A Note on the Application of Analysis of Variance in Medical Research

Some of the data related to bioscience are socioeconomic characteristics which are associated with different types of communicable or non-communicable diseases. For example, age, height, weight, gender, marital status, religion, education, occupation, income, food habit, working conditions, smoking habit, and utilization of time are associated with many noncommunicable diseases. This phenomenon was observed in many studies, home and abroad [ 1-20], especially these characteristics were found associated with level of obesity, prevalence of diabetes and prevalence of other non-communicable diseases. The level of obesity is measured by the ratio of body weight (in kg) to square of height (in m2). This measurement is known as body mass index (BMI) and it is a quantitative measurement. The study of association of this variable with any of the social characteristics is not possible if the variables are not classified into groups. For example, level of income and level of obesity are significantly associated [21]. Here level of obesity depends on level of income and this dependency can be studied if the values of both the variables are measured by numerical figures. In this type of analysis, the main objective is to verify whether the values of BMI vary with the variation of income and for which level(s) of income the BMI is significantly different. This type of information is not available from the study of association. This is possible if analysis of variance, one-way or multi-way, is applied. The analysis of variance helps to distinguish between the average values of BMI for any two or more levels of income. In this note one-way analysis of variance was presented to distinguish the level of BMI of children and adults of Bangladesh with respect to some social characters

The model for this analysis is

M = Grand mean of the study variable

ai = Effect of i –th level of any characteristic on which study variable depends,

eij = Random component. It is assumed that this random component follows normal distribution with mean zero and common variance.

Further assumption is that ai is not random variable

Under the assumption mentioned above the usual analysis of variance technique can be applied. It gives

Sum of squares of study variable,

Here Grand total of study variable, N = total number of observations =

Now The results can be presented in the following analysis of variance (Table 1,2 & 3).

Table 1:Anova.

In an investigation [16,20] using data of 662 children and adolescents of affluent families of Bangladesh it was observed that level of obesity measured by BMI was significantly associated with some of the socioeconomic characteristics of the children and their parents. The association indicated that level of BMI was significantly different for different levels of social characteristic. This differential behavior of level of obesity was studied here using the data of BMI instead of level of obesity. The analytical results were shown below. The analysis showed that due to the change in the levels of ages of children and adolescents the levels of BMI were significantly changed. The levels of BMI were also significantly different for those children and adolescents who had parents with different levels of education. Due to the change in the levels of family income there was significant difference in the level of BMI of the children. This analysis was almost similar as it was observed in other studies [16,20].

As another example the analytical results obtained from the data collected from 900 adults of Bangladesh [18,19] were presented here. This analysis indicated that the levels of BMI of the adults were significantly different according to the differences in the levels of residence, gender, age, education, occupation, income, smoking habit, marital status and prevalence of non-communicable diseases. This finding was also similar to those were observed earlier [ 18,19,22-25].

Table 2:Analysis of variance of BMI according to different social factors of Children and adolescents

Table 3: Analysis of variance of BMI according to different social factors of adults.

None.

No Conflicts of Interest.

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