Longitudinal Studies on Mathematical Aptitude and Intelligence Quotient of North Eastern Tribes in Tripura

Longitudinal studies are conducted on mathematical aptitude and intelligence quotient on North Eastern tribes in Tripura over successive interviews in a time span of more than 3 years, viz., 20 September 2011–28 November 2014. Analyzed longitudinal data indicate that both mathematical aptitude and intelligent quotient scores exhibit fluctuations over time and have upward trend immediately after first interaction with the interviewer, before stabilizing at a level slightly below the peak value of scores. Average level of mathematical aptitude is low, although the level of intelligence quotient score is comparatively high. Growth curves under different setups are estimated to infer about the status of tribal education and lifestyle. The score status is seen to be improving over time, although associated with mild fluctuations. Proliferation rates of different scores are estimated under different assumptions. In general, the proliferation rates reach stability towards the end of curves for large values of time. Postulating a simple model of association in scores over time based on martingales, we examine the fluctuation of scores. Excessive deviation results for martingales are derived. Under certain conditions on the martingale $$\{M_i:1\le i \le n\},$$ the excessive deviation $$P(\max _{1\le i \le n}|M_i|\ge \lambda n^{1/2})$$ is seen to be $$O(e^{-\frac{\lambda ^2}{2}(1+o(1))});\;\lambda \rightarrow \infty .$$ This is similar to the tail probability of normal distribution. Deviation of observations from response curve may be compared with normal deviate to detect the presence of assignable causes.