Robustness of analysis of covariance (ancova) under the distributions assumptions and variance homogeneity
<b>Aim: </b>As in all parametric methods, the ANCOVA method assumes that normal distributions of errors, homogeneity of variances, and error terms are independent of each other. However, unusual distributions in practice are more common than normal distribution. In this study, it is aime...
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| Format: | Article |
| Language: | English |
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Selcuk University Press
2020-03-01
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| Series: | Eurasian Journal of Veterinary Sciences |
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| Online Access: | http://eurasianjvetsci.org/pdf.php3?id=1279 |
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| author | Can Ateş Özlem Kaymaz Mustafa Agah Tekindal Beyza Doğanay Erdoğan |
| author_facet | Can Ateş Özlem Kaymaz Mustafa Agah Tekindal Beyza Doğanay Erdoğan |
| author_sort | Can Ateş |
| collection | DOAJ |
| description | <b>Aim: </b>As in all parametric methods, the ANCOVA method assumes that normal
distributions of errors, homogeneity of variances, and error terms are independent
of each other. However, unusual distributions in practice are more
common than normal distribution. In this study, it is aimed to examine ANCOVA
method or type 1 error rates under different distribution conditions and
homogeneity of variances.<p>
<b>Materials and Methods:</b> For this purpose, a simulation studies under different
scenarios was conducted. Random numbers were generated from Gamma,
Beta and Normal distributions considering different groups and different
sample sizes. In the simulation studies, 10000 replications were run under the
null hypothesis of no group differences and type-I error rates were calculated
for each scenario.<p>
<b>Results: </b>According to the results, in the case of the normal distribution with
homogeneous variance, the proportion of Type I error is high in the groups
with the sample size of n=20 and n=40. In the case of normal distribution with
the heterogeneous variance, the deviation has been observed in the groups
with the sample size of n = 10 and n = 30, and n = 40. These results are the
same as the results of Gamma distribution. In the Beta distribution, , there is a
deviation in the groups with n=10 and n=20 where the sample sizes are small.<p>
<b>Conclusion:</b> The results showed that type-I error rate is affected by skewness
of the distribution, sample size and homogeneity of variance. Further work
can be extended by simulation studies under different distributions and parameter
values. |
| format | Article |
| id | doaj-art-e04143da2d814cad8378a5698ff439e9 |
| institution | Kabale University |
| issn | 1309-6958 2146-1953 |
| language | English |
| publishDate | 2020-03-01 |
| publisher | Selcuk University Press |
| record_format | Article |
| series | Eurasian Journal of Veterinary Sciences |
| spelling | doaj-art-e04143da2d814cad8378a5698ff439e92025-01-03T01:36:25ZengSelcuk University PressEurasian Journal of Veterinary Sciences1309-69582146-19532020-03-0136158651279Robustness of analysis of covariance (ancova) under the distributions assumptions and variance homogeneityCan Ateş0Özlem Kaymaz1Mustafa Agah Tekindal2Beyza Doğanay Erdoğan3Department of Biostatistics, Faculty of Medicine, Van Yüzüncü Yıl University, Van, TurkeyDepartment of Statistics, Faculty of Sciences, Ankara University, Ankara, TurkeyDepartment of Biostatistics, Faculty of Veterinary Medicine, Selcuk University, Konya, TurkeyDepartment of Biostatistics, Faculty of Medicine, Ankara University, Ankara, Turkey<b>Aim: </b>As in all parametric methods, the ANCOVA method assumes that normal distributions of errors, homogeneity of variances, and error terms are independent of each other. However, unusual distributions in practice are more common than normal distribution. In this study, it is aimed to examine ANCOVA method or type 1 error rates under different distribution conditions and homogeneity of variances.<p> <b>Materials and Methods:</b> For this purpose, a simulation studies under different scenarios was conducted. Random numbers were generated from Gamma, Beta and Normal distributions considering different groups and different sample sizes. In the simulation studies, 10000 replications were run under the null hypothesis of no group differences and type-I error rates were calculated for each scenario.<p> <b>Results: </b>According to the results, in the case of the normal distribution with homogeneous variance, the proportion of Type I error is high in the groups with the sample size of n=20 and n=40. In the case of normal distribution with the heterogeneous variance, the deviation has been observed in the groups with the sample size of n = 10 and n = 30, and n = 40. These results are the same as the results of Gamma distribution. In the Beta distribution, , there is a deviation in the groups with n=10 and n=20 where the sample sizes are small.<p> <b>Conclusion:</b> The results showed that type-I error rate is affected by skewness of the distribution, sample size and homogeneity of variance. Further work can be extended by simulation studies under different distributions and parameter values.http://eurasianjvetsci.org/pdf.php3?id=1279analysis of covariancebetagammanormalrobustnesstype-i error |
| spellingShingle | Can Ateş Özlem Kaymaz Mustafa Agah Tekindal Beyza Doğanay Erdoğan Robustness of analysis of covariance (ancova) under the distributions assumptions and variance homogeneity Eurasian Journal of Veterinary Sciences analysis of covariance beta gamma normal robustness type-i error |
| title | Robustness of analysis of covariance (ancova) under the distributions assumptions and variance homogeneity |
| title_full | Robustness of analysis of covariance (ancova) under the distributions assumptions and variance homogeneity |
| title_fullStr | Robustness of analysis of covariance (ancova) under the distributions assumptions and variance homogeneity |
| title_full_unstemmed | Robustness of analysis of covariance (ancova) under the distributions assumptions and variance homogeneity |
| title_short | Robustness of analysis of covariance (ancova) under the distributions assumptions and variance homogeneity |
| title_sort | robustness of analysis of covariance ancova under the distributions assumptions and variance homogeneity |
| topic | analysis of covariance beta gamma normal robustness type-i error |
| url | http://eurasianjvetsci.org/pdf.php3?id=1279 |
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