































   Advancements in Agricultural Development 
  Volume 5, Issue 2, 2024 
  agdevresearch.org 

 

1. James R. Lindner, Professor, Auburn University, 5040 Haley Center, Auburn University, AL, 36849, jrl0039@auburn.edu, 

 https://orcid.org/0000-0002-1448-3846  
2. Nicholas J. Lindner, Research Technician III, Duke University, Viral Vector Core, Duke University School of Medicine, 

Durham, NC, 27716, nicholas.lindner@duke.edu,  https://orcid.org/0000-0002-7140-6820  
152 

 

Interpreting Likert-type Scales, Summated Scales, 
Unidimensional Scales, and Attitudinal Scales:  

I neither Agree nor Disagree, Likert or Not 
 

J. R. Lindner1, N. J. Lindner2 
 

 
Article History 
Received: May 31, 2023 
Accepted: July 31, 2023 
Published: January 31, 2024 
 
 
Keywords 
human behavioral research; 
behavioral scaling; educational 
research; psychological research; true 
limits; effect size; quality education 
  

Abstract 
This paper provides a rationale and convention for discussing the true 
limits and interpretation of data collected using unidimensional, 
summated, Likert-type, and attitudinal scales used in research 
investigating human behavior, sociology, education, psychology, and 
other related fields of study. All vague quantifiers must be described in 
methods and findings. The true limits of the scale and of each vague 
quantifier should be described. This information should be placed in the 
methods section. A five-point summated scale, for example, can be 
interpreted as follows: Strongly Agree = 5 - 4.51, Agree = 4.5 - 3.51, 
Neither Agree nor Disagree = 3.5 - 2.51, Disagree = 2.5 - 1.51, Strongly 
Disagree = 1.5 - 1. This paper also provides a rationale and convention for 
the use of nonstandardized effect size (ES) estimates to describe the 
magnitude and strength of the effect. This is accomplished by subtracting 
one summated M from another summated M and interpreted using the 
following convention: Small (ES = .19 and lower); Medium (ES = .20 - .49); 
and Large (ES = .50 and higher). The rationale for this is based on the 
intuitiveness of the measure, true limits of the scale, and scale intervals.  

mailto:jrl0039@auburn.edu
https://orcid.org/0000-0002-1448-3846
mailto:nicholas.lindner@duke.edu
https://orcid.org/0000-0002-7140-6820


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Introduction and Problem Statement 
 
The use of unidimensional, summated, Likert-type, or attitudinal scales are ubiquitous in 
research related to human behavior, sociology, education, psychology, and the field of 
agricultural leadership, education, and communications. Interpreting summated scores has 
mostly focused on the appropriateness of using single items versus summated scales. In a meta-
analysis of the research reported in the Journal of Agricultural Education, Warmbrod (2014) 
found that the use of summated scores resulted in higher congruent interpretations than single 
items scores. In A technique for the Measurement of Attitude, Likert’s (1932) work focused on 
the use of summated scales to measure attitudes, not single items. Because of the impact of 
Likert’s (1932) work, summated scales are often referred to as Likert-type. The treatment of 
Likert-type scores as ordinal or interval has also been widely debated (Norman, 2010; Sullivan & 
Arino, 2013). Clason and Dormody (1994) noted the commonality of treating Likert-type scores 
as interval level data in agricultural education research. They write that it is “difficult to see 
how normally distributed data can arise in a single Likert-type item” (p. 34). Notwithstanding 
the criticism of how data are often treated, Clason and Dormody (1994) suggest that the focus 
of analysis should be on answering relevant research questions. The authors of this paper 
concur. Others have found that treating single item Likert-type scores as interval scores 
changes research conclusions (Gardner et al., 1998; Sisson & Stocker, 1989). The debate over 
the appropriateness of treating single or summated Likert-type scores as interval scores will 
continue and is not addressed in this paper. Warmbrod (2014) reminded us, however, that the 
use of the term “Likert-type” scale was synonymous with summated scale. Single items should 
be referred to appropriately; e.g., attitudinal scale, rating scale. Miller (1998) enunciated the 
appropriate analysis for the reporting of ordinal and interval and provides justification for such. 
Collectively Miller’s (1998) and Warmbrod’s (2014) advice is as sound today as when they first 
reported it. Building on their work, interpretation of scores may help us better understand and 
communicate findings.  

