































   Advancements in Agricultural Development 
  Volume 5, Issue 4, 2024 
  agdevresearch.org 

 

1. Donald M. Johnson, University Professor, University of Arkansas, E108 AFLS Building, Fayetteville, AR 72701, 

dmjohnso@uark.edu,  https://orcid.org/0000-0003-2592-654X 
2. Will Doss, Assistant Professor, University of Arkansas, E108 AFLS Building, Fayetteville, AR 72701, wd009@uark.edu,  

https://orcid.org/0000-0002-3163-7528 
3. Christopher M. Estepp, Associate Professor, University of Arkansas, E108 AFLS Building, Fayetteville, AR 72701, 

estepp@uark.edu,  https://orcid.org/0000-0001-7268-9044 
4. Henry O. Akwah, Precision Agriculture Instructor, 308 ASB, University of Arkansas Community College – Batesville, 2005 

White Drive, Batesville, AR 72501, henryofosu.akwah@uaccb.edu,  https://orcid.org/0009-0007-3164-3614 
5. George W. Wardlow, Professor and Head, University of Arkansas, E108 AFLS Building, Fayetteville, AR 72701, 

wardlow@uark.edu,  https://orcid.org/0000-0001-5701-8250 
 
42 

 

A Discrepancy in Discrepancy Scores? Comparing the Borich 
and Ranked Discrepancy Models for Determining Professional 

Development Needs 
 

D. M. Johnson1, W. Doss2, C, M. Estepp3, H. O. Akwah4, G. W. Wardlow5 

 
 

Article History 
Received: June 18, 2024 
Accepted: September 30, 2024 
Published: November 6, 2024 
 
 
Keywords 
measurement theory; statistical 
theory; research methods;  
SDG 4: Quality Education.   

Abstract 
The Borich (1980) model has been widely used to determine professional 
development (PD) needs of school-based agricultural education (SBAE) 
teachers over the past 40-plus years. However, recent criticism, primarily 
focused on a purported statistical issue, has led to development of the 
Ranked Discrepancy Model [RDM (Narine & Harder, 2021)] as a potential 
alternative. This article provides perspective on the statistical issue in 
question and compares the results of using the Borich model and the 
RDM to assess precision agriculture (PA) PD needs of Arkansas SBAE 
teachers (N = 44). Our quantitative results indicated the two models 
produced different PD priorities, especially among the highest rated 
priorities. The mean weighted discrepancy scores [MWDSs (Borich 
model)] and the ranked discrepancy scores [RDSs (RDM)] had a shared 
variance of 54.8%; the PD priority rankings established by the two 
methods had a shared variance of 47.6%. Additionally, the number of tied 
priorities with the RDM complicated identifying priority PD workshop 
topics. We recommend further research and dialogue before wholesale 
abandonment of the Borich model for the RDM as a method of 
determining PD needs. 

 

mailto:dmjohnso@uark.edu
https://orcid.org/0000-0003-2592-654X
mailto:wd009@uark.edu
https://orcid.org/0000-0002-3163-7528
mailto:estepp@uark.edu
https://orcid.org/0000-0001-7268-9044
mailto:henryofosu.akwah@uaccb.edu
https://orcid.org/0009-0007-3164-3614
mailto:wardlow@uark.edu
https://orcid.org/0000-0001-5701-8250


Johnson et al.  Advancements in Agricultural Development 
 

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Introduction 
 
Beginning with Barrick et al. (1983), the Borich (1980) needs assessment model has been widely 
used to determine the professional development (PD) needs of school-based agricultural 
education (SBAE) teachers (Garton & Chung, 1997; Johnson et al., 1990; Newman & Johnson, 
1994; Smalley et al., 2019). Responding to needs assessments based on the Borich model, 
teachers rate the importance of and their ability to perform specific competencies, typically on 
a 1 to 5 (1 = low importance/ability and 5 = high importance/ability) scale. Weighted 
discrepancy scores are calculated for each respondent on each competency by subtracting the 
ability rating from the importance rating and multiplying this difference by the mean 
importance rating for the competency. Lastly, mean weighted discrepancy scores (MWDSs) are 
determined by calculating the mean of the weighted discrepancy scores for each competency. 
Competencies with higher MWDSs indicate higher priority PD needs.  
 
