
Count (percent)
2013-2014
2014-2015
2015-2016
2016-2017
2017-2018
Total

Math 30-1
50 (76.92%)
44 (66.67%)
34 (66.67%)
42 (76.36%)
40 (76.92%)
210 (72.66%)

Math 30-2
15 (23.08%)
22 (33.33%)
17 (33.33%)
13 (23.64%)
12 (23.08%)
79 (27.34%)

Total
65
66
51
55
52
289

For the periods of 2013-2016, 2016-2018 and 2013-2018, we have observed some descriptive
statistics and have summarized them in Table II-1, Table II-2 and Table II-3. In the second
column of each table, (for each item) the first line is the differences of the means of students with
prerequisite of Math30-1 and Math30-2. The second line of each item is the differences of the
medians.
The remaining parts of the tables are the differences of the means and medians for the marks of
their statistics course at Mount Royal University. This includes test 1, test 2, test, Minitab test,
final exam and overall marks.

Table II-1 (2013-2016):
Prerequisite
High School Mark:
Test 1 Mark:

Mean
Median
Mean

(Math 30-1) – (Math 30-2)
-6.93
-10.00
5.26

Test 2 Mark:
Test 3 Mark:
Minitab Test Mark:
Final Exam Mark:
Overall Mark:

Median
Mean
Median
Mean
Median
Mean
Median
Mean
Median
Mean
Median

5.00
10.68
3.40
8.05
10.00
1.35
-1.05
10.75
11.85
8.17
8.55

Table II-2 (2016-2018):
Prerequisite
High School Mark:
Test 1 Mark:
Test 2 Mark:
Test 3 Mark:
Minitab Test Mark:
Final Exam Mark:
Overall Mark:

Mean
Median
Mean
Median
Mean
Median
Mean
Median
Mean
Median
Mean
Median
Mean
Median

(Math 30-1) – (Math 30-2)
-1.86
-4.00
3.93
0.00
12.75
13.40
15.86
15.85
9.25
4.70
10.57
12.50
10.51
11.30

Table II-3 (2013-2018):
Prerequisite
High School Mark:
Test 1 Mark:
Test 2 Mark:
Test 3 Mark:

Mean
Median
Mean
Median
Mean
Median
Mean

(Math 30-1) – (Math 30-2)
-5.08
-8.00
5.00
3.40
11.33
13.40
10.80

Minitab Test Mark:
Final Exam Mark:
Overall Mark:

Median
Mean
Median
Mean
Median
Mean
Median

11.60
4.50
3.70
11.20
12.50
9.25
9.50

From the above summary, it is clear (intuitively) that the mean and median of Math 30 marks for
the students with Math 30-2 are higher than whose with Math 30-1. On the other hand, the
students with Math 30-2 have lower marks in their nursing statistics course than whose with
Math 30-1. Are these differences statistically significant? We are conducting the following two
groups of hypothesis testing:
Hypothesis I:

H0: mean1 – mean 2 = 0 vs Ha: mean1 – mean2 ≠ 0

and
Hypothesis II:

H0: median1 – median 2 = 0 vs Ha: median1 – median2 ≠ 0.

Here, mean1 is referring to the mean value of the students with prerequisite Math 30-1 for each
of the items considered and mean2 for the students with prerequisite Math 30-2. Similarly,
median1 is referring to the median value of the students with prerequisite Math 30-1 for each of
the items considered and median2 for the students with prerequisite Math 30-2.
We have conducted the two samples t-test and several non-parametric tests (Mann-Whitney,
Kruskal-Wallis and Mood Median Test). The results are summarized into the following tables
(Table III-1, Table III-2 and Table III-3):

Table III-1 (2013-2016):
p-value
High School
Test 1
Test 2
Test 3
Minitab Test
Final Exam
Overall

Two Sample T-Test
0.000
0.019
0.001
0.028
0.692
0.001
0.002

Mann-Whitney
0.000
0.011
0.000
0.034
0.722
0.001
0.002

Kruskal-Wallis
0.000
0.011
0.000
0.034
0.722
0.001
0.002

Mood Median Test
0.009
0.435
0.005
0.021
0.605
0.004
0.009

Table III-2 (2016-2018):
p-value
High School
Test 1
Test 2
Test 3
Minitab Test
Final Exam
Overall