Purpose 
 
The primary purpose of this paper was to provide a rationale and convention for discussing the 
true limits and interpretation of data collected using unidimensional, summated, Likert-type, 
and attitudinal scales used in research investigating human behavior, sociology, education, 
psychology, and other related fields of study. A secondary purpose was to provide a rationale 
and acceptable convention for the use of nonstandardized effect size (ES) estimates. 

Discussion and Commentary 
 
Accurately interpreting scores, regardless of whether they are obtained from single items or 
summated Likert-type scores that are reported as means (M) and standard deviations (SD), is 
critical. A very common summated scale would include five terms to describe a research 
participant’s level of agreement to a particular statement: Strongly Agree, Agree, Neither Agree 
nor Disagree, Disagree, and Strongly Disagree. These terms are referred to by Dillman et al. 

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(2014) as vague quantifiers. They further explained “[t]he problem with vague quantifiers is 
that they are vague; that is, there is not a single and clear meaning for each of the labels in the 
same way there is with natural metrics” (p. 151).  

When one individual responds to a single question, the response is directly tied to a specific 
vague quantifier (see Table 1).  

Table 1 
 
Examples of How Single Items Questionnaires May be Developed 
Statements Vague Quantifiers and Associated Values 
Advancements in Agricultural Development has a 
positive influence on agricultural development 
practices worldwide through the rapid publication 
of research. 

Strongly 
Agree 

Agree 
Neither 

Agree nor 
Disagree 

Disagree 
Strongly 
Disagree 

Advancements in Agricultural Development has a 
positive influence on agricultural development 
practices worldwide through the rapid publication 
of research. 

SA A NAD D SD 

Advancements in Agricultural Development has a 
positive influence on agricultural development 
practices worldwide through the rapid publication 
of research. 

1 2 3 4 5 

Advancements in Agricultural Development has a 
positive influence on agricultural development 
practices worldwide through the rapid publication 
of research. 

5 4 3 2 1 

Advancements in Agricultural Development has a 
positive influence on agricultural development 
practices worldwide through the rapid publication 
of research. 

     

 
In the examples provided in this paper the following conventions were used: Strongly Agree 
(SA) = 5, Agree (A) = 4, Neither Agree nor Disagree (NAD) = 3, Disagree (D) = 2, and Strongly 
Disagree (SD) = 1. Whether the data are ordinal or interval is irrelevant. For example, individual 
one indicates that they Agree that “Advancements in Agricultural Development (AAD) has a 
positive influence on agricultural development practices worldwide through the rapid 
publication of research.” In describing the individual’s response, researchers should report that 
individual one agreed with the statement. Now consider two individuals, with one selecting 
Agree and one selecting Neither Agree nor Disagree. With two individuals responding, there are 
more options for describing the findings. One option is to note that one individual agreed and 
one individual neither agreed nor disagreed. Another option is to note that the summated 
score mean response was an M = 3.5, SD = .71. Here, the interpretation is more difficult as the 

     

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mean lies exactly halfway between two vague quantifiers. This is where an a priori convention 
for describing findings is needed. It would be an appropriate convention to state that SA = 5 - 
4.51, A = 4.5 - 3.51, NAD = 3.5 - 2.51, D = 2.5 - 1.51, SD = 1.5 - 1. Using this rule, researchers 
would note that although individual participants had different responses, on the whole 
participants neither agreed nor disagreed that “Advancements in Agricultural Development has 
a positive influence on agricultural development practices worldwide through the rapid 
publication of research.” An assumption for this rule is that the five-point summated scales 
have four equal intervals (see Figure 1): SD—D, D—NAD, NAD—A, and A—SA.  

Figure 1 
 
Intervals and Interpretations of a Five-Point Summated Scale 
 
 Interval One Interval Two Interval Three Interval Four  
 

Strongly 
Agree Agree Neither Agree 

nor Disagree Disagree Strongly 
Disagree 

5 4 3 2 1 
 
 SA A NAE D SD  
 5-4.51 4.50 - 3.51 3.50 - 2.51 2.50 - 1.51 1.50 - 1  
 
Note. An n point summated scale will have n-1 equal intervals 
 
Simply reporting a mean score would be meaningless without describing the vague quantifier. 
The true limits of a scale are the lowest and highest numerical values assigned to the vague 
quantifiers. Similarly, the true limits of an individual vague quantifier are the lowest and highest 
numerical values assigned to that quantifier.  