Narine and Harder (2021) criticized the Borich (1980) model because it requires researchers to 
calculate means “for single items measured with ordinal scales (i.e., individual competency 
items)” (p. 98). As an alternative, they proposed the Ranked Discrepancy Model (RDM). With 
the RDM, respondents still use individual Likert-type items to rate the importance and their 
ability relative to a set of competencies, but percentages are used to calculate the ranked 
discrepancy scores (RDSs) used to establish PD priorities. Using data from a needs assessment 
of county Extension agents, Narine and Harder used the Borich model and the RDM and found 
“a great deal of consistency in rankings, despite the RDM discarding the use of the group mean 
in calculations” (Narine & Harder, 2021, p. 108). Despite this finding, further research is needed 
prior to wholesale abandonment of the Borich model for the RDM. 
 

Conceptual Framework 
 
Stevens (1946) proposed a scale of measurement containing four levels (nominal, ordinal, 
interval, and ratio) and statistics for use with variables measured at each level. Stevens’ 
measurement scale constituted a hierarchy moving from nominal to ratio, with each successive 
level incorporating all the characteristics of the previous level(s). For example, interval level 
measurements incorporate the characteristics of mutual exclusivity (from the nominal level) 
and order (from the ordinal level), while adding the characteristic of equality of intervals. Of 
relevance to our discussion is Stevens’ stipulation that the mean is not appropriate for variables 
measured below the interval level.  
 
Use of the Borich (1980) model of needs assessment requires the calculation of mean 
importance ratings and MWDSs based on single-item, Likert-type ordinal scales, which is 
contrary to Stevens (1946) and was one of Narine and Harder’s (2021) primary criticisms of the 
Borich model. While many scholars (Jamieson, 2004; Narine & Harder, 2021; Stevens, 1946) 
have been adamant in considering data from these scales as ordinal and argued against 
calculating means, other scholars (Gaito, 1980; Harwell & Gatti, 2001; Lord, 1953; Norman, 

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2010; Zumbo & Zimmerman, 1993), who also have recognized these measurement scales as 
ordinal, have argued in favor of calculating means on these items.  
 
According to Gaito (1980) this fundamental disagreement has resulted from confusion between 
measurement theory and statistical theory. In measurement theory, “The validity or 
authenticity aspect brings into focus the meaning underlying the numbers that are used to 
indicate amounts of the characteristics of concern” (Gaito, p. 567). From a measurement theory 
perspective, the differences in the characteristic being measured may not be equal between 
scale numbers, so the level of measurement is ordinal. This is a measurement issue related to 
the meaning of numbers relative to the characteristic being measured. 
 
Gaito (1980) stated that in statistical theory, the “meaning of numbers does not enter the 
picture because, as Lord (1953) stated, ‘the numbers do not know where they came from’” (p. 
566). Thus, according to statistical theory, the mathematical difference between a rating of 1 
and 2 and between a rating of 4 and 5 are equal. Consequently, from a statistical perspective 
use of the mean (and other parametric statistics) is permissible. Gaito concluded by stating: 

In mathematical statistics literature one will not find scale properties as a requirement 
for the use of various statistical procedures. This requirement is merely a figment of the 
imagination of a number of psychologists because of a confusion of measurement 
theory and statistical theory. Statistical procedures do not require specific scale 
properties (pp. 547–548).  

 
Norman (2010) further clarified the difference between measurement theory and statistical 
theory stating, “We cannot, strictly speaking, make further inferences about differences in the 
underlying, latent characteristic reflected in Likert numbers [a measurement issue], but this 
does not invalidate conclusions about the numbers [a statistical issue]” (p. 629). Harwell and 
Gatti (2001) argued “statistical techniques should not be held hostage to measurement scales 
because there is no requirement underlying these procedures that ties them to such scales” (p. 
107). In the context of the Borich (1980) model, the issue is not whether we can calculate 
means on these responses, but rather, how to interpret the means in relation to the 
characteristics being measured. However, with the Borich model, no direct interpretation of the 
mean importance ratings is necessary and the resultant MWDSs are interpreted as ordinal 
measures for determining PD priorities (i.e., no one argues that a competency with a MWDS of 
6.0 represents one additional 'unit' of PD need compared to a competency with a MWDS of 5.0, 
only that the need is greater for the competency with the higher MWDS). 
 
