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

  • Ratan DasguptaEmail author
Conference paper


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.


Lifestyle status Mathematical aptitude IQ Proliferation rate Martingale Excessive deviation Kokborok 

MS Subject Classification:

62P25 60G20 


  1. Dasgupta, R. (2015). Rates of convergence in CLT for two sample U-statistics in Non iid case and multiphasic growth curve. In R. Dasgupta (Ed.), Growth curve and structural equation modeling (Vol. 132, pp. 35–58). Springer Proceedings in Mathematics & Statistics.Google Scholar
  2. Dasgupta, R. (1993). Moment bounds for some stochastic processes. Sankhyā A, 55, 152–180.zbMATHGoogle Scholar
  3. Dasgupta, R. (1994). Nonuniform speed of convergence to normality while sampling from finite population. Sankhyā A, 56(2 special issue), 227–337.Google Scholar
  4. Dasgupta, R. (2006). Nonuniform rates of convergence to normality. Sankhyā A, 68, 620–635.Google Scholar
  5. Dasgupta, R. (2013). Non uniform rates of convergence to normality for two sample U-statistics in Non iid case with applications. In Advances in Growth Curve Models: Topics from the Indian Statistical Institute (Vol. 46, pp 60–88). Springer Proceedings in Mathematics & Statistics.Google Scholar
  6. Duminy, P. A., Dreyar, H.J., Steyn, P. D. G., Behr, A. L., & Vos A.J. (1991). Education for the student teacher 2. South Africa: Maskew Miller Longman.Google Scholar
  7. Rider, P. R. (1957). The midrange of a sample as an estimator of the population midrange. Journal of the American Statistical Association, 52(280), 537–542.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Theoretical Statistics and Mathematics UnitIndian Statistical InstituteKolkataIndia

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