Two Sample T-Test
0.438
0.075
0.012
0.003
0.093
0.034
0.011

Mann-Whitney
0.609
0.083
0.004
0.000
0.069
0.016
0.002

Kruskal-Wallis
0.606
0.083
0.004
0.000
0.068
0.016
0.002

Mood Median Test
0.546
0.170
0.005
0.008
0.219
0.004
0.004

Mann-Whitney
0.001
0.002
0.000
0.000
0.098
0.000
0.000

Kruskal-Wallis
0.001
0.002
0.000
0.000
0.097
0.000
0.000

Mood Median Test
0.019
0.005
0.000
0.000
0.027
0.000
0.000

Table III-3 (2013-2018):
p-value
High School
Test 1
Test 2
Test 3
Minitab Test
Final Exam
Overall

Two Sample T-Test
0.000
0.003
0.000
0.000
0.116
0.000
0.000

The hypothesis tests indicate the students having Math30-2 marks are higher than the students
having Math-30-1 marks in the mean values and in the median values. Moreover, the differences
between them are statistically significant.
The tests also indicate that the students with prerequisite Math 30-1 had higher marks for the
nursing statistics course (for all the items under consideration) than the students with Math 30-2.
And also the differences between them are statistically significant.
The next question would be “Are the high school Math 30 marks correlated with the nursing
statistics course for both the students with Math 30-1 and the students with math 30-2?” We
have calculated these correlations and summarized the results into the following tables (Table
IV-1, Table IV-2, and Table IV-3):

Some Correlations

Table IV-1 (2013-2016):
Correlation
High School vs T1
High School vs T2
High School vs T3
High School vs Minitab
High School vs Final
High School vs Overall

Math 30-1
0.236
0.248
0.175
0.321
0.299
0.317

Math 30-2
0.275
0.267
0.226
0.415
0.476
0.429

Math 30-1 & Math 30-2
0.182
0.165
0.130
0.326
0.255
0.258

Math 30-2
0.232
0.299
0.083
0.046
0.331
0.256

Math 30-1 & Math 30-2
0.144
0.327
0.258
0.200
0.398
0.374

Math 30-2
0.249
0.279
0.190
0.287
0.410
0.367

Math 30-1 & Math 30-2
0.176
0.224
0.180
0.291
0.315
0.306

Table IV-2 (2016-2018):
Correlation
High School vs T1
High School vs T2
High School vs T3
High School vs Minitab
High School vs Final
High School vs Overall

Math 30-1
0.142
0.390
0.371
0.373
0.462
0.489

Table IV-3 (2013-2018):
Correlation
High School vs T1
High School vs T2
High School vs T3
High School vs Minitab
High School vs Final
High School vs Overall

Math 30-1
0.213
0.301
0.261
0.344
0.381
0.395

All the correlation values are low, which indicates weak correlations between high school math
30 marks and the marks of nursing statistics course taken at Mount Royal University. This may

seemingly contradict to our intuitive impression. As some similar study suggest a high
correlation between high school mathematics performance and university calculus performance.
A plausible explanation might be university calculus course highly relates to and depend on the
high school mathematics knowledge while the nursing statistics course (introductory level
statistics course) does not depend on high school mathematics knowledge as much. As long as
the statistics course is well taught and properly learned, students should be able to perform well
in introductory statistics course that offered by universities.

Conclusion

The data we have collected over the past five years has suggested that the students with
prerequisite Math 30-1 have higher marks for the nursing statistics course than the students with
Math 30-2. And also the differences between them are statistically significant. However, it does
not have significant impact on their success in learning statistics course.
Over the years, the nursing program at Mount Royal University has very high marks for
admission. Therefore most students in the nursing program have high mathematics marks in
their high schools regardless from Math 30-1 or Math 30-2. In fact, the sample mean value for
Math 30-2 is about 7% higher than Math 30-1; and the sample median value for Math 30-2 is
about 10% higher than Math 30-1. However, in average, the students with Math 30-1 perform
better than the students with Math 30-2 in their introductory statistics course. As most students
with Math 30-2 have high Math 30-2 marks from their schools, they are also quite successful in
learning statistics course. Therefore, there is not significant impact with the prerequisite change.
When we set Math 30-1 or Math 30-2 as the prerequisite for the nursing statistics course, we do
not put the minimum marks needed. Students with marks greater than or equal to 50% for Math
30-1 or Math 30-2 will be allowed to take nursing statistics course. With high admission
requirement to get into nursing program, most students have high Math30-2 marks from their
high schools. There are a few students fail or withdraw from the nursing statistics course quite
often due to the lower Math 30 marks. In the future, if there were more students with lower
Math 30-2 marks in the program, their success in the statistics course needs to be observed. If
the lower Math 30-2 marks affect their performance and success in the statistics course, a
suitable minimum Math 30-2 mark might be needed for the prerequisite. We will keep observing
students’ performance in the nursing statistics course and make suggestions and
recommendations when needed.