 
 
 
 
 
 
 

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Purpose and Objectives 
 
The purpose of this study was to compare the results of the Borich (1980) model and the RDM 
(Narine & Harder, 2021) using data collected from a precision agriculture (PA) needs 
assessment of Arkansas SBAE teachers (Akwah, 2024). Specific objectives were to: 
1. Determine and compare the PD priorities as determined by the Borich model and the RDM; 
2. Determine the correlation between MWDSs obtained using the Borich model and RDSs 

obtained using the RDM; 
3. Determine the correlation between PD priority rankings determined by the Borich model 

and the RDM.  
 

Methods 
 
Data were collected from a survey administered to a non-probability sample of Arkansas SBAE 
teachers (N = 44) immediately before an introductory PA workshop conducted in July 2023. The 
survey was administered in-person using a paper survey instrument. The instrument contained 
29 PA competencies where teachers rated (a) the importance of teaching and (b) their ability to 
teach each competency using two 1 to 5 Likert-type scales (1 = no importance/ability, 2 = below 
average importance/ability, 3 = average importance/ability, 4 = above average 
importance/ability, and 5 = high importance/ability). A panel of four experts in PA and in social 
science research, who were informed of the research objectives and participant characteristics, 
reviewed the instrument and judged it to possess face and content validity (Gates et al., 2018). 
Coefficients of stability were established using 13 agricultural education graduate students who 
completed the instrument twice (14-day interval), resulting in coefficients of stability values of r 
= .94 for importance and r = .87 for ability.  
 
MWDSs were calculated for each competency using Equation 1 (Borich, 1980). In calculating a 
MWDS for a specific competency, each respondent’s ability rating for the competency was 
subtracted from their importance rating for that same competency, then multiplied by the 
mean importance rating for that competency. Finally, the MWDS was determined by calculating 
the mean of all weighted discrepancy scores for that competency. When using 1 to 5 scales to 
measure importance and ability, MWDSs can range from -4 to 20, with higher scores indicating 
greater PD needs.  
 

MWDS = Σ [(Importance –Ability) * Mi] / N      (1) 
 
RDSs were calculated using Equation 2 (Narine & Harder, 2021). In the equation, NR% (percent 
of negative ranks) represents the percent of respondents rating their ability lower than the 
importance of a competency; PR% (percent of positive ranks) is the percent of respondents 
rating their ability higher than the importance of the competency; and TR% (percent of tied 
ranks) is the percent of respondents giving ability and importance the same rating. RDSs can 
range from -100 to 100; lower negative scores represent greater PD needs while positive scores 

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indicate no need for PD. One advantage of the RDM is the range of RDSs is the same regardless 
of the number of points on the rating scales (Narine & Harder).  
 

RDS = NR% (-1) + PR% (1) + TR% (0)        (2) 
 
Once MWDSs and RDSs were calculated, PD priorities were established for the 29 PA 
competencies based on both the Borich (1980) model and the RDM (Narine & Harder, 2021). 
The two sets of priorities were then examined to determine similarities and differences. Next, 
the two sets of scores were correlated to determine the percentage of shared variance. 
(Because positive MWDSs indicate PD needs, while negative RDSs indicate PD needs, the 
absolute value of the correlation coefficient was reported). Finally, the two sets of PD priority 
rankings were correlated to determine the percentage of shared variance. 
 

Results 
 
Mean weighted discrepancy scores (MWDSs) and ranked discrepancy scores (RDSs) were 
calculated for each of the 29 PA competencies (C1 – C29) and priority rankings were made 
based on each type of score (Table 1). The Borich (1980) and the Ranked Discrepancy  (Nadine 
& Harder, 2021) models produced different PD priorities. Based on MWDSs the two highest PD 
priorities were C29 and C26; when prioritized using RDSs, these competencies were ranked at 
10.5 (as part of a four-way tie). Based on RDSs, the two highest PD priorities were C21 and C23; 
these competencies were rated as the 8th and 7th highest priorities, respectively, using MWDSs. 
There was greater agreement between priorities for the lower priority competencies. For 
example, three of the four lowest priority competencies based on both MWDSs and RDSs were 
C14, C15, and C16. 
  

