Index

Abstract

This paper examined the statistical approach adopted by schools to communicate their academic achievement to stakeholders. The paper looked at the most frequently adopted method, the use of percentage scores, and discussed the limitations of its usage. The paper also explored the use of the weighted average of scores and compared it to the use of percentage scores. Data from the West Africa Examinations Council and standardised test scores from a selected high school were used for the paper’s analyses and illustrations. The paper demonstrated that the weighted average of scores accounted for quality of grades obtained as well as the number of candidates presented by a school. The paper identified the use of weighted average of scores as a preferred option to percentage scores in communicating academic achievement to stakeholders. Major recommendation suggested by this paper is for the adoption of weighted average of scores to communicate academic achievement of schools to stakeholders.

Keywords: Academic achievement, Weighted average of scores, Stakeholder engagement, School effectiveness, Student test scores, Standardised test.

Received: 22 August 2017 / Revised: 5 October 2017 / Accepted: 12 October 2017 / Published: 27 October 2017

Contribution/ Originality

This study documents the use of weighted average of scores as the preferable means of communicating student test scores to stakeholders.


1. INTRODUCTION

Stakeholders have expectations of schools that go beyond the schools meeting just the minimum acceptable standards. The schools should provide education that will shape the character of the students to become good citizens and at the same time equip them with the requisite knowledge to contribute to the economic growth and development of the nation. Character formation and intellectual development go together. In the legitimate, moral-ethical, and social-political frames of school perspectives, Kowalski (2010 ) postulates that in addition to the school meeting legal standards and having a sense of moral purpose, the school must be efficient in preparing the students to pass their examinations. The reality for students is that, in the pursuit of their highest levels of academic and personal achievement, taking tests is not an option.  Testing is an important part of education. It provides objective information about students’ progress and a means to measure school output. Test scores have become key determinants of academic achievement of schools. They are also used to convince stakeholders, especially parents or guardians, that schools are efficient and up to the task. In addition to tests scores being used to judge performance of schools, they also are used to make important decisions about students, for example, for classification, retention, and promotion (Moses and Nanna, 2007 ).

School must provide evidence to parents to show that they are meeting expectations by establishing a clear and accurate system of grading and reporting academic achievement. The reporting should enable stakeholders to gain understanding of how the test scores reflect students’ achievement and progress and how the school is meeting stakeholder expectations. The medium used in communicating test scores should satisfy the condition of providing true reflection of students’ achievement. Clark and Smitherman (2013 ) describe the results of test as a snapshot of a student’s academic achievement at a certain period in time. Stakeholders should make meaning out of this snapshot.

When communicating academic achievement of schools to stakeholders using test scores, it is essential for educators to keep in mind the most pressing question stakeholders ask: what do the scores mean? The format of presentation should include vital information to address this question so that stakeholders can make meaning out of the test scores. Information communicated to stakeholders, especially, parents or guardians, is to enable them to be abreast of the academic performance of students in order to provide the necessary support to help the student progress. Suskie (2009 ) notes that sharing assessment results is an opportunity to tell an important story with a meaningful point.