The data are not normally distributed in either of the two previously reported examples; let us 
now consider that option. Consider an example based on a single item scale score with 30 
individuals responding. For this example, let us assume responses were as follows: SA(f = 5, 
16.7%), A(f = 12, 40%), NAD(f = 12, 40%), and D(f = 1, 3.3%). It would be sufficient to describe 
the data in terms of the frequencies and percentages provided in the previous sentence. 
Additionally, because the data are normally distributed, reporting M and SD would also be 
appropriate (M = 3.67, SD = .88). A descriptive interpretation of this finding based on this rule is 
that participants tended to agree that “AAD had a positive influence on agricultural 
development practices worldwide through the rapid publication of research.” 

Now let us consider a summated unidimensional, attitudinal, summated scale, or Likert-type 
scale; see Table 2.  

 

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Table 2 
 
Examples of how Scaled Questions May be Written 
Agricultural professionals’ attitudes toward the 
influence of Advancements in Agricultural 
Development 

Strongly 
Agree 

Agree 
Neither 

Agree nor 
Disagree 

Disagree 
Strongly 
Disagree 

Advancements in Agricultural Development has a 
positive influence on agricultural development 
practices 

5 4 3 2 1 

Advancements in Agricultural Development 
reports research that have practical implications 
for agricultural professionals 

5 4 3 2 1 

Advancements in Agricultural Development 
presents research that reports practical 
implications in a timely manner 

5 4 3 2 1 

Advancements in Agricultural Development is a 
trusted source for agricultural professionals to 
publish their research 

5 4 3 2 1 

 
Note that these are statements of behavior or attitude and that they have direction. In a 
summated scale, a total score or grand mean (MG) score must be calculated. In our field of 
study, MG scores tend to be the preference, but the choice of mean statistic does not matter. 
Rather, the key to understanding the results is the interpretation of the scores. In this example, 
there are four statements used to define the construct being measured. Let us assume one 
respondent selected 4, 5, 4, and 4; M = 4.25 and SD = .50. Using the same convention described 
previously, the finding should be interpreted as the participant agreeing that “AAD had a 
positive influence on agricultural development practices worldwide through the rapid 
publication of research.” With one respondent, it is impossible to estimate reliability. With two 
individuals responding there are more options for describing the findings. Let us assume a 
second responded select 4, 5, 5, and 5; M = 4.75 and SD = .50. In this example, one participant 
tended to agree, and one participant tended to strongly agree. The responsibility then falls on 
the investigator on how to interpret the finding. Based on the rule previously provided, the MG 
score would suggest that respondents collectively tended to agree (M = 4.5, SD = .53) that “AAD 
had a positive influence on agricultural development practices worldwide through the rapid 
publication of research.” Estimating reliability again would be problematic given the small 
sample size and our understanding of the Central Limit Theorem (Field, 2018), which postulates 
that data tends to become normally distributed as n approaches 30.  

Continuing this example with an expanded sample size of n = 30 assuming responses were as 
follows: R1|D(f = 1, 3.3%), NAD(f = 12, 40%), A(f = 12, 40%), and SA(f = 5, 16.7%); R2|NAD(f = 
11, 36.7%), A(f = 14, 46.7%), and SA(f = 5, 16.7%); R3|D(f = 3, 10.0%), NAD(f = 11, 36.7%), A(f = 
5, 16.7%), and SA(f11, 36.7%); and R4|D(f = 4, 13.3%), NAD(f = 7, 23.3%), A(f = 11, 36.7%), and 

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SA(f = 8, 26.7%). Reliability is estimated for the summated unidimensional scale at a Cronbach 
alpha of .96. An MG and standard deviation for the summated scale are calculated (M = 3.77, SD 
= .85). The appropriate interpretation would be that participants agreed, “AAD had a positive 
influence on agricultural development practices worldwide through the rapid publication of 
research.” The findings must be described using the same vague quantifiers used to collect the 
data and based on a rule set a priori. 

