April  2017, 2(2): 141-175. doi: 10.3934/bdia.2017015

Identifying electronic gaming machine gambling personae through unsupervised session classification

Faculty of Computer Science, Dalhousie University, 6050 University Avenue, Halifax, NS B3H 4R2, Canada

Received  May 2017 Revised  October 2017 Published  April 2017

The rising accessibility in gambling products, such as Electronic Gaming Machines (EGM), has increased interest in the effects of gambling; in particular, the potential for impulse control disorders, such as problem gambling. Nevertheless, empirical research of EGM gambling behaviour is scarce. In this exploratory study, we apply data mining techniques on 46,416 gambling sessions, collected in situ from 288 EGMs. Our research focused on identifying the at-risk behavioural markers of sessions to help distinguish gambling personae. Our data included measures of gambling involvement, out-of pocket expense of sessions, amount won, and cost of gambling. This research, discusses the methodology used to collect and analyze the required gambling measures, explains the criteria used for identifying valid sessions, and combines outlier mining methods to identify instances of heavily involved gambling (i.e., outliers). Our results suggest that sessions were classified as potential non-problem, potential low-risk, potential moderate risk, and potential problem gambling sessions. Further, outlier sessions were more heavily involved in terms of gambling intensity and amount redeemed, despite having low duration times. Finally, our methods suggest that the lack of player identification does not prevent one from identifying the potential incidence of problem gambling behaviour.

Citation: Maria Gabriella Mosquera, Vlado Keselj. Identifying electronic gaming machine gambling personae through unsupervised session classification. Big Data & Information Analytics, 2017, 2 (2) : 141-175. doi: 10.3934/bdia.2017015
References:
[1]

C. C. Aggarwal, Outlier Analysis, Springer, New York, 2013.  Google Scholar

[2]

American Psychiatric Association, Diagnostic and Statistical Manual of Mental Disorders, 4th edition, American Psychiatric Association, Washington, DC, 1994. Google Scholar

[3]

G. Banks, R. Fitzgerald and L. Sylvan, Gambling: Productivity Commission Inquiry Report, Technical Report 50,2010, http://www.pc.gov.au/inquiries/completed/gambling-2009/report/gambling-report-volume1.pdf(visited on: 09/12/2012). Google Scholar

[4]

M. Berry and G. Linoff, Data Mining Techniques for Marketing, Sales, and Customer Relationship Management, 2nd edition, Wiley Publishing Inc., Indianapolis, 2004. Google Scholar

[5]

J. BravermanR.A. LaBrie and H.J. Shaffer, A taxometric analysis of actual Internet sport gambling behavior, Psychological Assessment, 23 (2011), 234-244.  doi: 10.1037/a0021404.  Google Scholar

[6]

J. BravermanD.A. LaPlanteS.E. Nelson and H.J. Shaffer, Using cross-game behavioral markers for early identification of high-risk Internet gamblers, Psychology of Addictive Behaviors, 27 (2013), 868-877.  doi: 10.1037/a0032818.  Google Scholar

[7]

J. Braverman and H.J. Shaffer, How do gamblers start gambling: Identifying behavioral markers for high-risk Internet gambling, European Journal of Public Health, 22 (2012), 273-278.  doi: 10.1093/eurpub/ckp232.  Google Scholar

[8]

S. Carpendale, Evaluating information visualizations, in Information Visualization, Lecture Notes in Computer Science, A simple univariate outlier identification procedure, 4950 (2008), 19-45. doi: 10.1007/978-3-540-70956-5_2.  Google Scholar

[9] National Research Council, Pathological Gambling: A Critical Review, National Academies Press, Washington D.C., 1999.   Google Scholar
[10]

P. Delfabbro, A. Osborn, M. Nevile, L. Skelt and J. MacMillen, Identifying Problem Gamblers in Gambling Venues, Technical report, 2007. Google Scholar

[11]

M.J. DixonK.A. HarriganM. JarrickV. MacLarenJ.A. Fugelsang and E. Sheepy, Psychophysiological arousal signatures of near-misses in slot machine play, International Gambling Studies, 11 (2011), 393-407.  doi: 10.1080/14459795.2011.603134.  Google Scholar

[12]

L. DixonR. Trigg and M. Griffiths, An empirical investigation of music and gambling behaviour, International Gambling Studies, 7 (2007), 315-326.  doi: 10.1080/14459790701601471.  Google Scholar

[13]

S. DragicevicG. Tsogas and A. Kudic, Analysis of casino online gambling data in relation to behavioural risk markers for high-risk gambling and player protection, International Gambling Studies, 11 (2011), 377-391.  doi: 10.1080/14459795.2011.629204.  Google Scholar

[14]

M. ElleryS.H. Stewart and P. Loba, Alcohol's effects on video lottery terminal (vlt) play among probable pathological and non-pathological gamblers, Journal of Gambling Studies, 21 (2005), 299-324.  doi: 10.1007/s10899-005-3101-0.  Google Scholar

[15]

J. Ferris and H. Wynne, The Canadian Problem Gambling Index: Final Report, Technical Report, 2001, http://www.ccgr.ca/en/projects/resources/CPGI-Final-Report-English.pdf(visited on: 06/28/2013). Google Scholar

[16]

G. Data, Canadian Gaming Market Report, Technical report, 2011, http://www.gamblingdata.com/files/Gambling%20Data%20Canadian%20Gaming%20Market%20Report%20Final_0.pdf (visited on: 04/10/2013). Google Scholar

[17]

GSA, G2S Message Protocol v1. 1 Game-to-system, Technical Report GSA-P0075. 024. 00-2011, GSA, 2011. Google Scholar

[18]

GSA, G2S Message Protocol v2. 0 Game-to-system, Technical Report GSA-P0075. 0800. 00-2006, GSA, 2006. Google Scholar

[19]

J. Han and M. Kamber, Data Mining: Concepts and Techniques, 3rd edition, Morgan Kaufmann, Waltham, 2012. Google Scholar

[20]

K.A. Harrigan and M. Dixon, Par sheets, probabilities, and slot machine play: Implications of problem and non-problem gambling, Journal of Gambling Issues, 23 (2009), 81-110.   Google Scholar