Table-1. WAEC League Table for 2004

Pos
NAME OF SCHOOL
No. of Stds
Number of Subjects Passed
Passes in 6 to 8 Subs
% passes in 6 to 8 Subs
8
7
6
5
4
3
2
1
0
1
Wesley Girls High Sch
381
374
6
1
381
100
1
Notre Dame Sem/Sec Sch
77
31
45
1
77
100
1
Sefwi Bekwai Sec Sch
71
35
29
7
71
100
1
Kukuom Agric Sec Sch
51
14
32
5
51
100
1
Diaso Sec Sch
52
0
47
5
52
100
6
Yaa Asantewaa Sec Sch
429
404
20
4
1
428
99.77
7
St James Seminary
187
139
44
3
1
186
99.47
8
Opoku Ware Sch
491
458
26
4
1
1
1
488
99.39
9
St Louis Sec Sch
274
186
81
5
2
272
99.27
10
Ghana Sec Tech Sch
383
342
33
5
1
0
1
0
1
380
99.22
11
Mozano Comm Sec Sch
226
173
45
6
1
1
224
99.12
12
Holy Child Sch
222
204
13
3
2
220
99.1
13
Mfantsipim Sch
545
438
87
15
5
540
99.08
14
St. Roses' Sec Sch
273
256
9
5
2
1
270
98.9
15
Prempeh College
813
709
76
19
6
1
1
0
1
804
98.89
16
St. Monica Girls' Sec Sch
386
346
29
6
4
1
381
98.7
17
Aburi Girls' Sec Sch
323
75
230
12
5
1
317
98.14
18
St. Peter's Sec Sch
358
238
98
14
7
1
350
97.77
19
St Charles Sec Sch
81
38
33
8
1
0
0
1
79
97.53
20
Adeiso Sec Sch
87
0
79
6
1
1
85
97.7
21
Adisadel College
472
415
39
6
5
5
2
460
97.46
22
Armed Forces Sec – Kumasi
333
274
34
16
5
3
0
0
1
324
97.3
23
Achimota Sch
521
206
267
33
9
3
2
0
1
506
97.12
24
Benkum Sec Sch
347
174
125
38
9
1
337
97.12
25
Nandom Sec Sch
171
131
25
10
5
166
97.08
26
Presby Boys' Sec Sch – Legon
787
532
193
36
14
4
3
2
3
761
96.7
27
Mfantsiman Girls' Sec Sch
502
395
67
23
12
3
1
1
485
96.61
28
Archbishop Porter Girls' Sec Sch
233
152
56
17
5
1
1
0
1
225
96.57
29
Kumasi Academy
295
201
61
20
6
5
2
282
95.59
30
Namong Sec Sch
203
78
96
19
7
1
1
1
193
95.07
31
St Augustine's College
459
342
73
23
12
5
3
0
1
438
95.42

Source: WAEC, League Table of Schools, 2004

Bobowski (2016 ) intimates that one of the most powerful (and often underestimated) allies of an educator, is an informed parent who understands their child’s academic needs and is in a position to reinforce what happens in the classroom. She goes on to point out that a powerful partnership is created that can take learning to the next level is created between school and home when educators share test scores with parents.

Using percentage of students attaining a certain score – passing the examination - tends to be the most common means of communicating students’ academic achievement to stakeholders. The use of percentage lends itself to easy computation. Raw scores are converted into percentages and these can easily be compared. Knapp (2010 ) observes that percentages are widely used to communicate results because irrespective of the size of the samples, various groups can be compared whether the samples sizes are equal or unequal. 

In Ghana, the use of percentages to communicate the academic achievement of schools to stakeholders is pervasive. The West Africa Examination Council (WAEC), the body charged with the responsibility to conduct standardised tests for students, uses percentage of students who pass in the number of subjects taken at the examinations as basis to compare academic achievement of schools. A ranking of schools, based on percentage pass, is presented to stakeholders. For example, using the percentage of the number of students who passed in six to eight subjects, the WAEC presented a ranking of schools as depicted in Table1. Table 1 shows the top 32 schools in the ranking.

The total number of candidates presented by Wesley Girls’ High School is 381. Therefore, the percentage of the candidates who obtained between 6 to 8 passes is given by:

The number of students who obtained between 6 to 8 passes     X   100%
         The total number of students presented

=      381     X   100% = 100%
381

Similarly, for Opoku Ware Secondary School, 4 students obtained 6 passes, 26 had 7 passes and 458 with 8 passes. The total number of students who obtained between 6 to 8 passes is 488 (that is 4 + 6 + 458). The total number of candidates presented by Opoku Ware is 491.   Hence, the percentage number of the candidates who obtained between 6 to 8 passes is given by:

488           X     100%         
491
= 99.39%.

A similar calculation was done for all the schools to obtain the percentage number of students who obtained between 6 to 8 passes in the examinations.  It is from these percentages that the schools were ranked.

1.1. Emerging Issues: Disadvantages of the Percentage Ranking Methodology

The ranking based on the percentage number of passes in 6 to 8 subjects does not give a fair representation of the performance of schools. The quality of passes is not reflected in the percentages. The grades A, B, C, D and E are lumped together in one category of a pass. The grade A, which indicates an excellent performance, should not be put in the same class as the grade E.  The grades have different weights when candidates are being considered for admission into tertiary institutions.

Again, the performance of a student who obtained 6 passes is equated to that of a student who obtained 8 passes. Table 1 shows that both Wesley Girls’ High School and Diaso Secondary School had 100% and are ranked 1st.  

However, a look at the table reveals that no student in Diaso obtained 8 passes whereas 374 students in Wesley Girls’ obtained 8 passes.  It will be mind boggling to accept the view that both schools have equivalent performances in the year and therefore, must be ranked at the same position on the WAEC league table. The ranking does not also give a fair basis for communicating the performance of the schools. Whereas Diaso Secondary School for example was ranked 1st with no student obtaining 8 passes, Opoku Ware Secondary School which had 458 students obtaining 8 passes was ranked 8th.   Thus, the percentage of students presented to the WAEC examinations by Diaso and Opoku Ware schools with 8 passes are 0% and 93% respectively.