As noted previously, a five-point scale will have four intervals and five interpretations; see Table 
3 in the Recommendations. So, while the intervals are at equal distances, the interpretations 
are not. A four-point scale would have three intervals and a six-point scale would have five 
intervals. When dealing with the type of scales described herein this cannot be overcome. 
Hence, the need to discuss statistical significances and effect sizes to better understand the 
findings of a study. This same problem occurs whether the data are treated as ordinal or 
interval. Stated as a caution, extending the numerical values of the beginning and ending of a 
scale to create equal intervals would also be problematic in that it would over or under inflate 
mean scores.  

Interpretations of findings 
When analyzing findings of data collected using these scales, it is important to collectively 
consider the interpretation of the Vague Quantifiers (VQ), Statistical Significance (SS), and 
Effect Size (ES). Each interpretation provides one incomplete understanding of the findings. It is 
at the intersection of all three interpretations alone that presents a complete picture or 
maximized interpretation of the findings; this can and should be presented (see Figure 2).  

Figure 2 
 
Maximizing Interpretation and the Relationship and Interpretation of Findings  

 

     

 

Vague 
Quantifier 

(VQ) 

 
Statistical 

Significance 
(SS) 

 Effect Size 
(ES) 

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Making and Understanding Interpretations 
As described previously, all findings should be interpreted using, at a minimum, an appropriate 
VQ. If comparisons between groups or variables are made, then SS should be provided. 
Subsequently, an ES should be calculated to describe the magnitude and strength of the effect 
(Field, 2018). It is the reporting and analysis of these three interpretations that provides the 
most meaningful information related to the research and its consumer.  

 According to Field (2018), common measures of ES include Cohen’s d and Pearson’s correlation 
r (Cohen, 1988, 1992). The calculation and reporting of ES will help the researchers determine if 
the effect was small, medium, or large, and ultimately will add strength to data interpretations, 
discussions, and recommendations. Cohen (1988) operationally defined effect sizes as: small (d 
= .2) differences that are difficult to detect; medium effect sizes (d = .5) as differences that are 
evident by looking at them; and large (d = .8) differences that are clearly different. Cohen 
(1988) then cautions researchers by writing “the reader is counseled to avoid the use of these 
conventions, if he can, in favor of exact values provided by theory or experience in the specific 
area in which he is working” (p. 184). Cohen (1992) also noted that calculating and reporting ES 
and the value of power analysis in the establishment of sample sizes is often overlooked. The 
use of nonstandardized effect sizes could also be provided as means of describing the 
magnitude and strength of the effect. In our example above this would be achieved simply by 
subtracting one summated M from another summated M and interpreted using the convention 
provided in the recommendations below. The rationale for this is based on the intuitiveness of 
the measure, true limits of the scale, and scale intervals. Problems with logical interpretations 
exist when findings result in illogical descriptions. A couple of many possible examples are 
provided below.  

Group A, MG = 3.50 (Neither Agree nor Disagree) and Group B, MG = 3.51 (Agree).  

Group C, MG = 1.51 (Disagree) and Group D, MG = 2.5 (Disagree) 

These problems provide a strong rationale for further descriptions using both statistical 
significance and effect size. For illustrative purposes, assumptions about statistical significance 
are made. For the type of research discussed in this paper, statistical significance is normally set 
a priori at an alpha of .05. Setting a statistical significance level a priori limits concerns about p -
hacking or searching for significant differences after the research is completed (Head et al., 
2015).  Group A neither agreed nor disagreed that “AAD has a positive influence on agricultural 
development practices worldwide through the rapid publication of research.” Group B agreed 
that “AAD has a positive influence on agricultural development practices worldwide through 
the rapid publication of research.” There was no statistical significant difference between the 
two groups and the nonstandardized effect size was small. So, while the interpretations of the 
vague quantifiers indicate one conclusion, that there is a difference, a “so-what,” or 
“meaningful” difference does not exist. This is referred to as a difference without distinction, a 
formal logical fallacy. Implications and recommendations based on this difference would be 
minimal to non-existent. Groups C and Group D disagreed that “AAD has a positive influence on 
agricultural development practices worldwide through the rapid publication of research.” There 

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was statistically significant differences between the two groups and the nonstandardized effect 
size was large. So, while the interpretations of the vague qualifiers indicate one conclusion, that 
there was no difference, a “so-what”, or “meaningful” difference does exist. Implications and 
recommendations based on this difference should be maximized and highlighted despite the 
lack of difference in vague quantifiers.  

