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The Power and Type I Error of Wilcoxon-Mann-Whitney, Welch's 't,' and Student's 't' Tests for Likert-Type Data

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Title: The Power and Type I Error of Wilcoxon-Mann-Whitney, Welch's 't,' and Student's 't' Tests for Likert-Type Data
Language: English
Authors: Simsek, Ahmet Salih (ORCID 0000-0002-9764-3285)
Source: International Journal of Assessment Tools in Education. 2023 10(1):114-128.
Availability: International Journal of Assessment Tools in Education. Pamukkale University, Faculty of Education, Kinikli Campus, Denizli 20070, Turkey. e-mail: ijate.editor@gmail.com; Web site: https://ijate.net/index.php/ijate
Peer Reviewed: Y
Page Count: 15
Publication Date: 2023
Document Type: Journal Articles
Reports - Research
Descriptors: Error of Measurement, Likert Scales, Nonparametric Statistics, Statistical Analysis, Statistical Studies, Monte Carlo Methods, Statistical Significance, Sample Size, Effect Size, Data Collection, Data Analysis, Generalizability Theory
ISSN: 2148-7456
Abstract: Likert-type item is the most popular response format for collecting data in social, educational, and psychological studies through scales or questionnaires. However, there is no consensus on whether parametric or non-parametric tests should be preferred when analyzing Likert-type data. This study examined the statistical power of parametric and non-parametric tests when each Likert-type item was analyzed independently in survey studies. The main purpose of the study is to examine the statistical power of Wilcoxon-Mann-Whitney, Welch's t, and Student's t tests for Likert-type data, which are pairwise comparison tests. For this purpose, a Monte Carlo simulation study was conducted. The statistical significance of the selected tests was examined under the conditions of sample size, group size ratio, and effect size. The results showed that the Wilcoxon-Mann-Whitney test was superior to its counterparts, especially for small samples and unequal group sizes. However, the Student's t-test for Likert-type data had similar statistical power to the Wilcoxon-Mann-Whitney test under conditions of equal group sizes when the sample size was 200 or more. Consistent with the empirical results, practical recommendations were provided for researchers on what to consider when collecting and analyzing Likert-type data.
Abstractor: As Provided
Entry Date: 2023
Accession Number: EJ1393760
Database: ERIC
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  Data: The Power and Type I Error of Wilcoxon-Mann-Whitney, Welch's 't,' and Student's 't' Tests for Likert-Type Data
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  Data: <searchLink fieldCode="AR" term="%22Simsek%2C+Ahmet+Salih%22">Simsek, Ahmet Salih</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-9764-3285">0000-0002-9764-3285</externalLink>)
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  Data: <searchLink fieldCode="SO" term="%22International+Journal+of+Assessment+Tools+in+Education%22"><i>International Journal of Assessment Tools in Education</i></searchLink>. 2023 10(1):114-128.
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  Data: International Journal of Assessment Tools in Education. Pamukkale University, Faculty of Education, Kinikli Campus, Denizli 20070, Turkey. e-mail: ijate.editor@gmail.com; Web site: https://ijate.net/index.php/ijate
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  Data: Journal Articles<br />Reports - Research
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  Data: <searchLink fieldCode="DE" term="%22Error+of+Measurement%22">Error of Measurement</searchLink><br /><searchLink fieldCode="DE" term="%22Likert+Scales%22">Likert Scales</searchLink><br /><searchLink fieldCode="DE" term="%22Nonparametric+Statistics%22">Nonparametric Statistics</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+Analysis%22">Statistical Analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+Studies%22">Statistical Studies</searchLink><br /><searchLink fieldCode="DE" term="%22Monte+Carlo+Methods%22">Monte Carlo Methods</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+Significance%22">Statistical Significance</searchLink><br /><searchLink fieldCode="DE" term="%22Sample+Size%22">Sample Size</searchLink><br /><searchLink fieldCode="DE" term="%22Effect+Size%22">Effect Size</searchLink><br /><searchLink fieldCode="DE" term="%22Data+Collection%22">Data Collection</searchLink><br /><searchLink fieldCode="DE" term="%22Data+Analysis%22">Data Analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Generalizability+Theory%22">Generalizability Theory</searchLink>
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  Data: 2148-7456
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  Data: Likert-type item is the most popular response format for collecting data in social, educational, and psychological studies through scales or questionnaires. However, there is no consensus on whether parametric or non-parametric tests should be preferred when analyzing Likert-type data. This study examined the statistical power of parametric and non-parametric tests when each Likert-type item was analyzed independently in survey studies. The main purpose of the study is to examine the statistical power of Wilcoxon-Mann-Whitney, Welch's t, and Student's t tests for Likert-type data, which are pairwise comparison tests. For this purpose, a Monte Carlo simulation study was conducted. The statistical significance of the selected tests was examined under the conditions of sample size, group size ratio, and effect size. The results showed that the Wilcoxon-Mann-Whitney test was superior to its counterparts, especially for small samples and unequal group sizes. However, the Student's t-test for Likert-type data had similar statistical power to the Wilcoxon-Mann-Whitney test under conditions of equal group sizes when the sample size was 200 or more. Consistent with the empirical results, practical recommendations were provided for researchers on what to consider when collecting and analyzing Likert-type data.
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      – Text: English
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      Pagination:
        PageCount: 15
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      – SubjectFull: Error of Measurement
        Type: general
      – SubjectFull: Likert Scales
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      – SubjectFull: Nonparametric Statistics
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      – SubjectFull: Statistical Analysis
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      – SubjectFull: Statistical Studies
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      – SubjectFull: Monte Carlo Methods
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      – SubjectFull: Statistical Significance
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      – SubjectFull: Sample Size
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      – SubjectFull: Effect Size
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      – SubjectFull: Data Collection
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      – SubjectFull: Data Analysis
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      – SubjectFull: Generalizability Theory
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      – TitleFull: The Power and Type I Error of Wilcoxon-Mann-Whitney, Welch's 't,' and Student's 't' Tests for Likert-Type Data
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