Finally, the use of the percentage does not take into consideration the number of students presented by schools and hence gives no indication of a school’s contribution to the human resource development of the nation. It stops short of giving an indication of the number of students a school produces who are capable of pursuing further education. For example, Opoku Ware, which placed 8th, produced 488 students capable of pursuing further academic studies and Kukuom Secondary School, which ranked 1st produced 51 students. This approach may inadvertently, encourage Heads of institutions to admit fewer students if the percentage ranking is accepted in the form presented in Table 1.

1.2. Implications for Practice: Weighted Average Approach for Ranking of Schools

The weighted average method of ranking the performance of schools ensures that the quality of the passes are factored into the analysis by assigning different weights to the grades scored by students.  A weighted average over N items is defined as

(1/N) * SUM [wi * fi], where wi represents the weight (value or significance) of a single occurrence of type i, and fi represents the frequency of an item i.

A weight of 8 is assigned to the candidates with 8 passes, 7 to those with 7 passes and so on.  Those candidates who failed in all subjects are assigned a weight of zero. The number of passes under each weight is computed with the total number of students taking the examinations in a particular school as the base. 

Table 2 indicates that on a scale of 8, the weighted score for Wesley Girls High School is 7.979, while that of Opoku Ware School is 7.906 and that of St. James Seminary Secondary School is 7.717.  These average weighted scores for the schools can thus communicate the academic achievement of schools devoid of the inherent analytical problems associated with the percentage approach used to rank the schools. 

Table-2. Weighted average scores for schools

NAME OF SCHOOL
Total Number of Candidates Presented
Number of Subjects Passed
Average Score
8
7
6
5
4
3
2
1
0
Wesley  Girls High School
381
98%
2%
0%
0%
0%
0%
0%
0%
0%
7.979
Yaa Asantewaa Sec Sch
429
94%
5%
1%
0%
0%
0%
0%
0%
0%
7.928
Opoku Ware Secondary Sch
491
93%
5%
1%
0%
0%
0%
0%
0%
0%
7.906
St Roses Sec Sch
273
94%
3%
2%
1%
0%
0%
0%
0%
0%
7.894
Holy Child Sec Sch
222
92%
6%
1%
1%
0%
0%
0%
0%
0%
7.887
St Monica's Sec Sch
386
90%
8%
2%
1%
0%
0%
0%
0%
0%
7.852
Ghana Sec Technical Sch
383
89%
9%
1%
0%
0%
0%
0%
0%
0%
7.849
Prempeh College
813
87%
9%
2%
1%
0%
0%
0%
0%
0%
7.818
Adisadel College
472
88%
8%
1%
1%
1%
0%
0%
0%
0%
7.797
Mfantsipim Sec Sch
545
80%
16%
3%
1%
0%
0%
0%
0%
0%
7.758
Mozano Commercial Sec Sch
226
77%
20%
3%
0%
0%
0%
0%
0%
0%
7.717
St James Seminary
187
74%
24%
2%
1%
0%
0%
0%
0%
0%
7.717
Armed Forces Sec/Tech Sch
333
82%
10%
5%
2%
1%
0%
0%
0%
0%
7.700
Mfantsiman Girls Sec Sch
502
79%
13%
5%
2%
1%
0%
0%
0%
0%
7.657
Nandom Sec Sch
171
77%
15%
6%
3%
0%
0%
0%
0%
0%
7.649
St Louis Sec Sch
274
68%
30%
2%
1%
0%
0%
0%
0%
0%
7.646
St Peter's Sec Sch
358
66%
27%
4%
2%
0%
0%
0%
0%
0%
7.578
St Augustine's College
459
75%
16%
5%
3%
1%
1%
0%
0%
0%
7.571
Accra Academy
532
76%
13%
6%
2%
2%
0%
0%
0%
0%
7.541
Presby Boys Sec Sch
787
68%
25%
5%
2%
1%
0%
0%
0%
0%
7.529
Kumasi Academy
295
68%
21%
7%
2%
2%
1%
0%
0%
0%
7.495

Source: WAEC League Table of Schools, 2004

Table 3 presents a comparison between the ranking of the top 60 schools using both percentages and the calculation of weighted average of results.

