The Statistical Bias in Genetic Model Analysis with Varying Model Parameters

Abstract

This study was presented by considering models with or without interactions for large and small sample sizes. The paper, therefore seeks to analyze the relationships between heredity (response) and the predictors (age and sex) for large and small sample sizes and for model with interaction (full) or without interaction (reduced). Ordinary Least Square (OLS) was employed to analyze the data of heredity, age and sex of human beings obtained from Sameera (2014). Correlation was considered to obtain the degree of relationships among the variables. Grand Mean Absolute Deviation (  was proposed as a measure of the statistical bias that exists in the relationship between parents and the offspring in genetic studies. It was observed that the grand mean of the model with interaction for small sample size is greater than the grand mean of the model without interaction for small sample size by 95.89%. The grand mean for model with interaction for large sample size was also greater than the grand mean of the model without interaction for large sample size, but with just percentage level of 26.61. The difference between the grand mean for model with interaction for small and large sample size was 8.51%, while that of model without interaction for small and large sample size was 94.87%. This shows that the model without interaction becomes stronger as the sample size increases, even more than the strength gained by model with interaction for increased sample sizes. The correlations between all the variables, heredity, age and sex are all positive, this reveals that, the relationships between parents and offspring in terms of genetic behavior is positive, irrespective of full or reduced models. It also shows that interaction of age and sex in genetic analysis of heredity is encouraged. Heredity and sex has the highest relationship than other pair for both models. The application of  reveals that large sample size reduces the statistical bias in genetic model analysis, irrespective of whether full or reduced model used. Also, full model reduces the statistical bias in genetic model analysis, irrespective of the sample size. Hence, the proposed measure suggests that for bias to be reduced in genetic analysis, the sample size should be large and full model (with interaction) be used.