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Table 1 
 
Comparison of PA Professional Development Priorities Based on Borich and RDM Scores 
 Scores Ranks by Model 

Competency MWDS RDS Borich RDM 
C1 9.50 -95.4 24 5.5T 
C2 10.54 -95.4 13 5.5T 
C3 10.78 -95.4 10 5.5T 
C4 10.07 -90.9 19 14T 
C5 9.88 -86.4 22 18.5T 
C6 10.14 -86.4 17 18.5T 
C7 10.40 -90.9 14 14T 
C8 10.77 -93.2 11 10.5T 
C9 9.91 -81.8 21 24 

C10 10.62 -86.4 12 18.5T 
C11 11.53 -84.1 5 22.5T 
C12 10.36 -86.4 15 18.5T 
C13 7.64 -79.5 29 26T 
C14 8.22 -79.5 27 26T 
C15 8.59 -77.3 26 28.5T 
C16 8.19 -77.3 28 28.5T 
C17 9.66 -84.1 23 22.5 
C18 10.09 -86.4 18 18.5T 
C19 9.99 -86.4 20 18.5T 
C20 9.09 -79.5 25 26T 
C21 10.95 -97.7 8 1.5T 
C22 10.88 -95.4 9 5.5T 
C23 10.97 -97.7 7 1.5T 
C24 10.35 -93.2 16 10.5T 
C25 11.24 -95.4 6 5.5T 
C26 12.08 -93.2 2 10.5T 
C27 11.63 -90.9 4 14T 
C28 11.77 -95.4 3 5.5T 
C29 12.33 -93.2 1 10.5T 

 
Figure 1 presents a visual display of the priority rankings for each competency based on MWDSs 
and the RDSs. Overall, the RDM (Narine & Harder, 2021) tended to place lower priority on the 
competencies the Borich (1980) model prioritized, and prioritized competencies given lower 
priority by the Borich model. The mean absolute difference in priority rankings across all 29 
competencies using the two models was 4.62 (SD = 4.60) ranks. 
 
 
 
 

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Figure 1 
 
Priority Rankings for PA Competencies Based on the Borich and RDM Models  
 

 
There was a significant (p < .001) correlation between MWDSs and RDSs (|r| = .74), indicating 
one set of scores explained 54.8% of the variance in the other set of scores. This was 
substantially lower than the .98 correlation (r2 = .96) between MWDSs and RDSs reported by 
Narine and Harder (2021). Because the ultimate purpose of the Borich and Ranked Discrepancy 
models is the prioritization of teacher PD needs, a Spearman rank-order rho correlation was 
calculated between the two sets of priority rankings, resulting in an rs = .69 (p < .001), indicating 
one set of rankings explained 47.6% of the variance in the other set of rankings.  
 

Conclusions, Discussion, and Recommendations 
 
Contrary to Narine and Harder (2021), we found substantial differences between the PD 
priorities established by the Borich (1980) and Ranked Discrepancy (Narine & Harder, 2021) 
models. For example, if a PD workshop were to be offered based on the five highest priorities 
by each method, the Borich model would prioritize, in order, competencies C29, C26, C28, C27, 
and C11. However, if prioritized by the RDM, the workshop would prioritize competencies C21 
and C23, followed by three competencies selected from the tied ranks of C1, C2, C3, C22, C25, 

1
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5
6
7
8
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14
15
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Pr
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rit
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Competency number

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and C28. Depending upon the competencies selected from the six tied RDM ranks, the two 
workshops would include either zero or one common competency. Consequently, two different 
PD workshops would be planned and delivered based on whether the Borich model or the RDM 
was used to prioritize PD content. With the RDM, the prevalence of tied priority rankings 
complicated decision making, particularly if only a limited number of competencies could be 
addressed. As a result, the best allocation of scarce PD resources was not clear. 
 
The Pearson-product moment correlation between the MWDSs (Borich model) and the RDSs 
(Ranked Discrepancy Model) indicated one discrepancy model failed to explain 45.2% of the 
variance in the other discrepancy model. When comparing ranked PD priorities, the Spearman 
correlation indicated that one discrepancy model failed to explain 52.4% of the variance in 
rankings by the other discrepancy model.  
 
