SOCR: Statistics Online Computational Resource

Abstract

The need for hands-on computer laboratory experience in undergraduate and graduate statistics education has been firmly established in the past decade. As a result a number of attempts have been undertaken to develop novel approaches for problem-driven statistical thinking, data analysis and result interpretation. In this paper we describe an integrated educational web-based framework for: interactive distribution modeling, virtual online probability experimentation, statistical data analysis, visualization and integration. Following years of experience in statistical teaching at all college levels using established licensed statistical software packages, like STATA, S-PLUS, R, SPSS, SAS, Systat, etc., we have attempted to engineer a new statistics education environment, the Statistics Online Computational Resource (SOCR). This resource performs many of the standard types of statistical analysis, much like other classical tools. In addition, it is designed in a plug-in object-oriented architecture and is completely platform independent, web-based, interactive, extensible and secure. Over the past 4 years we have tested, fine-tuned and reanalyzed the SOCR framework in many of our undergraduate and graduate probability and statistics courses and have evidence that SOCR resources build student's intuition and enhance their learning.

Figure 1

Virtual card experiment: Card drawing simulation and modeling the frequency distributions of outcomes.

Figure 2

Confidence intervals experiment: A virtual experiment that provides empirical evidence for consistence of the heuristic and the constructive definitions of confidence intervals. The experiment also shows the empirical effects of the sample size and the confidence level on the confidence intervals.

Figure 3

Overall and daily statistics of the SOCR resources traffic for the month of August 2006.

Figure 4

National and international SOCR resource utilization. This figure illustrates the geographic location of the 100 most recent global SOCR visitors on one randomly chosen day (08/12/2006).

Figure 5

Distribution modeling toolbox: A (standard) Beta distribution, its parameters and shape change and effects of interactive region changes on the probability.

Figure 6

A virtual wavelet game: The interplay between the spatial, frequency, location and signal-intensity parameters and their effects on the data may be subtle and difficult to understand by students. This game demonstrates interactively the specific effects of each of these factors.

Figure 7

Experiment demonstrating distribution mixture modeling using expectation maximization parameter-estimation: An exploratory tool that demonstrates the effects of the starting mixture of isotropic kernels (location, size) on the final mixture of 3 anisotropic Gaussian models using expectation maximization to estimate the 18 parameters specifying the complete model. The demonstration ends with the classification of all 2D starting points based on which marginal kernel distribution is the most likely candidate that explains their presence in the observed sample (see kernel and point colorings).

Figure 8

SOCR modeler: A polynomial or a distribution model may be fit to real data entered manually as a spreadsheet, read from a file, or virtually generated by mouse clicks. Visual assessment of the model fit may be compared to the analytical model expression and to a statistical assessment of the quality of the fit obtained by using χ² goodness-of-fit test. Students may interactively determine the order of the polynomial model, or the distribution parameters of the model, by exploiting different values and observing the visual impact on the model fit.

Figure 9

SOCR analyses: 2-way analysis of variance (ANOVA) example on randomly generated data.

Figure 10

SOCR charts: a newly added tool for data summary and graphical data characterization. This is a demonstration of the Box-And-Whisker plot for 2 categories, each with 3 series within it. Summary statistics for all plots are provided on the bottom to complement the qualitative graphical descriptions with their quantitative counterparts.