[21]

K.A. Harrigan, Slot machine structural characteristics: Distorted player views of payback percentages, Journal of Gambling Issues, 20 (2007), 215-234.   Google Scholar

[22]

K.A. Harrigan, Slot machines: Pursuing responsible gaming practices for virtual reels and near misses, International Journal of Mental Health Addiction, 7 (2009), 68-83.  doi: 10.1007/s11469-007-9139-8.  Google Scholar

[23]

C. Hennig, Cluster-wise assessment of cluster stability, Computational Statistics & Data Analysis, 52 (2007), 258-271.  doi: 10.1016/j.csda.2006.11.025.  Google Scholar

[24]

D.C. Hoaglin, John W. Tukey and data analysis, Statistical Science, 18 (2003), 311-318.  doi: 10.1214/ss/1076102418.  Google Scholar

[25]

B. Iglewicz and S. Banerjee, A Simple Univariate Outlier Identification Procedure, Proceedings of Annual Meeting of the American Statistical Association, 2001. Google Scholar

[26]

R.A. LaBrieD.A. LaPlanteS.E. NelsonA. Schumann and H.J. Shaffer, Assessing the playing field: A prospective longitudinal study of Internet sports gambling behavior, Journal of Gambling Studies, 23 (2007), 347-362.  doi: 10.1007/s10899-007-9067-3.  Google Scholar

[27]

R.A. LaBrieS.A. KaplanD.A. LaPlanteS.E. Nelson and H.J. Shaffer, Inside the virtual casino: A prospective longitudinal study of actual Internet casino gambling, European Journal of Public Health, 18 (2008), 410-416.  doi: 10.1093/eurpub/ckn021.  Google Scholar

[28]

D. A. LaPlanteS. E. NelsonR. A. LaBrie and H. J. Shaffer, Stability and progression of disordered gambling: Lessons from longitudinal studies, Canadian Journal of Psychiatry, 53 (2008), 52-60.  doi: 10.1177/070674370805300108.  Google Scholar

[29]

D.A. LaPlanteS.E. NelsonR.A. LaBrie and H.J. Shaffer, Disordered gambling, type of gambling and gambling involvement in the British gambling prevalence survey 2007, European Journal of Public Health, 21 (2011), 532-537.  doi: 10.1093/eurpub/ckp177.  Google Scholar

[30]

H. Liu and V. Keselj, Combined mining of web server logs and web contents for classifying user navigation patterns and predicting users' future requests, Data & Knowledge Engineering, 61 (2007), 304-330.  doi: 10.1016/j.datak.2006.06.001.  Google Scholar

[31]

P. LobaS. H. StewartR. M. Klein and J. R. Blackburn, Manipulations of the features of standard video lottery terminal (VLT) games: Effects in pathological and non-pathological gamblers, Journal of Gambling Studies, 17 (2001), 94-98.   Google Scholar

[32]

V.V. MacLarenJ.A. FugelsangK. Harrigan and M. Dixon, The personality of pathological gamblers: A meta-analysis, Clinical Psychology Review, 31 (2011), 1057-1067.  doi: 10.1016/j.cpr.2011.02.002.  Google Scholar

[33]

K. Marshall, Gambling 2011, Technical Report 4,2011, http://www.statcan.gc.ca/pub/75-001-x/2011004/article/11551-eng.pdf(visited on: 04/10/2013). Google Scholar

[34]

S. MishraM.L. Lumiére and R.J. Williams, Gambling as a form of risk-taking: Individual differences in personality, risk-accepting attitudes, and behavioral preferences for risk, Personality and Individual Differences, 49 (2010), 616-621.  doi: 10.1016/j.paid.2010.05.032.  Google Scholar

[35] National Research Council, Pathological Gambling: A Critical Review, The National Academies Press, Washington D.C., 1999.   Google Scholar
[36]

S.R. NelsonD.A. LaPlanteA.J. PellerA. SchumannR.A. LaBrie and H.J. Shaffer, Real limits in the virtual world: Self-limiting behavior of Internet gamblers, Journal of Gambling Studies, 24 (2008), 463-477.  doi: 10.1007/s10899-008-9106-8.  Google Scholar

[37]

J. Pallant, SPSS Survival Manual: A Step By Step Guide to Data Analysis Using SPSS, 4th edition, Allen & Unwin, Sydney, 2011. Google Scholar

[38]

Y. Peng, K. Gang and Y. Shi (eds. ), Knowledge-rich data mining in financial risk detection, in Computational Science - ICCS 2009 (eds. G. Allen, J. Nabrzyski, E. Seidel, G. D. van Albada, J. Dongarra and P. M. A. Sloot), Springer Berlin Heidelberg, 5545 (2009), 534-542. doi: 10.1007/978-3-642-01973-9_60.  Google Scholar

[39]

D. T. PhamS. S. Dimov and C. D. Nguyen, Selection of k in k-means clustering, Journal of Mechanical Engineering Science, 219 (2005), 103-119.  doi: 10.1243/095440605X8298.  Google Scholar

[40]

A. Rakhlin and A. Caponnetto (eds. ), Stability of k-means clustering, in Advances in Neural Information Processing Systems 19 (eds. B. Schölkopf, J. Platt and T. Hoffman), MIT Press, (2006), 1121-1128. http://papers.nips.cc/paper/3116-stability-of-k-means-clustering (visited on: 12/10/2014) Google Scholar

[41]

Responsible Gambling Council, Electronic Gaming Machines and Problem Gambling, Saskachewan Liquour and Gaming Authority, 2006, http://www.responsiblegambling.org/docs/research-reports/electronic-gaming-machines-and-problem-gambling.pdf?sfvrsn=10 (visited on: 06/28/2013). Google Scholar

[42]

Responsible Gambling Council, Canadian Gambling Digest 2011-2012, Technical report, 2013, http://www.responsiblegambling.org/docs/default-document-library/20130605_canadian_gambling_digest_2011-12.pdf?sfvrsn=2 (visited on: 05/04/2015). Google Scholar

[43]

G. Schwartz, The Impulse Economy, Atria Books, New York, 2011. Google Scholar

[44]

