Spreadsheets in Education (eJSiE)

Pascal Pyramids: a mathematical exploration using spreadsheets

John E. Baker — Sun, 05 May 2013 19:51:30 PDT

The features of Pascal’s Triangle are generalised to 3-variable and 4-variable expressions resulting in the formation of pyramids of coefficients. The steps required to create the coefficients are also given.

Market Neutral Portfolio Selection: A Pedagogic Illustration

Clarence C. Y. Kwan — Wed, 10 Apr 2013 15:06:35 PDT

This paper considers market neutral portfolio selection, which is an advanced investment topic. It draws on an idea in the investment literature that short selling a stock in practice is like investing in an artificially constructed security. Such an idea allows this paper to extend textbook coverage of portfolio selection without short sales to a realistic long-short setting. Spreadsheet illustrations are provided, with and without using the derived analytical results. Thus, the pedagogic materials as covered in this paper can accommodate investment courses with different levels of analytical rigor.

Teaching Statistical Principles with a Roulette Simulation

Graham D. Barr et al. — Sun, 17 Mar 2013 15:21:31 PDT

This paper uses the game of roulette in a simulation setting to teach students in an introductory Stats course some basic issues in theoretical and empirical probability. Using an Excel spreadsheet with embedded VBA (Visual Basic for Applications), one can simulate the empirical return and empirical standard deviation for a range of bets in Roulette over some predetermined number of plays. In particular, the paper illustrates the difference between different playing strategies by contrasting a low payout bet (say a bet on “red”) and a high payout bet (say a bet on a particular number) by considering the expected return and volatility associated with the bets. The paper includes an Excel VBA based simulation of the Roulette wheel where students can make bets and monitor the return on the bets for one play or multiple plays. In addition it includes a simulation of the casino house advantage for repeated multiple plays; that is, it allows students to see how casinos may derive a new certain return equal to the house advantage by entertaining large numbers of bets which will systematically drive the volatility of the house advantage down to zero. This simulation has been shown to be especially effective at theUniversityofCape Townfor teaching first year Statistics students the subtler points of probability, as well as encouraging discussions around the risk-return trade-off facing gamblers. The program has also been shown to be useful for teaching students the principles of theoretical and empirical probabilities as well as an understanding of volatility.

Mass, Measurement, Materials, and More Mathematical Modeling: The Nuts and Bolts of Let’s Make an Error

Scott A. Sinex et al. — Tue, 26 Feb 2013 10:16:33 PST

How can you get students into analyzing and understanding errors? A second semester general chemistry experiment is presented that introduces students to error analysis via simple mass determinations using nuts, bolts, and washers. Students work in groups of four, each group having a triple beam pan balance. The three-hour laboratory consists of four parts: calibrating the balance using standard masses; making errors to discover the behavior of constant and proportional systematic errors via data analysis in Excel; analyzing the effects of an errant nut in a sequential addition of nuts to a bolt, graphical analysis, and sharing data in Google Docs (now Google Drive) for a collaborative online discussion by groups using the chat function, and finally a verification of the errant nut problem by simulation of results in an interactive animated spreadsheet. Each group has a different set of results and must figure out what is possibly wrong with their results using online chat. Students must use some algebraic detective work to find the outlier (the errant nut), and its influence on the regression line. Students are exposed to linear regression in first semester general chemistry.

Spreadsheet Activities with Conditional Progression and Automatically Generated Feedback and Grades

Thomas C. Juster — Tue, 26 Feb 2013 09:57:00 PST

Spreadsheet activities following the Spreadsheets Across the Curriculum (SSAC) model have been modified using VBA programming to automatically generate feedback, calculate grades, and ensure that students complete them in a linear fashion. Feedback is based not only on the value of cells, but also on the formulas used to compute the values. These changes greatly ease the burden of grading on instructors, and help students more quickly master tasks and concepts by providing immediate and directed feedback to their answers. Students performed significantly better on the new spreadsheet activities compared to traditional SSAC versions, with 87% achieving perfect scores of 100%.

Central Projection in Excel – an Introduction to Virtual Reality

Jan Benacka — Mon, 14 Jan 2013 09:31:37 PST

The article presents a method of explaining the principles of virtual reality through making revolvable and sizable central projections of 3D figures in Excel.

Dynamic Surface Charts for Scattered 4-D Data in Excel Spreadsheets

Daniel Hsieh et al. — Thu, 27 Dec 2012 17:11:24 PST

Visualizations that are low-cost in memory are desirable. We present a method for stitching three-dimensional scattered data from multiple worksheets into a dynamic “animation-like” surface chart in Excel. This method is useful when (1) the user hard-codes the data points to conserve memory; employing such strategy scales better than soft-coding data values, (2) the data values are hard-coded by an unknown source, or (3) the function is complex and requires a user-defined function to output values into cells. In particular, we demonstrate an application in biology where rigid motion (rotation and translation are the only transformations applied to an object in 3-D space) is used to model the free energy gain/loss by surveying various placements and orientations of membrane proteins with respect to their environment. Our strategy involves a simple concept of scrolling through an order of worksheets, and can be extended to even more dimensions (i.e. scrolling through workbooks if necessary)

Power System Load Flow Analysis using Microsoft Excel

K. S. Sastry Musti et al. — Wed, 12 Dec 2012 16:41:44 PST

This paper presents the design and development of a Microsoft Excel based Power System Load Flow Analysis (MSEBPSLF) tool and its application for system planning and operation. This is a simple desktop tool which provides an interactive and simplified interface for users to store different systems with different operating conditions and then to observe the response of the system. Four different load flow algorithms have been implemented to provide wider choice for the users. All intermediate numerical results are made available for verification purposes. End results are verified and benchmarked with standard applications such as PSS/E, PowerWorld, InterPSS etc. The standard IEEE 14-bus system is provided with the spreadsheet to provide a head start for users.

Improving How Microsoft Excel Displays Default Extremely Small Probability Values

David A. Larson et al. — Wed, 12 Dec 2012 14:51:09 PST

Microsoft Excel™’s default method of displaying probability values observed in the sample, in the case of very small values, is confusing to beginning students in statistics. This is because Excel displays them in engineering notation (3.52955E-.05, as opposed to .0000352955, for example). In addition, high quality statistical software programs, such as SAS/STAT™, never display an actual default probability value as small as .0000352955. For any probability value in a sample less than 1-in-10,000, SAS will display the given probability value as <.0001.

P-Value Approximations for T-Tests of Hypothesis

John A. Rochowicz Jr — Tue, 04 Dec 2012 01:51:19 PST

Mathematics can be analyzed in different ways and each method supports the other with the same results. This paper describes a number of approaches for finding the p-values necessary for making decisions about statistical t-tests of hypothesis. The concepts of areas under the Student’s t-curve and the mathematical connections between tests of hypothesis, probabilities and areas under a curve are presented. The EXCEL function TDIST and various approximation techniques from numerical analysis are discussed. Numerical analysis techniques include Simpson’s Rule for integration and Monte Carlo integration. Also an approximation from the National Bureau of Standards is provided. Comparisons of results from each method are presented. Numerical approximations are shown to be as important and as accurate as exact solutions.