The question emerged as to why the scores and the priority rankings differed between the two 
discrepancy models. Our conclusion was that use of the RDM (Narine & Harder, 2021) reduced 
valuable information contained in the survey data by not using a measure of overall perceived 
importance as a weighting factor. As an example, assume two competencies (A and B) were 
rated by five respondents on 1 to 5 importance and ability scales. Using the RDM, if four 
respondents (80%) rated competency A as five in importance and one in ability, and one 
respondent (20%) rated importance as one and ability as five, the RDS would be -60. Likewise, 
for competency B, if four respondents (80%) rated importance as two and ability as one, and 
one respondent (20%) rated importance as one and ability as two, the RDS would also be -60, 
and the two competencies would receive equal priority based on RDSs. However, given the 
importance ratings, respondents clearly see competency A as more important than competency 
B; thus, competency A should receive priority as a PD topic. In contrast to the RDM, because 
the Borich model weights the discrepancy score by the mean importance of the competency, 
the MWDS for competency A would be 10.08 while the MWDS for competency B would be 
1.08. Thus, by including the mean importance for each competency, the Borich model clearly 
identifies competency A as the priority PD topic. This demonstrates the efficacy of using 
perceived importance as a weighting factor in determining PD priorities.  
 
There can be legitimate discussion and disagreement related to the measurement and 
statistical issues of using either the Borich (1980) model or the RDM (Narine & Harder, 2021). 
The Borich model treats single-item scale responses as interval level data in the calculation of 
discrepancy scores, weighted discrepancy scores and, finally MWDSs. However, the argument 
from statistical theory that scale of measurement does not dictate statistical procedures (Gaito, 
1980; Harwell & Gatti, 2001; Lord, 1953; Norman, 2010; Zumbo & Zimmerman, 1993) supports 
this use. Conversely, use of the RDM essentially reduces measurement to -1, 0, or 1, and 
subsequently ignores the 0 scores. This leads to a reduction of information contained in the 
original data concerning the importance and ability relative to the competencies. Further, the 
RDM does not give weight to the overall importance ratings in prioritizing PD needs. 
 
We believe the arguments from statistical theory supporting use of the mean with individual 
Likert items to calculate MWDSs when using the Borich (1980) model are compelling; however, 

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for those not convinced and preferring the RDM (Narine & Harder, 2021), a modest suggestion 
would be to incorporate the median importance into the calculation by multiplying the RDS for 
each item by the median importance for that item. Perhaps the resulting score might be called 
a ‘median weighted ranked discrepancy score’ (MWRDS). When we calculated MWRDSs and 
correlated these scores to the MWDSs using our dataset, the correlation between scores 
increased to |r| = .88 (from |r| = .74) and the Spearman rho correlation between PD priority 
rankings increased to r = .86 (from r = .69). Additionally, the mean difference between priority 
rankings by the two models decreased from 4.62 (SD = 4.60) to 2.82 (SD = 3.49). Finally, use of 
the MWRDSs identified the same top five PD priorities as did use of the MWDSs. This illustrated 
the efficacy of taking item importance ratings into account when determining PD needs.  
 
Agricultural education is a pragmatic discipline (Barrick, 1989) often characterized by applied 
research conducted to solve practical problems (Dyer et al., 2003; Roberts et al., 2016). This is 
particularly true of needs assessments used to identify PD priorities for SBAE teachers. 
According to the pragmatist philosopher Henry James (1907), the “only test of probable truth is 
what works best in the way of leading us” (Lecture II, para. 55). The Borich model has been 
used to effectively identify teacher PD needs for over 40 years. Given our results, further 
research and discussion about measurement, statistical, and methodological issues are needed 
prior to abandoning the Borich (1980) model in favor of the RDM (Narine & Harder, 2021). 
 

Acknowledgments 
 
This work was supported, at least in part, by the USDA National Institute of Food and 
Agriculture, Hatch project 1024473 and the University of Arkansas Division of Agriculture. 
 
Author Contributions: D. M. Johnson – conceptualization, supervision, formal analysis, writing-
original draft, writing-review and editing; W. Doss – conceptualization, writing – review and 
editing; C. M. Estepp – conceptualization, writing – review and editing; H. O. Akwah – 
investigation; G. W. Wardlow – conceptualization, supervision, writing – review and editing. 
 

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