Maeghan Cahill

"Testing the Assumptions: A Simulation Study Monitoring the Effects of Manipulating
Regression and Statistical Inference Assumptions"

Advisor: Travis Atkinson
Fall 2007

Most statistical procedures allow for certain assumptions to be made in order for the results to be valid. What will change if these assumptions aren't met? We manipulate the assumptions involved in simple linear regression models, confidence intervals of population means, and confidence intervals of population proportions. We use Fathom to simulate data sets that do and do not satisfy the assumptions for these statistical procedures, and display the changes and problems that occur. For simple linear regression, we examine the change in SSE resulting from manipulating the model assumptions associated with this procedure. We also demonstrate that the coverage percentages for confidence intervals are not accurate if the assumptions are not met. For example, the coverage percentages for confidence intervals of population proportions is much less than expected when the probability of success in a population is either close to zero or close to one.

Laura Daley

"Chance vs. Skill: Assessing Shootouts in the NHL"

Advisor: Michael Schuckers

The shootout was adopted in the 2005-06 season by the National Hockey League, an ice hockey association consisting of 30 teams across the United States and Canada. The shootout eliminates ties in National Hockey League (NHL) competition. This investigation looks at the shootout in the 2005-06, 2006-07, and 2007-08 NHL seasons. We analyze results for shooters and goalies to determine the probability of scoring and whether it differs significantly from player to player. The data will be evaluated in an attempt to determine if chance or skill is the prevailing characteristic that influences the outcome of the shootout.

Team Work - Amanda Fuller, Jon MacMillan, Jeff McAdoo, Colleen Schopp, Alyce Simons

Graphical Degree Sequences

Advisor: Jim DeFranza

Abstract: The Hakimi Algorithm stated in [1] and [3] is used to determine whether or not a degree sequence is graphical. In this paper we consider degree sequences with no gaps and at least one degree repeated. More specifically, we investigate degree sequences with multiple blocks of repeated terms, and when the sum of the degree sequence can be determined as either odd or even. Using this knowledge, we also looked at the patterns that arise when applying the Hakimi Algorithm to degree sequences. From there, we formalize the ability to add vertices to a degree sequence or a graph and prove a theorem of the perfect graph for degree sequences with a block of four repeated terms. A review of definitions, algorithms and theorems create a foundation for the rest of the research done for this paper.

Ryan Kimber

"Who's Really Better? Comparing American and Latin American Baseball Players"

Advisor: Travis Atkinson

In certain experienced baseball circles, there is a common belief that Latin American players are naturally better than American players. I would imagine that this can be quite frustrating for American players, especially at the professional level. How can we determine whether or not this notion is actually true? I have decided to shed some light on the question at hand by using a multiple binary regression analysis to predict the ethnicity of players (0 for Latin Americans and 1 for Americans) based on numerous career offensive statistics such as career batting average, on base percentage, slugging percentage, and fielding percentage. As a result of my analysis, I found a model that correctly predicted the ethnicity of 73.6% of the Americans and 68.7% of the Latin Americans. Also, I performed a 2-sample t-test on all of the statistics I used and found all of the significant tests gave evidence for American supremacy at least in terms of offensive statistics.

Rob LaMere

"Estimating Win Probabilities Based on Betting Lines for Sporting Events"

Advisor: Robin Lock

We use betting lines and point spread systems for sports to determine probabilities of a team winning. For example, we investigate football or basketball schemes of betting to predict winners based on their specific betting line. The study is based on data collected from 1998 through 2007 NFL and NBA seasons. We look at the distribution of the difference between the favored team's score and the underdog's score and compare to the predicted point spread for each game. For both sports they follow the normal distribution. The distribution for the NFL data is assumed normal with a mean of 0.05 and a standard deviation of 13.19. The distribution of the NBA data is assumed normal with a mean of -.5 and a standard deviation of 11.40. The probability that a team can win is based on simple linear approximations based on the probability of winning and the point spreads.

Royce Lawrence

"Bowling and the Hot Hand"

Advisor: Michael Schuckers

Hot hand, or just luck? Ever wonder why streaks come as they do? In this paper we will investigate the theory of the hot hand; the tendency to perform at a higher level for a period of time. For example, a bowler may be more likely to continue to throw strikes after previous strikes. Using frame by frame bowling data and statistical methods, we determine if the hot hand actually exists in the sport of bowling.

Sarah MacFarland

"The Effects of Marriage on Spousal Happiness & Well-Being"

Advisor: Travis Atkinson

With a long standing appreciation for marriage, in addition to the extensive dynamics that surround family life, performing a research project encompassing both topics was of very high interest. Using raw data found on the Inter-University Consortium for Political and Social Research (ICPSR), the effects of marriage on the happiness and well being of Michigan couples was investigated. Three hundred seventy-three newlywed couples (who were all intra-racial and in their first marriage) were interviewed in Wayne County, Michigan during April-June, 1986, following their first four years of marriage. All couples, 174 White and 199 Black, were between the ages of 25 and 37. Certain Independent Variables, such as Marital Status, Total Marriage Satisfaction, Level of Happiness, and Hopeful About the Future were chosen for the final data set. General findings indicated that couples in their early years of marriage were very satisfied, and felt as though their lives were full resulting from their married lives in the early years.

Peter McGoldrick

"Statistical Analysis of the Impact of Midseason Trades in the NBA"

Advisor: Robin Lock

Abstract: NBA Teams often look to make midseason deals for reasons such as improving their current team or acquiring assets in order to have a stronger future. Due to salary cap restrictions, teams will often look for players with expiring contrasts or younger less expensive players. This has the potential to lead to trades that appear lopsided. I intend to take an in depth look at the team and individual statistics before and after a number of midseason trades.

The Journal of Quantitiative Analysis in Sports published an article entitled "A Starting Point for Analyzing Basketball Statistics." In it, a number of terms were defined to create a basis for further quantitative analysis of basketball statistics. I intend to use the terms and ideas from this article to provide a starting point for my work. I will collect data before and after the trade as to determine changes in overall team performance in terms of win/loss percentage, as well as offensive and defensisve ratings. By using statistical procedures, I will determine if there are significant changes in these categories before and after the trades.