Alternate Scales and Other Considerations 
If an investigator chooses to use a semantic differential scale (Osgood et al., 1957) or a 
Thurstone scale (1928), similar rules should be adopted a priori and interpretations made based 
on those rules. Semantic differential scales allow researchers to measure attitudes using a 
variety of adjectives with bipolar meanings, such as good and bad, or interesting and boring.  
Interpretations for a semantic differential scale would focus on participants’ positive or 
negative attitudes toward a construct. Thurstone scales allow researchers to measure attitudes 
towards favorable and unfavorable statements regarding a particular issue using a two-point 
scale: agree and disagree. Interpretations for a Thurstone scale would focus on participants’ 
tendency to agree or disagree to a particular issue.  

How vague quantifiers are defined determines how they can be interpreted. Consider a scale 
using vague quantifiers related to importance. If you used a unidimensional four-point scale 
and labeled the vague quantifiers important, moderately important, slightly important, and not 
important, those same terms must be used to describe the findings. If an investigator only used 
important and not important, then those are the only terms that should be used to describe the 
findings. If they used a unidimensional scale and reported M and SD, then the findings should 
be reported in terms of the rules set a priori using the one appropriate vague quantifier. 
Discussion of where in the interval M falls cannot be reflected in changing the language of the a 
priori defined VQs. This is the purpose of discussing the ES along with the SS. When reporting M 
and SD, it is likely not appropriate to discuss data not presented unless a logical justification can 
be provided. For example, an M of 4 should be described as participants having agreed; noting 
a majority or plurality of respondents neither agreed nor disagreed would not be appropriate 
without reporting all the data. Within that same example, a majority could also include those 
that agreed and those that strongly disagree. If the researcher is going to calculate and report 
M, then M should be used for interpretation.   

To this point, this discussion has focused on interpretations of means and standard deviations 
from unidimensional, summated, Likert-type, or attitudinal scales; this is regardless of whether 
the data are single item or summated scores and regardless of whether data are treated as 
ordinal or interval. This paper has not addressed the presentation of data in table format and 
whether M and SD or frequencies (f) or percentages (%) are most appropriate. While the 
reporting of f and % certainly provides more description than simply reporting M and SD, the 
latter is acceptable. In some instances, both f and % and M and SD are reported. The authors 
leave this discussion for another investigation, as ultimately it is the MG and SDG that are the 
focal point of this paper and discussion.  

 

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Recommendations   
Based on the previous discussions, the following recommendations are provided for 
interpreting scales described herein. Merely reporting means is insufficient for interpreting the 
types of scales described in this paper.  

1. The scale used must be appropriately described in the methods. All vague quantifiers must 
be described in methods and findings. The true limits of the scale and the true limits of each 
vague quantifier should be described as shown in Table 3. This information should be placed 
in the methods section and may follow this general format. A five-point summated scale 
was used to collect data for this study: Strongly Agree = 5 – 4.51, Agree = 4.5 – 3.51, Neither 
Agree nor Disagree = 3.5 – 2.51, Disagree = 2.5 – 1.51, Strongly Disagree = 1.5 – 1. 

Table 3 
 
Examples of Vague Quantifiers and Associated Values 

Five Point Scale Four Point Scale 

Vague Quantifier Values Vague Quantifier Values 

Strongly Agree 5.0 – 4.51 Strongly Agree 4.0 – 3.51 

Agree 4.5 – 3.51 Agree 3.5 – 2.51 

Neither Agree nor Disagree 3.5 – 2.51 Disagree 2.5 – 1.51 

Disagree 2.5 – 1.51 Strongly Disagree 1.5 – 1.00 

Strongly Disagree 1.5 – 1.00   

Note. The scale convention should be adjusted based on the number and order of 
vague quantifiers.  

