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http://krishi.icar.gov.in/jspui/handle/123456789/73509| Title: | TESTING OF VARIANCE COMPONENTS FOR CONTINUOUS DATA FROM NESTED UNBALANCED DESIGNS |
| Other Titles: | Not Available |
| Authors: | Ankita Susheel Kumar Sarkar Anil Kumar Sanjeev Panwar Shashi Shekhar Rajan Kumar |
| ICAR Data Use Licennce: | http://krishi.icar.gov.in/PDF/ICAR_Data_Use_Licence.pdf |
| Author's Affiliated institute: | ICAR::Indian Agricultural Statistics Research Institute |
| Published/ Complete Date: | 2022-04-14 |
| Project Code: | Not Available |
| Keywords: | Unbalanced data Variance components Nested design Effect size Approximate tests |
| Publisher: | International Journal of Agricultural and Statistical Sciences |
| Citation: | Ankita, Susheel Kumar Sarkar, Anil Kumar, Sanjeev Panwar, Shashi Shekhar and Rajan Kumar (2022). Testing of Variance Components for Continuous Data from Nested Unbalanced Designs. International Journal of Agricultural and Statistical Sciences. DocID: https://connectjournals.com/03899.2022.18.391 |
| Series/Report no.: | Not Available; |
| Abstract/Description: | Under unbalanced design, testing of variance ratios are generally neither independent nor distributed as chi- square variates and does not follow standard F-distribution. In this case, exact testing of variance ratios is not available in the literature. Procedure for unbalanced data (generally not independent and are not distributed as chi-square variates) has been developed for testing the variance components in one way and two way unbalanced nested designs. |
| Description: | In case of random effects models for balanced designs, the analysis is simple and no problem is encountered in testing the variance components since the sums of squares are independent, sums of squares are chi-square variates, ratio of variance components follow standard F-distribution and hence exact testing is possible. When a random effects model is considered in unbalanced designs, analysis of variance technique rarely produce exact tests for testing the hypothesis. Under the conventional normality assumptions, except for the error component, the analysis of variance fails to decompose the total sums of squares into independently distributed sums of squares. Also, sums of squares are neither chi-square variates nor multiple of chi-square variate. The sums of squares are not independent either. Another standardized measure that quantifies the difference between means and relationship between independent and the dependent variable is effect-size measure. Two generally used statistics for computing effect-size are eta and omega squared statistics. But, these statistics do not yield correct estimate of effect-size that are comparable across different designs [Bakeman (2005)]. In that scenario, generalized eta and omega statistics given by Olejnik and Algina (2003) can be used. There was a conversation on two-way factorial ANOVA with mixed effects and interactions [Nelder (1977, 1982, 1994, 2008)]. The major assessments about the two-way factorial ANOVA model is no substantial rationale for the imposed constraints on random interactions and a lack of clear interpretation of its variance components, especially for the main random effects in respect of the response [Nelder (1977), Wolfinger and Stroup (2000), Lencina et al. (2007)]. As a result, the usual model is more widely used nowadays. The unbalanced mixed ANOVA models are often analyzed under the linear mixed models (LMM) framework using the restricted maximum likelihood (REML) or generalized least squares approaches [Littell (2002), Stroup (2013), Jiang (2017)]. Kaur and Garg (2020) attempted for Computer aided construction of rectangular PBIB designs. Gupta and Sharma (2020) constructed a set of balanced incomplete block designs (BIBD) against the loss of two blocks where loss of some observations lie in between at most two common treatments. Gupta (2021) worked on nested partially balanced incomplete block designs and its analysis. Singh et al. (2021) presented mixture designs generated using orthogonal arrays. In this study, the one way random effects model for unbalanced nested design in which we have given the model, hypothesis to be tested, sums of squares and testing procedure for the hypothesis along with analysis of variance table. In the next section, we have explained model, hypothesis testing, sums of squares, hypothesis testing procedure and analysis of variance table for two way unbalanced nested design. Since in two way unbalanced case the means squares are generally not independent and are not distributed as chi-square variates, exact testing is not available for the main class variance component. We have obtained the expected size of approximate tests and the actual size for both conventional and approximate tests. Then with the help of a simulated data we found out the numerical for actual size of the conventional test and the actual and expected size of the approximate tests for some assumed values of the variance components. |
| ISSN: | 0973-1903 |
| Type(s) of content: | Research Paper |
| Sponsors: | Not Available |
| Language: | English |
| Name of Journal: | International Journal of Agricultural and Statistical Sciences |
| Journal Type: | International Journal |
| NAAS Rating: | 4.92 |
| Volume No.: | 18 - 1 |
| Page Number: | 391-397 |
| Name of the Division/Regional Station: | Design of Experiment |
| Source, DOI or any other URL: | https://connectjournals.com/03899.2022.18.391 |
| URI: | http://krishi.icar.gov.in/jspui/handle/123456789/73509 |
| Appears in Collections: | AEdu-IASRI-Publication |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| 391-397__10039_.pdf | 294.63 kB | Adobe PDF | View/Open |
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