S. Seo, A Review and Comparison of Methods for Detecting Outliers in Univariate Data Sets, M. S thesis, University of Pittsburg in Pensylvania, 2006. Google Scholar

[45]

H.J. Shaffer and D.A. Korn, Gambling and related mental disorders: A public health analysis, Annual Review of Public Health, 23 (2002), 171-212.  doi: 10.1146/annurev.publhealth.23.100901.140532.  Google Scholar

[46]

H.J. ShafferA.J. PellerD.A. LaPlanteS.E. Nelson and R.A. LaBrie, Toward a paradigm shift in Internet gambling research: From opinion and self-report to actual behavior, Addiction Research and Theory, 18 (2010), 270-283.  doi: 10.3109/16066350902777974.  Google Scholar

[47]

J. Sim and C.C. Wright, Understanding interobserver agreement: The Kappa statistic, Family Medicine, 37 (2005), 360-363.   Google Scholar

[48]

S. H. StewartP. CollinsJ. R. BlackburnM. Ellery and R. M. Klein, Heart rate increase to alcohol administration and video lottery terminal (VLT) play among regular VLT players, Psychology of Addictive Behaviors, 19 (2005), 94-98.  doi: 10.1037/0893-164X.19.1.94.  Google Scholar

[49]

S. Tufféry, Data Mining and Statistics for Decision Making, John Wiley & Sons, Ltd., Chichester, 2011. doi: 10.1002/9780470979174.  Google Scholar

[50]

A.J. Viera and J.M. Garrett, The Kappa statistic in reliability studies: Use, interpretation, and sample size requirements, Journal of the American Physical Therapy Association, 85 (2005), 257-268.   Google Scholar

[51]

C. Wheelan, Naked Statistics: Stripping the Dread from the Data, W. W. Norton and Company, New York, 2013. Google Scholar

[52]

R. J. Williams, R. A. Volberg and R. M. G. Stevens, The Population Prevalence of Problem Gambling: Methodological Influences, Standardized Rates, Jurisdictional Differences, and Worldwide Trends, Technical report, 2012, https://www.uleth.ca/dspace/bitstream/handle/10133/3068/2012-PREVALENCE-OPGRC%20(2).pdf?sequence=3 (visited on: 08/12/2013). Google Scholar

[53]

D. S. WilsonR. A. Kauffman and M. S. Purdy, A program for at-risk high school students informed by evolutionary science, PLoS ONE, 31 (2002), 76-77.  doi: 10.1371/journal.pone.0027826.  Google Scholar

[54]

I.H. Witten and E. Frank, Data mining: Practical machine learning tools and techniques, Newsletter: ACM SIGMOD Record Homepage archive, 31 (2002), 76-77.  doi: 10.1145/507338.507355.  Google Scholar

[55]

Z. Xuan and H. Shaffer, How do gamblers end gambling: Longitudinal analysis of Internet gambling behaviors prior to account closure due to gambling related problems, Journal of Gambling Studies, 25 (2009), 239-252.  doi: 10.1007/s10899-009-9118-z.  Google Scholar

show all references

References:
[1]

C. C. Aggarwal, Outlier Analysis, Springer, New York, 2013.  Google Scholar

[2]

American Psychiatric Association, Diagnostic and Statistical Manual of Mental Disorders, 4th edition, American Psychiatric Association, Washington, DC, 1994. Google Scholar

[3]

G. Banks, R. Fitzgerald and L. Sylvan, Gambling: Productivity Commission Inquiry Report, Technical Report 50,2010, http://www.pc.gov.au/inquiries/completed/gambling-2009/report/gambling-report-volume1.pdf(visited on: 09/12/2012). Google Scholar

[4]

M. Berry and G. Linoff, Data Mining Techniques for Marketing, Sales, and Customer Relationship Management, 2nd edition, Wiley Publishing Inc., Indianapolis, 2004. Google Scholar

[5]

J. BravermanR.A. LaBrie and H.J. Shaffer, A taxometric analysis of actual Internet sport gambling behavior, Psychological Assessment, 23 (2011), 234-244.  doi: 10.1037/a0021404.  Google Scholar

[6]

J. BravermanD.A. LaPlanteS.E. Nelson and H.J. Shaffer, Using cross-game behavioral markers for early identification of high-risk Internet gamblers, Psychology of Addictive Behaviors, 27 (2013), 868-877.  doi: 10.1037/a0032818.  Google Scholar

[7]

J. Braverman and H.J. Shaffer, How do gamblers start gambling: Identifying behavioral markers for high-risk Internet gambling, European Journal of Public Health, 22 (2012), 273-278.  doi: 10.1093/eurpub/ckp232.  Google Scholar

[8]

S. Carpendale, Evaluating information visualizations, in Information Visualization, Lecture Notes in Computer Science, A simple univariate outlier identification procedure, 4950 (2008), 19-45. doi: 10.1007/978-3-540-70956-5_2.  Google Scholar

[9] National Research Council, Pathological Gambling: A Critical Review, National Academies Press, Washington D.C., 1999.   Google Scholar
[10]

P. Delfabbro, A. Osborn, M. Nevile, L. Skelt and J. MacMillen, Identifying Problem Gamblers in Gambling Venues, Technical report, 2007. Google Scholar

[11]

M.J. DixonK.A. HarriganM. JarrickV. MacLarenJ.A. Fugelsang and E. Sheepy, Psychophysiological arousal signatures of near-misses in slot machine play, International Gambling Studies, 11 (2011), 393-407.  doi: 10.1080/14459795.2011.603134.  Google Scholar

[12]

L. DixonR. Trigg and M. Griffiths, An empirical investigation of music and gambling behaviour, International Gambling Studies, 7 (2007), 315-326.  doi: 10.1080/14459790701601471.  Google Scholar

[13]

S. DragicevicG. Tsogas and A. Kudic, Analysis of casino online gambling data in relation to behavioural risk markers for high-risk gambling and player protection, International Gambling Studies, 11 (2011), 377-391.  doi: 10.1080/14459795.2011.629204.  Google Scholar

[14]

