Using a Computational Approach for Generalizing a Consensus Measure to Likert Scales of Any Size n
There are many consensus measures that can be computed using Likert data. Although these measures should work with any number n of choices on the Likert scale, the measurements have been most widely studied and demonstrated for n = 5. One measure of consensus introduced by Akiyama et al. for n = 5 a...
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| Format: | Article |
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Wiley
2018-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2018/5726436 |
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| author | Mushtaq Abdal Rahem Marjorie Darrah |
| author_facet | Mushtaq Abdal Rahem Marjorie Darrah |
| author_sort | Mushtaq Abdal Rahem |
| collection | DOAJ |
| description | There are many consensus measures that can be computed using Likert data. Although these measures should work with any number n of choices on the Likert scale, the measurements have been most widely studied and demonstrated for n = 5. One measure of consensus introduced by Akiyama et al. for n = 5 and theoretically generalized to all n depends on both the mean and variance and gives results that can differentiate between some group consensus behavior patterns better than other measures that rely on either just the mean or just the variance separately. However, this measure is more complicated and not easy to apply and understand. This paper addresses these two common problems by introducing a new computational method to find the measure of consensus that works for any number of Likert item choices. The novelty of the approach is that it uses computational methods in n-dimensional space. Numerical examples in three-dimensional (for n=6) and four-dimensional (for n=7) spaces are provided in this paper to assure the agreement of the computational and theoretical approach outputs. |
| format | Article |
| id | doaj-art-41ca717c35c04157afc461749db4ddf4 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-41ca717c35c04157afc461749db4ddf42025-08-20T03:55:40ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252018-01-01201810.1155/2018/57264365726436Using a Computational Approach for Generalizing a Consensus Measure to Likert Scales of Any Size nMushtaq Abdal Rahem0Marjorie Darrah1Department of Mathematics, West Virginia University, WV 26506, USADepartment of Mathematics, West Virginia University, WV 26506, USAThere are many consensus measures that can be computed using Likert data. Although these measures should work with any number n of choices on the Likert scale, the measurements have been most widely studied and demonstrated for n = 5. One measure of consensus introduced by Akiyama et al. for n = 5 and theoretically generalized to all n depends on both the mean and variance and gives results that can differentiate between some group consensus behavior patterns better than other measures that rely on either just the mean or just the variance separately. However, this measure is more complicated and not easy to apply and understand. This paper addresses these two common problems by introducing a new computational method to find the measure of consensus that works for any number of Likert item choices. The novelty of the approach is that it uses computational methods in n-dimensional space. Numerical examples in three-dimensional (for n=6) and four-dimensional (for n=7) spaces are provided in this paper to assure the agreement of the computational and theoretical approach outputs.http://dx.doi.org/10.1155/2018/5726436 |
| spellingShingle | Mushtaq Abdal Rahem Marjorie Darrah Using a Computational Approach for Generalizing a Consensus Measure to Likert Scales of Any Size n International Journal of Mathematics and Mathematical Sciences |
| title | Using a Computational Approach for Generalizing a Consensus Measure to Likert Scales of Any Size n |
| title_full | Using a Computational Approach for Generalizing a Consensus Measure to Likert Scales of Any Size n |
| title_fullStr | Using a Computational Approach for Generalizing a Consensus Measure to Likert Scales of Any Size n |
| title_full_unstemmed | Using a Computational Approach for Generalizing a Consensus Measure to Likert Scales of Any Size n |
| title_short | Using a Computational Approach for Generalizing a Consensus Measure to Likert Scales of Any Size n |
| title_sort | using a computational approach for generalizing a consensus measure to likert scales of any size n |
| url | http://dx.doi.org/10.1155/2018/5726436 |
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