 
Calculate, report, and interpret the M and SD of scales based on rules set a priori. If data 
does not have a purposeful and meaningful order (other than the order the questions were 
asked), then report by highest mean or percentage first. When using M and SD in a table 
also add a note at the bottom of the table describing all vague quantifiers. Discuss those 
items with the highest and lowest means or those items of interest if data are 
dichotomized. 

2. Report statistical analysis and highlight differences. Alpha for statistical analysis should be 
set a priori. In the type of research being discussed herein alpha is typical set a priori at .05. 
Caution is warranted against data dredging or p-hacking (Head, et al., 2015).  

3. Calculate and report effect sizes using an appropriate standardized or nonstandardized 
convention. This will aid in the interpretation of the data and provide a strong response to 
the “so what” question of differences detected. In our field, medium and large ES have the 

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most value when making implications and recommendations. Small ES often do not reach 
the “so what” level of value.  

4. A nonstandardized effect size calculation can help in describing the magnitude and strength 
of the effect. For a summated, unidimensional, attitudinal, and Likert-type scale, this can be 
accomplished by simply subtracting mean scores. A convention for interpreting 
nonstandardized effect sizes should be reported.  

The convention for a nonstandardized effect size scales described in this paper could be 
interpreted as shown below.  

Small (ES = .19 and lower) 

Medium (ES = .20 - .49) 

Large (ES = .50 and higher) 

Using the type of scaling described in this paper, a nonstandardized effect size calculation 
may be the most appropriate, but as Cohen cautioned such calculations and interpretations 
should be ultimately determined by what researchers in a given field of study are 
attempting to accomplish. The convention provided above is based on the minimum and 
maximum values of the vague quantifiers provided above. Referring to Figure 1, note that a 
difference of .5 at the lowest and highest end of a scale would move the interpretation from 
one vague quantifier category to another, and from the middle of the other vague 
quantifier categories to another. For a standardized effect size calculation, Cohen’s d and 
Pearson’s correlation r are widely recognized as robust and useful. Their use, however, is 
limited for a variety of reasons including complications in calculations. Hence, the 
recommendation to consider a nonstandardized convention is provided. 

5. From our example earlier in the paper, what follows is a sample of how findings can be 
described; this is a general format of which infinite other formats can be generated. Overall 
participants tended to Agree (M = 3.77, SD .85) that “AAD had a positive influence on 
agricultural development practices worldwide through the rapid publication of research.” 
Faculty (M = 4.1, SD = .76) tended to Agree with the statement while Graduate Students (M 
= 3.43, SD = .83) tended to Neither Agree nor Disagree. Comparing attitudes between 
faculty and graduate students using a t-test (alpha set a priori at .05), t (28) = 2.30, p < .05, a 
statistical difference existed. Faculty were more likely to agree, and this finding was 
statistically significant, and the ES (.67) was large.  

6. When illogical findings occur in statistical testing, additional discussion is warranted. For 
example, let us assume that Master’s students had a mean score of 3.5 (Neither Agree nor 
Disagree) on the construct discussed in Table 2. Second, assume doctoral students had a 
mean score of 3.51 (Agree). While differences between master’s students and doctoral 
students are interpreted as being different, there is no statistical difference, no practical 
difference, and the effect size is minimal. There is no “so what” here and caution is 

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warranted against conclusions being drawn from the differences in interpretation. Now 
consider augmenting the example. Let us assume master’s students had a mean score of 
3.51 (Agree) on the construct discussed in Table 2; doctoral students had a mean score of 
4.5 (Agree). Data suggests the interpretation is the same for both. Let us assume there is a 
statistical difference between the groups and that the effect size is large. In this example, 
additional discussion should focus on the true differences despite having the same vague 
quantifiers; statistical significance, and a large effect size. 

The attributes and viability of the recommendations provided above will be borne out over 
time (Lindner et al., 2016). If the recommendations prove to be appropriate, they will be 
adopted, if not they will be discarded, perhaps because they were not useful or a better 
alternative was available (Lindner et al., 2001).   

Acknowledgements 
 
James Lindner – conceptualization, methodology, writing original draft, review, and editing; 
Nicholas Lindner – writing original draft, review, and editing. 
 

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