M. ElleryS.H. Stewart and P. Loba, Alcohol's effects on video lottery terminal (vlt) play among probable pathological and non-pathological gamblers, Journal of Gambling Studies, 21 (2005), 299-324.  doi: 10.1007/s10899-005-3101-0.  Google Scholar

[15]

J. Ferris and H. Wynne, The Canadian Problem Gambling Index: Final Report, Technical Report, 2001, http://www.ccgr.ca/en/projects/resources/CPGI-Final-Report-English.pdf(visited on: 06/28/2013). Google Scholar

[16]

G. Data, Canadian Gaming Market Report, Technical report, 2011, http://www.gamblingdata.com/files/Gambling%20Data%20Canadian%20Gaming%20Market%20Report%20Final_0.pdf (visited on: 04/10/2013). Google Scholar

[17]

GSA, G2S Message Protocol v1. 1 Game-to-system, Technical Report GSA-P0075. 024. 00-2011, GSA, 2011. Google Scholar

[18]

GSA, G2S Message Protocol v2. 0 Game-to-system, Technical Report GSA-P0075. 0800. 00-2006, GSA, 2006. Google Scholar

[19]

J. Han and M. Kamber, Data Mining: Concepts and Techniques, 3rd edition, Morgan Kaufmann, Waltham, 2012. Google Scholar

[20]

K.A. Harrigan and M. Dixon, Par sheets, probabilities, and slot machine play: Implications of problem and non-problem gambling, Journal of Gambling Issues, 23 (2009), 81-110.   Google Scholar

[21]

K.A. Harrigan, Slot machine structural characteristics: Distorted player views of payback percentages, Journal of Gambling Issues, 20 (2007), 215-234.   Google Scholar

[22]

K.A. Harrigan, Slot machines: Pursuing responsible gaming practices for virtual reels and near misses, International Journal of Mental Health Addiction, 7 (2009), 68-83.  doi: 10.1007/s11469-007-9139-8.  Google Scholar

[23]

C. Hennig, Cluster-wise assessment of cluster stability, Computational Statistics & Data Analysis, 52 (2007), 258-271.  doi: 10.1016/j.csda.2006.11.025.  Google Scholar

[24]

D.C. Hoaglin, John W. Tukey and data analysis, Statistical Science, 18 (2003), 311-318.  doi: 10.1214/ss/1076102418.  Google Scholar

[25]

B. Iglewicz and S. Banerjee, A Simple Univariate Outlier Identification Procedure, Proceedings of Annual Meeting of the American Statistical Association, 2001. Google Scholar

[26]

R.A. LaBrieD.A. LaPlanteS.E. NelsonA. Schumann and H.J. Shaffer, Assessing the playing field: A prospective longitudinal study of Internet sports gambling behavior, Journal of Gambling Studies, 23 (2007), 347-362.  doi: 10.1007/s10899-007-9067-3.  Google Scholar

[27]

R.A. LaBrieS.A. KaplanD.A. LaPlanteS.E. Nelson and H.J. Shaffer, Inside the virtual casino: A prospective longitudinal study of actual Internet casino gambling, European Journal of Public Health, 18 (2008), 410-416.  doi: 10.1093/eurpub/ckn021.  Google Scholar

[28]

D. A. LaPlanteS. E. NelsonR. A. LaBrie and H. J. Shaffer, Stability and progression of disordered gambling: Lessons from longitudinal studies, Canadian Journal of Psychiatry, 53 (2008), 52-60.  doi: 10.1177/070674370805300108.  Google Scholar

[29]

D.A. LaPlanteS.E. NelsonR.A. LaBrie and H.J. Shaffer, Disordered gambling, type of gambling and gambling involvement in the British gambling prevalence survey 2007, European Journal of Public Health, 21 (2011), 532-537.  doi: 10.1093/eurpub/ckp177.  Google Scholar

[30]

H. Liu and V. Keselj, Combined mining of web server logs and web contents for classifying user navigation patterns and predicting users' future requests, Data & Knowledge Engineering, 61 (2007), 304-330.  doi: 10.1016/j.datak.2006.06.001.  Google Scholar

[31]

P. LobaS. H. StewartR. M. Klein and J. R. Blackburn, Manipulations of the features of standard video lottery terminal (VLT) games: Effects in pathological and non-pathological gamblers, Journal of Gambling Studies, 17 (2001), 94-98.   Google Scholar

[32]

V.V. MacLarenJ.A. FugelsangK. Harrigan and M. Dixon, The personality of pathological gamblers: A meta-analysis, Clinical Psychology Review, 31 (2011), 1057-1067.  doi: 10.1016/j.cpr.2011.02.002.  Google Scholar

[33]

K. Marshall, Gambling 2011, Technical Report 4,2011, http://www.statcan.gc.ca/pub/75-001-x/2011004/article/11551-eng.pdf(visited on: 04/10/2013). Google Scholar

[34]

S. MishraM.L. Lumiére and R.J. Williams, Gambling as a form of risk-taking: Individual differences in personality, risk-accepting attitudes, and behavioral preferences for risk, Personality and Individual Differences, 49 (2010), 616-621.  doi: 10.1016/j.paid.2010.05.032.  Google Scholar

[35] National Research Council, Pathological Gambling: A Critical Review, The National Academies Press, Washington D.C., 1999.   Google Scholar
[36]

S.R. NelsonD.A. LaPlanteA.J. PellerA. SchumannR.A. LaBrie and H.J. Shaffer, Real limits in the virtual world: Self-limiting behavior of Internet gamblers, Journal of Gambling Studies, 24 (2008), 463-477.  doi: 10.1007/s10899-008-9106-8.  Google Scholar

[37]

J. Pallant, SPSS Survival Manual: A Step By Step Guide to Data Analysis Using SPSS, 4th edition, Allen & Unwin, Sydney, 2011. Google Scholar

[38]

Y. Peng, K. Gang and Y. Shi (eds. ), Knowledge-rich data mining in financial risk detection, in Computational Science - ICCS 2009 (eds. G. Allen, J. Nabrzyski, E. Seidel, G. D. van Albada, J. Dongarra and P. M. A. Sloot), Springer Berlin Heidelberg, 5545 (2009), 534-542. doi: 10.1007/978-3-642-01973-9_60.  Google Scholar

[39]