Table-3. Top 60 Schools Ranking Using Percentages and Weighted Average Method

NAME OF SCHOOL
Weighted Average Score
Percentage Rank
Weighted Average Rank
NAME OF SCHOOL
Weighted Average Score
Percentage
Rank
Weighted Average Rank
Wesley  Girls High
7.98
1
1
TI Ahmadiyya 
7.22
40
31
Yaa Asantewaa 
7.93
6
2
Krobo Girls' 
7.21
45
32
Opoku Ware 
7.91
8
3
Pope John 
7.19
37
33
St Roses 
7.89
14
4
Kukuom Agric 
7.18
4
34
Holy Child 
7.89
12
5
Namong 
7.16
30
35
St Monica's 
7.85
16
6
Aburi Girls 
7.16
17
36
Ghana  Technical
7.85
10
7
Boa-Amponsem 
7.14
43
37
Prempeh College
7.82
15
8
St Mary 
7.13
41
38
Adisadel College
7.80
21
9
Bishop Herman's 
7.12
50
39
Mfantsipim 
7.76
13
10
St Thomas Acquinas 
7.11
36
40
Mozano Commercial 
7.72
11
11
Koforidua /Tec
7.10
53
41
St James Seminary
7.72
7
12
SDA  , Agona
7.09
39
42
Armed Forces /Tech
7.70
22
13
Kumasi High
7.09
57
43
Mfantsiman Girls 
7.66
27
14
Kumasi Girls' 
7.08
55
44
Nandom 
7.65
25
15
Nkawie  Tech
7.07
46
45
St Louis 
7.65
9
16
Okomfo Anokye 
7.06
54
46
St Peter's 
7.58
18
17
University Practice 
7.01
66
47
St Augustine's College
7.57
31
18
OLA Girls  , Kenyasi
7.01
52
48
Accra Academy
7.54
32
19
Toase 
6.98
51
49
Presby Boys 
7.53
26
20
OLA  , Ho
6.97
48
50
Kumasi Academy
7.50
29
21
Mansoman 
6.97
67
51
Archbishop Porter Girls 
7.48
28
22
Anglican  , Kumasi
6.93
58
52
St John's 
7.42
33
23
Tarkwa 
6.93
61
53
Lassia Tuolo Snr 
7.40
35
24
Dunkwa  Tech
6.91
44
54
Sefwi Bekwai 
7.39
3
25
Diaso 
6.90
5
55
Notre Dame Seminary 
7.39
2
26
New/Juaben /Commercial
6.90
59
56
Sunyani 
7.38
34
27
Okuapeman 
6.88
63
57
Benkum 
7.33
24
28
Adeiso 
6.87
20
58
St Charles 
7.28
19
29
St Augustine's 
6.85
62
59
Achimota
7.25
23
30
Aburaman 
6.84
42
60

Source: WAEC League Table of Schools, 2004

The positions of some of the schools have changed. Some schools, which were among the top 60 schools, have fallen out of the top ranking. For example, Notre Dame Seminary Secondary School which ranked 1st with Wesley Girls’ High School has moved to the 26th position.  University Practice Secondary School has moved up from 66th position to 47th position and St. Martin’s Secondary School and Adventist Day Secondary School had fallen out of the top 60 schools. 

The weighted average method of calculation takes into consideration the number of students presented by a school. It introduces a factor that standardizes the number of students presented as well as those who obtained a particular number of passes. For example, Kukuom presented 51 students and 14 obtained 8 passes; on the other hand, Opoku Ware presented 491 students and 458 obtained 8 passes. The ratio of students who obtained 8 passes to number of students presented gives a standard value for students who obtained 8 passes for the two schools.

