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. 2013 Fall;35(3):131-139.
doi: 10.1111/test.12012.

Technology-enhanced Interactive Teaching of Marginal, Joint and Conditional Probabilities: The Special Case of Bivariate Normal Distribution

Ivo D Dinov  1 , Scott Kamino  1 , Bilal Bhakhrani  1 , Nicolas Christou  1
Affiliations

Technology-enhanced Interactive Teaching of Marginal, Joint and Conditional Probabilities: The Special Case of Bivariate Normal Distribution

Ivo D Dinov et al. Teach Stat. 2013 Fall.

Abstract

Data analysis requires subtle probability reasoning to answer questions like What is the chance of event A occurring, given that event B was observed? This generic question arises in discussions of many intriguing scientific questions such as What is the probability that an adolescent weighs between 120 and 140 pounds given that they are of average height? and What is the probability of (monetary) inflation exceeding 4% and housing price index below 110? To address such problems, learning some applied, theoretical or cross-disciplinary probability concepts is necessary. Teaching such courses can be improved by utilizing modern information technology resources. Students' understanding of multivariate distributions, conditional probabilities, correlation and causation can be significantly strengthened by employing interactive web-based science educational resources. Independent of the type of a probability course (e.g. majors, minors or service probability course, rigorous measure-theoretic, applied or statistics course) student motivation, learning experiences and knowledge retention may be enhanced by blending modern technological tools within the classical conceptual pedagogical models. We have designed, implemented and disseminated a portable open-source web-application for teaching multivariate distributions, marginal, joint and conditional probabilities using the special case of bivariate Normal distribution. A real adolescent height and weight dataset is used to demonstrate the classroom utilization of the new web-application to address problems of parameter estimation, univariate and multivariate inference.

Keywords: blended instruction; science education; statistics education; teaching; technology-enhanced; webapp.

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Figures

Fig. 1
Fig. 1
The Statistics Online Computational Resource (SOCR) bivariate Normal distribution web-application (webapp) user interface. The webapp is initiated using the settings parameters on the top-left. The control panel allows specification of the type and range of the probability density calculation. The graphs on the bottom illustrate the visual representations of the probabilities as areas under the curves/surfaces.
Fig. 2
Fig. 2
Distributions of adolescents’ height (inches), left, and weight (pounds), right.
Fig. 3
Fig. 3
Estimation of the mean and standard deviation for adolescents’ height (left) and weight (right), and the corresponding Kolmogorov–Smirnoff test quantitatively indicating the good fit between the data and the corresponding Normal distribution models.
Fig. 4
Fig. 4
Using Statistics Online Computational Resource (SOCR) linear regression applet to compute the correlation ρ = Corr(C2 = height, C3 = weight).
Fig. 5
Fig. 5
Supports for the marginal distributions of X = height, left, and Y = weight, right.
Fig. 6
Fig. 6
Joint probability calculations: P(65 < X < 70∩ 120 < Y < 140) = 0.4894.
Fig. 7
Fig. 7
Conditional probability calculations: P(120 ≤ Y ≤ 140|X = 67.95) = 0.661.
See this image and copyright information in PMC

References

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