D. T. PhamS. S. Dimov and C. D. Nguyen, Selection of k in k-means clustering, Journal of Mechanical Engineering Science, 219 (2005), 103-119.  doi: 10.1243/095440605X8298.  Google Scholar

[40]

A. Rakhlin and A. Caponnetto (eds. ), Stability of k-means clustering, in Advances in Neural Information Processing Systems 19 (eds. B. Schölkopf, J. Platt and T. Hoffman), MIT Press, (2006), 1121-1128. http://papers.nips.cc/paper/3116-stability-of-k-means-clustering (visited on: 12/10/2014) Google Scholar

[41]

Responsible Gambling Council, Electronic Gaming Machines and Problem Gambling, Saskachewan Liquour and Gaming Authority, 2006, http://www.responsiblegambling.org/docs/research-reports/electronic-gaming-machines-and-problem-gambling.pdf?sfvrsn=10 (visited on: 06/28/2013). Google Scholar

[42]

Responsible Gambling Council, Canadian Gambling Digest 2011-2012, Technical report, 2013, http://www.responsiblegambling.org/docs/default-document-library/20130605_canadian_gambling_digest_2011-12.pdf?sfvrsn=2 (visited on: 05/04/2015). Google Scholar

[43]

G. Schwartz, The Impulse Economy, Atria Books, New York, 2011. Google Scholar

[44]

S. Seo, A Review and Comparison of Methods for Detecting Outliers in Univariate Data Sets, M. S thesis, University of Pittsburg in Pensylvania, 2006. Google Scholar

[45]

H.J. Shaffer and D.A. Korn, Gambling and related mental disorders: A public health analysis, Annual Review of Public Health, 23 (2002), 171-212.  doi: 10.1146/annurev.publhealth.23.100901.140532.  Google Scholar

[46]

H.J. ShafferA.J. PellerD.A. LaPlanteS.E. Nelson and R.A. LaBrie, Toward a paradigm shift in Internet gambling research: From opinion and self-report to actual behavior, Addiction Research and Theory, 18 (2010), 270-283.  doi: 10.3109/16066350902777974.  Google Scholar

[47]

J. Sim and C.C. Wright, Understanding interobserver agreement: The Kappa statistic, Family Medicine, 37 (2005), 360-363.   Google Scholar

[48]

S. H. StewartP. CollinsJ. R. BlackburnM. Ellery and R. M. Klein, Heart rate increase to alcohol administration and video lottery terminal (VLT) play among regular VLT players, Psychology of Addictive Behaviors, 19 (2005), 94-98.  doi: 10.1037/0893-164X.19.1.94.  Google Scholar

[49]

S. Tufféry, Data Mining and Statistics for Decision Making, John Wiley & Sons, Ltd., Chichester, 2011. doi: 10.1002/9780470979174.  Google Scholar

[50]

A.J. Viera and J.M. Garrett, The Kappa statistic in reliability studies: Use, interpretation, and sample size requirements, Journal of the American Physical Therapy Association, 85 (2005), 257-268.   Google Scholar

[51]

C. Wheelan, Naked Statistics: Stripping the Dread from the Data, W. W. Norton and Company, New York, 2013. Google Scholar

[52]

R. J. Williams, R. A. Volberg and R. M. G. Stevens, The Population Prevalence of Problem Gambling: Methodological Influences, Standardized Rates, Jurisdictional Differences, and Worldwide Trends, Technical report, 2012, https://www.uleth.ca/dspace/bitstream/handle/10133/3068/2012-PREVALENCE-OPGRC%20(2).pdf?sequence=3 (visited on: 08/12/2013). Google Scholar

[53]

D. S. WilsonR. A. Kauffman and M. S. Purdy, A program for at-risk high school students informed by evolutionary science, PLoS ONE, 31 (2002), 76-77.  doi: 10.1371/journal.pone.0027826.  Google Scholar

[54]

I.H. Witten and E. Frank, Data mining: Practical machine learning tools and techniques, Newsletter: ACM SIGMOD Record Homepage archive, 31 (2002), 76-77.  doi: 10.1145/507338.507355.  Google Scholar

[55]

Z. Xuan and H. Shaffer, How do gamblers end gambling: Longitudinal analysis of Internet gambling behaviors prior to account closure due to gambling related problems, Journal of Gambling Studies, 25 (2009), 239-252.  doi: 10.1007/s10899-009-9118-z.  Google Scholar

