Performance assessment index in any given population is always dependent on time so that success or failure of subject(s), group or organization as the case may be can often times be assessed. In this paper we proposed and developed a nonparametric statistical method for determining at what points in a series or sequence of trials or tests in time or space subjects are most likely to attain their highest (peak) or lowest (trough, in economic parlance) scores. Classification criteria and performance assessment index was also developed that would enable researchers, policy planners and implementers statistically gauge achievements by subjects and groups that could help inform introduction of necessary remedial intervention measures. A chi-square test statistic was developed to test any desired hypothesis. The proposed method was illustrated with some sample data on the grade point averages (GPAs) of a random sample of 24 Undergraduate students (male and female in equal size for all years) of Electronics courses (I, II, III and IV) starting from their first year to their fourth year of study at the University of Nigeria Nsukka Nigeria. The same sample size on the GPAs of Physics courses (I, II, III and IV) were also collected and analyzed in other to determine the reliability of the first result and for robust conclusions. Results showed that the expected performance assessment index was lowest and negative in year two with and rising slowly to its highest and positive value in fourth year with This means that the undergraduate students on the average performed the poorest in year two and increased slowly in performance and came to the highest level of performance in year four. In testing the null hypothesis H0 of equal proportions of undergraduate students of Electronics who on the average have highest and lowest scores through their four years of study in the University, H0 was rejected with the calculated chi-square test statistic and critical chi-square test statistic, at the 5 % significant level. This indicates that differential performances in years 1,2, and 4 and hence for the observed differences in performance over the years. While the differential performance by students in year 3 was found not to be statistically significant. In conclusion some undergraduate students of Electronics would therefore seem to need intensive and structured remedial measures especially before their penultimate years to enable them enhance their academic performance in Electronics in the University.

Keywords: chi-square test statistic, maximum scores, minimum scores, nonparametric statistics, performance.