Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2023 Oct;83(5):885-906.
doi: 10.1177/00131644221130482. Epub 2022 Oct 27.

Equidistant Response Options on Likert-Type Instruments: Testing the Interval Scaling Assumption Using Mplus

Georgios Sideridis  1   2 , Ioannis Tsaousis  2 , Hanan Ghamdi  3
Affiliations

Equidistant Response Options on Likert-Type Instruments: Testing the Interval Scaling Assumption Using Mplus

Georgios Sideridis et al. Educ Psychol Meas. 2023 Oct.

Abstract

The purpose of the present study was to provide the means to evaluate the "interval-scaling" assumption that governs the use of parametric statistics and continuous data estimators in self-report instruments that utilize Likert-type scaling. Using simulated and real data, the methodology to test for this important assumption is evaluated using the popular software Mplus 8.8. Evidence on meeting the assumption is provided using the Wald test and the equidistant index. It is suggested that routine evaluations of self-report instruments engage the present methodology so that the most appropriate estimator will be implemented when testing the construct validity of self-report instruments.

Keywords: Likert-type; Mplus; interval scaling; survey assumptions.

PubMed Disclaimer

Conflict of interest statement

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Figures

Figure 1
Figure 1
Assuming Equal Interval Scaling (Upper Panel) or Unequal (Lower Panel) Note. The unequal threshold system suggests that the frequency of responses lessens as they become more extreme (strong disagreements or agreements). Upper panel: Equal distances between response options. Lower panel: Unequal distances between response options.
Figure 2
Figure 2
OCCs for Item 5 of the “Caring” Subscale of the PYDS With Category Boundary Locations b1-i5 = −2.56, b2-i5 = −1.55, and b3-i5 = 0.006 Note. The vertical lines point to the theta estimate required by a person to have a 50% chance of responding in that category or higher. GRM = graded response model; OCCs = operating characteristic curves; PYDS = Positive Youth Development Scale.
Figure 3
Figure 3
CCCs for Item 5 of the “Caring” Subscale of the PYDS (i.e., Other People’s Feelings Matter to Me) Note. CCCs = category characteristic curves; GRM = graded response model; PYDS = Positive Youth Development Scale; T1 = theta required to respond disagree compared with strongly disagree; T2 = theta required to respond agree compared with disagree; T3 = theta required to respond strongly agree compared with agree.
Figure 4
Figure 4
TIF and Conditional SEM of the Caring Subscale of the PYDS. Note. The scaling at zero is for information and the secondary scaling is at +3 logits for SEM. PYDS = Positive Youth Development Scale; TIF = Test Information Function; SEM = Standard Error of Measurement.
See this image and copyright information in PMC

References

    1. Akdogan R., Turkum A. S. (2018). Insight scale for nonclinical university students: Validity and reliability analysis. Measurement and Evaluation in Counseling and Development, 51, 250–262.
    1. Aldawsari H., Laux J., Dari T., Gaballa H. (2021). The revised Arabic Schwartz outcome scale-10 (SOS-10-AR). Measurement and Evaluation in Counseling and Development, 54, 120–129.
    1. Andrich D. (1978. a). A rating formulation for ordered response categories. Psychometrika, 43(4), 561–573.
    1. Andrich D. (1978. a). A rating formulation for ordered response categories. Psychometrika, 43(4), 561–573.
    1. Andrich D. (1978. b). Scaling attitude items constructed and scored in the Likert tradition. Educational and Psychological Measurement, 38, 665–680. 10.1177/001316447803800308 - DOI

LinkOut - more resources