Figure 1.  Binned EGM Gambling Sessions Based on Hours Played
Figure 2.  Valid EGM Gambling Sessions
Figure 3.  Test of Normality: Boxplot Analysis
Figure 4.  Test of Normality: Normal Q-Q Plot Analysis
Figure 5.  Scatterplot: Clustered sessions
Figure 6.  Between Groups One-Way ANOVA: Means Plots
Figure 7.  Boxplot Analysis on Clustered Data: Duration
Figure 8.  Scatterdot: Cluster 1 Outlier Analysis
Figure 9.  Scatterdot: Cluster 2 Outlier Analysis
Figure 10.  Scatterdot: Cluster 4 Outlier Analysis
Table 1.  Descriptive Statistics Measures of EGM Sessions
Variables Mean SD Median Mode Max. Min.
Durationa 42.03 109.09 15.67 3.87 1099.72 0.17
Bets 373 606 170 3 13,282 2
Intensity 16 10 19 20 68 0
Redeemedb 70.49 150.75 30.00 20.00 6,425.00 5.00
Vouchersb 50.44 384.18 0.05 0 40,833.05 0
Net Lossb 52.09 133.39 19.90 0 6,424.69 0
%Loss 75.46 40.97 99.97 100.00 100.00 0
a. Measured in minutes.
b. Measured in Euros.
Variables Mean SD Median Mode Max. Min.
Durationa 42.03 109.09 15.67 3.87 1099.72 0.17
Bets 373 606 170 3 13,282 2
Intensity 16 10 19 20 68 0
Redeemedb 70.49 150.75 30.00 20.00 6,425.00 5.00
Vouchersb 50.44 384.18 0.05 0 40,833.05 0
Net Lossb 52.09 133.39 19.90 0 6,424.69 0
%Loss 75.46 40.97 99.97 100.00 100.00 0
a. Measured in minutes.
b. Measured in Euros.
Table 2.  Spearman™s Rank-Order Correlation Analysis
Spearman™s Rho
Duration Bets Intensity Redeemed Vouchers Net Loss %Loss
Duration $r_{s}$ . .515** -.208** .341** -.334** .374** .406**
Sig. . .000 .000 .000 .000 .000 .000
Bets $r_{s}$ .515** . .606** .690** .224** .356** -.150**
Sig. .000 . .000 .000 .000 .000 .000
Intensity $r_{s}$ -.208** .606** . .433** .640** -.003 -.608**
Sig. .000 .000 .000 .000 .511 .000 0.000
Redeemed $r_{s}$ .341** .690** .433** . .177** .584** -.068**
Sig. .000 .000 .000 . .000 .000 .000
Vouchers $r_{s}$ -.334** .224** .640** .177** . -.512** -.980**
Sig. .000 .000 .000 .000 . .000 .000
Net Loss $r_{s}$ .374** .356** -.003 .584** -.512** . .592**
Sig. .000 .000 .511 .000 .000 . .000
%Loss $r_{s}$ .406** -.150** -.608** -.068** -.980** .592** .
Sig. .000 .000 .000 .000 .000 .000 .
** Correlation is significant at the 0.01 level (2-tailed).
Spearman™s Rho
Duration Bets Intensity Redeemed Vouchers Net Loss %Loss
Duration $r_{s}$ . .515** -.208** .341** -.334** .374** .406**
Sig. . .000 .000 .000 .000 .000 .000
Bets $r_{s}$ .515** . .606** .690** .224** .356** -.150**
Sig. .000 . .000 .000 .000 .000 .000
Intensity $r_{s}$ -.208** .606** . .433** .640** -.003 -.608**
Sig. .000 .000 .000 .000 .511 .000 0.000
Redeemed $r_{s}$ .341** .690** .433** . .177** .584** -.068**
Sig. .000 .000 .000 . .000 .000 .000
Vouchers $r_{s}$ -.334** .224** .640** .177** . -.512** -.980**
Sig. .000 .000 .000 .000 . .000 .000
Net Loss $r_{s}$ .374** .356** -.003 .584** -.512** . .592**
Sig. .000 .000 .511 .000 .000 . .000
%Loss $r_{s}$ .406** -.150** -.608** -.068** -.980** .592** .
Sig. .000 .000 .000 .000 .000 .000 .
** Correlation is significant at the 0.01 level (2-tailed).
Table 3.  Crosstabulation: Sample 1 v. Full Sample (k = 4)
Cluster Membership (Sample 1) v. Cluster Membership (Full Sample) Crosstabulation)
Cluster Mship. (Full Sample)
1 2 3 4 Total
Cluster Mship. 1 Count 6944 15 0 0 6,959
(Sample 1) Expected Count 2,071.5 2,171.1 123.2 2,593.2 6,959
% within Cluster (sample 1) 99.8% 0.2% 0% 0% 100%
% within Cluster (full sample) 100% 0.2% 0% 0% 29.8%
% of Total 29.8% 0.1% 0% 0% 29.8%
2 Count 0 7,263 0 44 7,307
Expected Count 2,175.1 2,279.7 129.4 2,722.9 7,307
% within Cluster (sample 1) 0% 99.4% 0% 0.6% 100%
% within Cluster (full sample) 0% 99.8% 0% 0.5% 31.3%
% of Total 0% 31.1% 0% 0.2% 31.3%
3 Count 0 0 413 0 413
Expected Count 122.9 128.9 7.3 153.9 413
% within Cluster (sample 1) 0% 0% 100% 0% 100%
% within Cluster (full sample) 0% 0% 100% 0% 1.8%
% of Total 0% 0% 1.8% 0% 1.8%
4 Count 0 0 0 8,649 8,649
Expected Count 2,574.5 2,698.4 153.1 3,223 8,649
% within Cluster (sample 1) 0% 0% 0% 100% 100%
% within Cluster (full sample) 0% 0% 0% 99.5% 37.1%
% of Total 0% 0% 0% 37.1% 37.1%
Total Count 6,944 7,278 413 8,693 23,328
Expected Count 6,944 7,278 413 8,693 23,328
% within Cluster (sample 1) 29.80% 31.20% 1.8% 37.3% 100%
% within Cluster (full sample) 100% 100% 100% 100% 100%
% of Total 29.80% 31.20% 1.8% 37.3% 100%
Cluster Membership (Sample 1) v. Cluster Membership (Full Sample) Crosstabulation)
Cluster Mship. (Full Sample)
1 2 3 4 Total
Cluster Mship. 1 Count 6944 15 0 0 6,959
(Sample 1) Expected Count 2,071.5 2,171.1 123.2 2,593.2 6,959
