The participants of the sample population were not limited to how many times they were allowed to play each of the gambling games (Game 21, Slots, and Roulette); the mean (average) of all the bets were used for each game played.

The mean for the bets of the sample group was found by using the mathematics formula:

Mean = (bet(1)+bet(2)+bet(3)+….+bet(n))/n

where n is the number of times played.

An Excel spreadsheet was used to record and calculate all of the participants' data (e.g. number of and how much each bet was) on all games played [Appendix A]. Each participant had three means (playing alone, playing with a participant of the same gender, and playing with a participant of the opposite gender) for each game played [Appendix C]. Sixty worksheets (one per participant) were created for documenting this data [Appendix A].

In the Excel spreadsheet, three other worksheets were created to analyze the data for each game played. The means from each participant were copied to these worksheets along with the gender and identity number given each participant. From this data, the mean and standard deviation were calculated.

The mean was found by using the mathematic formula:

X = (X(1)+ X(2)+ X(3)+….+X(n))/n

where n is the number of participants and, X() is the mean of each participant.

Since this model is dealing with a sample that is being used to estimate properties of a population, the standard deviation formula is:

Standard deviation = (((X1- X)+( X2 - X) + (X3 - X)….+(Xn- X)) / (n-1))x(1/2)

Where n is the number of participants, X() is the mean of each participant, and X is the mean of all of the means

During prior evaluation for this project, it was determined that the data be checked for statistical significance by using the Chi-squared statistical test [Appendix D]. This test is a measure that combines the strength of the relationship with information about the size of the sample to give one summary number (e.g. the validity of your data). If the summary number is equal to or larger than the "magic" number, the relationship in the table is considered to be statistical significant. The origin of the "magic" number comes from a table of percentiles representing what should happen by chance. The interpretation of the value of this "magic" number is straightforward. If a relationship that has a chi-squared statistic larger than the "magic" number is observed, one can assume that the relationship in the sample did not occur by chance. In this case, one can say that the relationship is statistically significant. Of all relationships that have occurred just by chance, 5%of them will erroneously earn the title of statistically significant. However, if the size of the sample is too small, a real relationship may not be detected. The chi-squared statistic depends on both the strength of the relationship and the size of the sample.

The actual computation and assessment of statistical significance was tedious but not mathematically difficult. There are many methods. The method chosen for this model comes from the book, Seeing Through Statistics by Jessica M Utts [7].

There are four basic steps:

· Compute the expected numbers. · Compare the observed and expected numbers. · Compute the chi-squared statistic. · Make a decision.

Using Excel, worksheets were added to calculate the Chi-squared statistic. To help the team to understand the mathematical behavior of the process, simple functions were used in the Excel program. The following steps were followed in sequence:

Step1: Compute the Expected Numbers:

The formula used for finding the expected number in any row and column combination is: Expected number = (row total)x(column total) / (table total)

Step2: Compare the Observed and Expected Numbers:

Compute for each of the cells of the table: (Observed number - Expected number)2/(Expected number)

Step3: Compute the Chi-Squared Statistic:

Compute the chi-squared statistic, by adding the numbers in all of the cells from step 2. This result is the chi-squared statistic.

Step4: Make the Decision:

Using a statistics textbook [8], one would need to look up the appropriate number in a table called "percentiles of the chi-squared distribution" using the frequency table:

Frequency = (row-1) x (column-1)