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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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Selcuk University Press
2020-03-01
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| Series: | Eurasian Journal of Veterinary Sciences |
| Subjects: | |
| Online Access: | http://eurasianjvetsci.org/pdf.php3?id=1279 |
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| Summary: | <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. |
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| ISSN: | 1309-6958 2146-1953 |