% within Cluster (sample 1) 99.8% 0.2% 0% 0% 100%
% within Cluster (full sample) 100% 0.2% 0% 0% 29.8%
% of Total 29.8% 0.1% 0% 0% 29.8%
2 Count 0 7,263 0 44 7,307
Expected Count 2,175.1 2,279.7 129.4 2,722.9 7,307
% within Cluster (sample 1) 0% 99.4% 0% 0.6% 100%
% within Cluster (full sample) 0% 99.8% 0% 0.5% 31.3%
% of Total 0% 31.1% 0% 0.2% 31.3%
3 Count 0 0 413 0 413
Expected Count 122.9 128.9 7.3 153.9 413
% within Cluster (sample 1) 0% 0% 100% 0% 100%
% within Cluster (full sample) 0% 0% 100% 0% 1.8%
% of Total 0% 0% 1.8% 0% 1.8%
4 Count 0 0 0 8,649 8,649
Expected Count 2,574.5 2,698.4 153.1 3,223 8,649
% within Cluster (sample 1) 0% 0% 0% 100% 100%
% within Cluster (full sample) 0% 0% 0% 99.5% 37.1%
% of Total 0% 0% 0% 37.1% 37.1%
Total Count 6,944 7,278 413 8,693 23,328
Expected Count 6,944 7,278 413 8,693 23,328
% within Cluster (sample 1) 29.80% 31.20% 1.8% 37.3% 100%
% within Cluster (full sample) 100% 100% 100% 100% 100%
% of Total 29.80% 31.20% 1.8% 37.3% 100%
Table 4.  Crosstabulation: Sample 2 v. Full Sample (k = 4)
Cluster Membership (Sample 2) v. Cluster Membership (Full Sample) Crosstabulation)
Cluster Mship. (Full Sample)
1 2 3 4 Total
Cluster Mship. 1 Count 6,871 0 0 0 6,871
(Sample 2) Expected Count 2,053.1 2,148.1 122.3 2,547.5 6,871
% within Cluster (sample 2) 100% 0% 0% 0% 100%
% within Cluster (full sample) 99.6% 0% 0% 0% 29.8%
% of Total 29.8% 0% 0% 0% 29.8%
2 Count 28 7,162 0 0 7,190
Expected Count 2,148.5 2247.8 128 2,665.7 7,190
% within Cluster (sample 2) 0.4% 9, 9.6% 0% 0% 100%
% within Cluster (full sample) 0.4% 99.2% 0% 0% 31.10%
% of Total 0.1% 31.0% 0% 0% 31.10%
3 Count 0 0 411 0 411
Expected Count 122.8 128.5 7.3 152.4 411
% within Cluster (sample 2) 0% 0% 100% 0% 100%
% within Cluster (full sample) 0% 0% 100% 0% 1.8%
% of Total 0% 0% 1.8% 0% 1.8%
4 Count 0 56 0 8,560 8,616
Expected Count 2,574.6 2,693.6 153.4 3,194.4 8,616
% within Cluster (sample 2) 0% 0.6% 0% 99.4% 100%
% within Cluster (full sample) 0% 0.8% 0% 100% 37.30%
% of Total 0% 0.2% 0% 37.1% 37.3%
Total Count 6,899 7,218 411 8,560 23,088
Expected Count 6,899 7,218 411 8,560 23,088
% within Cluster (sample 2) 29.9% 31.3% 1.8% 37.1% 100%
% within Cluster (full sample) 100% 100% 100% 100% 100%
% of Total 29.9% 31.3% 1.8% 37.1% 100%
Cluster Membership (Sample 2) v. Cluster Membership (Full Sample) Crosstabulation)
Cluster Mship. (Full Sample)
1 2 3 4 Total
Cluster Mship. 1 Count 6,871 0 0 0 6,871
(Sample 2) Expected Count 2,053.1 2,148.1 122.3 2,547.5 6,871
% within Cluster (sample 2) 100% 0% 0% 0% 100%
% within Cluster (full sample) 99.6% 0% 0% 0% 29.8%
% of Total 29.8% 0% 0% 0% 29.8%
2 Count 28 7,162 0 0 7,190
Expected Count 2,148.5 2247.8 128 2,665.7 7,190
% within Cluster (sample 2) 0.4% 9, 9.6% 0% 0% 100%
% within Cluster (full sample) 0.4% 99.2% 0% 0% 31.10%
% of Total 0.1% 31.0% 0% 0% 31.10%
3 Count 0 0 411 0 411
Expected Count 122.8 128.5 7.3 152.4 411
% within Cluster (sample 2) 0% 0% 100% 0% 100%
% within Cluster (full sample) 0% 0% 100% 0% 1.8%
% of Total 0% 0% 1.8% 0% 1.8%
4 Count 0 56 0 8,560 8,616
Expected Count 2,574.6 2,693.6 153.4 3,194.4 8,616
% within Cluster (sample 2) 0% 0.6% 0% 99.4% 100%
% within Cluster (full sample) 0% 0.8% 0% 100% 37.30%
% of Total 0% 0.2% 0% 37.1% 37.3%
Total Count 6,899 7,218 411 8,560 23,088
Expected Count 6,899 7,218 411 8,560 23,088
% within Cluster (sample 2) 29.9% 31.3% 1.8% 37.1% 100%
% within Cluster (full sample) 100% 100% 100% 100% 100%
% of Total 29.9% 31.3% 1.8% 37.1% 100%
Table 5.  Descriptive Statistics: Cluster 1 Sessions
Cluster 1 Sessions a
Variables Mean SD Median Max. 25th 75th
Duration$^{b}$ 47.14 56.17 27.65 412.77 12.33 59.20
Bets 122 168 68 3,648 34 142
Intensity 4.09 3.10 3.35 11.27 1.32 6.58
Redeemed$^{c}$ 30.02 45.04 20.00 1,215.00 10.00 40.00
Vouchers$^{c}$ 1.60 23.41 .00 1,962.93 .00 .00
Net Loss$^{c}$ 29.48 45.13 20.00 1,215.00 10.00 40.00
%Loss 97.36 15.70 100.00 100.00 100.00 100.00
a. n = 13,843
b. Measured in minutes.
c. Measured in Euros.
Cluster 1 Sessions a
Variables Mean SD Median Max. 25th 75th
Duration$^{b}$ 47.14 56.17 27.65 412.77 12.33 59.20
Bets 122 168 68 3,648 34 142
Intensity 4.09 3.10 3.35 11.27 1.32 6.58
Redeemed$^{c}$ 30.02 45.04 20.00 1,215.00 10.00 40.00
Vouchers$^{c}$ 1.60 23.41 .00 1,962.93 .00 .00
Net Loss$^{c}$ 29.48 45.13 20.00 1,215.00 10.00 40.00
%Loss 97.36 15.70 100.00 100.00 100.00 100.00
a. n = 13,843
b. Measured in minutes.
c. Measured in Euros.
