Presentation on theme: "Tracking and Analyzing Student Success Data Part 3."— Presentation transcript:
Tracking and Analyzing Student Success Data Part 3
State/Territory Area (km 2 ) Afghanistan 645,807606,467 Albania 28,74825,643 Algeria 2,381,7412,556,276 American Samoa 197205 Andorra 464577 Anguilla 9688 Antigua & Barbuda 442498 Argentina 2,777,4092,537,555 Armenia 29,74325,859 Aruba 193210 Australia 7,682,5577,365,389 Austria 83,85881,434 Azerbaijan 86,53091,752 Bahamas 13,9629,125 Bahrain 694725 Bangladesh 142,61598,722 Barbados 431517 Belgium 30,51825,417 Belize 22,96520,648 Benin 112,620108,768 ……… Which column lists the correct areas?
A Bit of History Late 1800s: Astronomer Simon Newcomb noticed that the early pages of log table books were more grubby than the later pages Users were looking-up numbers that started with digit 1 more often than numbers starting with, say, digit 5. If the leading (first) digit is d, then the frequency of occurrence (probability) of the leading digit is Log 10 (1 + 1/d)
If the leading (first) digit is d, then the frequency of occurrence (probability) of the leading digit is Log 10 (1 + 1/d) Leading digit (d) 123456789 Probability of occurrence 30%18%12%10%8%7%6%5%< 5% NumberLeading (first) digit 3503 420574 0.646
A Bit of History (cont’d) Late 1930s: Physicist Frank Benford rediscovered Newcomb’s formula: Log 10 (1+1/d) Benford’s Law Source: The Law of Anomalous Numbers, F. Benford, Proceedings of the American Philosophical Society, Vol. 78, 1938, pp: 551-572.
What can the deviations from the Benford’s Law tell us?
Deviation from Benford’s Law less deviationmore deviation
Final Exam Score vs. Deviation from Benford’s Law (Chemistry) Thanks to professors Randall Hall & Leslie Butler for providing the exam score data
Final Exam Score vs. Deviation from Benford’s Law For every 1/5 th of deviation from Benford’s Law, the exam score is decreased by 1/2 standard deviation
To what degree is the average time correlated with the final exam scores? -0.03 (about 7 times less than the correlation found by using only the first digits; almost no correlation)
The correlation (-0.2) is small but surprisingly good (?) * Typical correlations encountered in educational research ~ 0.3 * High school GPA & SAT ® -math correlated at 0.23 * SAT ® -math and first-year college GPA correlated at 0.26 Source: College Board Research Report No 2008-5: Validity of the SAT ® for Predicting First-Year College Grade Point Average, Jennifer L. Kobrin, et al.
Using average time: 0% of the students can be flagged Students who sat for the final exam Students who did not sit for the final exam
Using Benford’s Law: ~19% of the students can be flagged Students who sat for the final exam Students who did not sit for the final exam
* In time to completion data the first digit (or deviations from the Benford’s Law) carries more actionable information than all of the digits combined! Summary * Possibility of weighting the deviations from Benford's Law to identify at-risk students so that instructors can intervene effectively * Possibility of weighting the deviations from Benford’s Law in deciding on specific study plans/personalized learning resources within Mastering