Table-4. Percentage and Weighted Average Scores of a selected school
A1
  
B2
B3
C4
  
C5
  
C6
D7
E8
F9
Total Entry
% Pass
Total
Weighted Score
  
Weighted Average
Mathematics
38
43
62
36
48
20
22
11
6
280
97.9
5.23
304
301
372
180
192
60
44
11
0
1464
Integrated Science
16
48
44
37
48
30
28
18
11
280
96.1
4.53
128
336
264
185
192
90
56
18
0
1269
Social Studies
7
36
59
92
35
27
15
9
0
280
100
4.94
56
252
354
460
140
81
30
9
0
1382
English Language
13
21
45
60
53
35
19
22
12
280
95.7
4.28
104
147
270
300
212
105
38
22
0
1198
Accounting
2
6
28
25
20
9
4
3
0
97
100
4.84
16
42
168
125
80
27
8
3
0
469
Bus. Management
18
23
41
5
2
3
3
1
1
97
98.9
6.19
144
161
246
25
8
9
6
1
0
600
General Knowledge in Art
0
0
9
7
16
11
6
1
0
50
100
3.98
0
0
54
35
64
33
12
1
0
199
Lit-in-English
0
0
7
13
14
8
3
4
0
49
100
4.02
0
0
42
65
56
24
6
4
0
197
French
2
2
5
6
8
6
11
5
0
45
100
3.71
16
14
30
30
32
18
22
5
0
167
History
0
6
9
10
6
8
4
2
2
45
95.5
4.53
0
42
54
50
24
24
8
2
0
204
Economics
17
34
16
6
10
6
3
3
2
97
97.9
5.85
136
238
96
30
40
18
6
3
0
567
Geography
0
0
14
10
6
2
3
5
5
45
88.9
3.89
0
0
84
50
24
6
6
5
0
175
Biology
20
28
49
14
6
4
1
1
1
124
99.2
6.12
160
196
294
70
24
12
2
1
0
759
Physics
23
36
36
19
5
7
10
2
4
124
96.7
6.53
184
252
216
95
20
21
20
2
0
810
Chemistry
11
43
38
12
8
1
1
1
9
124
92.0
3.18
88
301
228
60
32
3
2
1
0
715
Elective Mathematics
15
29
37
12
11
3
5
3
7
122
92.7
5.50
120
203
222
60
44
9
10
3
0
671

Source: WAEC Examination Records, St. Augustine’s College, 2012

The weighted average calculation also places a distinction between the number of subjects passed, that is, passes in 8 subjects cannot be put in the same category as passes in 6 subjects. Weights are assigned to each category of passes such that passes in 8 subjects have a higher recognition than passes in 7 subjects, which in turn have a higher recognition than passes in 6 subjects.

At the school level, the weighted average approach can be adopted to communicate academic achievement to reflect more accurately how students are performing in various subjects. Schools generally communicate the percentage of students who passed in specific subjects. A weight of 8 is assigned to grade A1, 7 to grade B2, 6 to grade B3 and so on.  The grade F9 is assigned a weight of zero. Table 4 depicts the performance of students of a particular school in the various subjects using both percentage and weighted average to present the results.

As seen from Table 4, percentage score fails to present accurate information of students’ achievement since it does factor into its computation the quality of passes. For example, using percentages to communicate student performance will present students who sat for Accounting (100% pass) as performing better than those who sat for Business Management (98.9% pass). However, computing the results using weighted average shows that the performance of students in Accounting (M= 4.84) is lower than the performance of students in Business Management (M = 6.12). Similarly, using percentages present students’ performance in General Knowledge in Arts as better than the performance in History, but the computation of weighted average of the results proves otherwise.

2. CONCLUSION

Engaging stakeholders has the potential to expand opportunities for schools to benefit from enhanced stakeholder participation culminating in the continuing support for school programmes and provision of needed resources. Communicating academic achievement to stakeholders is an essential element to foster stakeholder engagement. This paper concludes that the adoption of the method of weighted average of scores is a better option in presenting the academic achievement of schools to stakeholders. Stakeholder interest in the performance of students goes beyond the number of subjects passed to a focus on the quality of the grades obtained and those grades represent in terms of opportunities for further studies.  A major recommendation based on the conclusion drawn is that the Ghana Education Service should consider replacing the ranking of schools and individual subjects by calculating percentage passed with calculations based on weighted average of scores. Schools should also consider the use of weighted average of scores to analyse students’ test scores.

Funding: This study received no specific financial support.
Competing Interests: The author declares that there are no conflicts of interests regarding the publication of this paper.

REFERENCES

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Clark, M. and D. Smitherman, 2013. Communicating achievement test results with parents. CSe, 16(3): 38 – 40.

Knapp, T.R., 2010. Percentages:  The most useful statistics ever invented. Retrieved from www.statlit.org/knapp.htm [Accessed July 27, 2017].

Kowalski, T., 2010. The school principal: Visionary leadership and competent management. New York: Routledge

Moses, M.S. and M.J. Nanna, 2007. The testing culture and the persistence of high stakes testing reforms. Education and Culture, 23(1): 55-72. View at Google Scholar | View at Publisher

Suskie, L., 2009. Assessing student learning: A common sense guide. San Francisco, CA: Jossey-Bass.