Introduction
The use of instrumental methods of analysis allows weighted and data-driven decision-making, the study of patterns in distributions, and the identification of relationships. This paper proposed using the concept of probabilities to calculate the probabilities of the occurrence of specific events, as well as ranking. The ultimate goal of this paper was to identify measures of academic success for each professor and for each of the three universities and compare them to each other. Such a strategy will not only allow us to assess which universities and professors are doing better in their educational functions but also create further solutions that will help tune academic models more reliably.
Analysis
Calculating Probabilities
One of the main objectives of the current study was to calculate the probabilities of occurrence for both individual events and conditional events. In the case of particular events, data on the number of students who graduated, the number of students who published a research paper, and the total number of students are known for each professor at each of the three universities. To calculate the probabilities of individual events, the number of favorable cases was divided by the total number.
For example, for J.W. Blake of WWCC, the likelihood that a student would graduate was calculated by dividing 256 by 264. A similar practice was applied to the possibility that a student would publish a research paper. Thus, the final probabilities for the three universities were compiled and are shown in Table 1.
Table 1. Results of calculating the probabilities of graduating and making a publication for the three universities
As can be seen, the probability of student publication is higher for NWCC, but overall, the three universities are not much different. The situation is slightly different for the likelihood of publication: EWCC shows the highest overall proportion of students who have made publications, while NWCC, which has the highest proportion of students who have graduated, has the lowest. It is also noteworthy that the likelihood of graduating from a publication is, on average, about 2.6 times lower than the likelihood of graduating a student. In other words, about one in three graduating students makes a scholarly publication.
Conditional probability is calculated by determining whether events are dependent or independent. By definition, for independent events, the outcome of one has no effect on the result of the other, which is the situation for the data under study (Pérez et al., 2022). Thus, the probability of a student graduating from university does not affect the likelihood of making a publication and vice versa.
Therefore, for such events, the conditional probability is equal to the likelihood of the original event, that is, P(A | B) = P(A) (LT, 2023). Table 2 summarizes the results for the conditional probabilities of each university. It can be seen that the probability of publishing a scholarly paper under the condition of graduating from a university is higher for the EWCC and the lowest for the NWCC.
Table 2. Results of conditional probability calculations
Ranking
The second task of the analysis was to rank both individual professors within a single university and entire universities. The ranking was accomplished using =RANK.EQ(), which allows the automatic assignment of numbers to values based on their value (CFI, 2023). A format in descending order was chosen, so the highest probabilities received the lowest numbers.
Table 3 shows the overall ranking results for each professor at each of the three universities. From the results, at WWCC, the highest score was for A.F. Paul, and the worst performer in the educational function was W.H. Greiner. Similarly, for the EWCC, Professor K.G. Ross had the most alumni and publications, and I.A. Frank had the least. For the NWCC, the best score was characteristic of M.A. Carter, and the lowest was that of M.P. Drake.
Table 3. Results of the overall ranking of professors at each university
Conclusion
To summarize, it bears repeating that statistical analysis tools are helpful in making reliable, evidence-based decisions. For this paper, analysis was used to calculate probabilities and rank professors at three universities based on them. The overall result is that most graduates were characteristic of NWCC, and most publications, as well as publications under the condition of student graduation, were characteristic of EWCC. The best results came from Professors A.F. Paul (WWCC), K.G. Ross (EWCC), and M.A. Carter (NWCC). Thus, based on the results, decision-makers can adjust their performance, reward the best professors, and determine how to use their example to help professionals who are doing worse.
References
CFI. (2023). RANK function. Corporate Finance Institute. Web.
LT. (2023). Conditional probability and independent events. LibreTexts Statistics. Web.
Pérez, G., Crispim, C. M., & Pizzinga, A. (2022). Independent events and their complements. International Journal of Mathematical Education in Science and Technology, 53(12), 3470-3483.