Table 6.  Descriptive Statistics: Cluster 2 Sessions
Cluster 2 Sessions a
Variables Mean SD Median Max. 25th 75th
Duration$^{b}$ 14.34 17.26 9.07 326.85 4.57 17.32
Bets 247 299 153 5,344 75 302
Intensity 17.26 3.17 17.81 21.91 14.77 20.03
Redeemed$^{c}$ 54.98 94.35 30.00 2,450.00 10.00 50.00
Vouchers$^{c}$ 44.06 412.79 .20 40,833.05 .00 20.00
Net Loss$^{c}$ 42.74 90.52 19.75 2,450.00 4.60 50.00
%Loss 71.77 43.03 99.25 100.00 19.05 100.00
a. n = 14,496
b. Measured in minutes.
c. Measured in Euros.
Cluster 2 Sessions a
Variables Mean SD Median Max. 25th 75th
Duration$^{b}$ 14.34 17.26 9.07 326.85 4.57 17.32
Bets 247 299 153 5,344 75 302
Intensity 17.26 3.17 17.81 21.91 14.77 20.03
Redeemed$^{c}$ 54.98 94.35 30.00 2,450.00 10.00 50.00
Vouchers$^{c}$ 44.06 412.79 .20 40,833.05 .00 20.00
Net Loss$^{c}$ 42.74 90.52 19.75 2,450.00 4.60 50.00
%Loss 71.77 43.03 99.25 100.00 19.05 100.00
a. n = 14,496
b. Measured in minutes.
c. Measured in Euros.
Table 7.  Descriptive Statistics: Cluster 3 Sessions
Cluster 3 Sessions a
Variables Mean SD Median Max. 25th 75th
Duration$^{b}$ 782.53 160.19 780.66 1,099.72 686.27 899.45
Bets 246 524 86 6,715 39 227
Intensity .32 .66 .12 7.25 .05 .31
Redeemed$^{c}$ 52.34 127.88 20.00 1,530.00 10.00 50.00
Vouchers$^{c}$ .00 .00 .00 .00 .00 .00
Net Loss$^{c}$ 52.34 127.88 20.00 1,530.00 10.00 50.00
%Loss 100.00 .00 100.00 100.00 100.00 100.00
a. n = 824
b. Measured in minutes.
c. Measured in Euros.
Cluster 3 Sessions a
Variables Mean SD Median Max. 25th 75th
Duration$^{b}$ 782.53 160.19 780.66 1,099.72 686.27 899.45
Bets 246 524 86 6,715 39 227
Intensity .32 .66 .12 7.25 .05 .31
Redeemed$^{c}$ 52.34 127.88 20.00 1,530.00 10.00 50.00
Vouchers$^{c}$ .00 .00 .00 .00 .00 .00
Net Loss$^{c}$ 52.34 127.88 20.00 1,530.00 10.00 50.00
%Loss 100.00 .00 100.00 100.00 100.00 100.00
a. n = 824
b. Measured in minutes.
c. Measured in Euros.
Table 8.  Descriptive Statistics: Cluster 4 Sessions
Cluster 4 Sessions a
Variables Mean SD Median Max. 25th 75th
Duration$^{b}$ 25.84 29.94 16.07 394.65 7.57 32.75
Bets 688 844 413 13,282 193 855
Intensity 26.12 4.00 25.35 68.32 23.59 27.43
Redeemed$^{c}$ 116.87 218.11 50.00 6,425.00 20.00 120.00
Vouchers$^{c}$ 97.40 499.21 .45 33,602.76 .20 100.00
Net Loss$^{c}$ 78.06 193.43 19.90 6,424.69 .00 70.00
%Loss 58.59 45.74 97.32 100.00 .00 99.73
a. n = 17,253
b. Measured in minutes.
c. Measured in Euros.
Cluster 4 Sessions a
Variables Mean SD Median Max. 25th 75th
Duration$^{b}$ 25.84 29.94 16.07 394.65 7.57 32.75
Bets 688 844 413 13,282 193 855
Intensity 26.12 4.00 25.35 68.32 23.59 27.43
Redeemed$^{c}$ 116.87 218.11 50.00 6,425.00 20.00 120.00
Vouchers$^{c}$ 97.40 499.21 .45 33,602.76 .20 100.00
Net Loss$^{c}$ 78.06 193.43 19.90 6,424.69 .00 70.00
%Loss 58.59 45.74 97.32 100.00 .00 99.73
a. n = 17,253
b. Measured in minutes.
c. Measured in Euros.
Table 9.  Between-Groups One-Way ANOVA
ANOVA
Sum of Squares df Mean Square F Sig.
Duration Between Groups 386.957 3 128.986 85580.335 .000
Within Groups 69.952 46412 .002
Total 456.909 46415
Intensity Between Groups 847.409 3 282.470 110089.371 .000
Within Groups 119.085 46412 .003
Total 966.493 46415
Redeemed Between Groups 1.542* 3 .514 991.576 .000
Within Groups 24.052 46412 .001
Total 25.593 46415
ANOVA
Sum of Squares df Mean Square F Sig.
Duration Between Groups 386.957 3 128.986 85580.335 .000
Within Groups 69.952 46412 .002
Total 456.909 46415
Intensity Between Groups 847.409 3 282.470 110089.371 .000
Within Groups 119.085 46412 .003
Total 966.493 46415
Redeemed Between Groups 1.542* 3 .514 991.576 .000
Within Groups 24.052 46412 .001
Total 25.593 46415
Table 10.  Kruskal-Wallis Results
Ranks
Cluster Membership N Mean Rank
Duration 1 13,843 28907.31
2 14,496 16544.68
3 824 46004.50
4 17,253 23146.26
Total 46,416
Intensity 1 13,843 7706.21
2 14,496 21919.71
3 824 1090.35
4 17,253 37786.01
Total 46,416
Redeemed 1 13,843 16455.75
2 14,496 22349.74
3 824 17893.58
4 17,253 29601.97
Total 46,416
Ranks
Cluster Membership N Mean Rank
Duration 1 13,843 28907.31
2 14,496 16544.68
3 824 46004.50
4 17,253 23146.26
Total 46,416
Intensity 1 13,843 7706.21
2 14,496 21919.71
3 824 1090.35
4 17,253 37786.01
Total 46,416
Redeemed 1 13,843 16455.75
2 14,496 22349.74
3 824 17893.58
4 17,253 29601.97
Total 46,416
Table 11.  Scatterdot: Cluster 1 Outlier Analysis
Descriptive Statistics: Cluster 1 Sessions (Normal v. Outliers)
Normal Outlier
Mean SD Median Count Mean SD Median Count
Duration 23.89 16.98 10815 130.20 67.56 3028
Bets 93 93 62 224 292 116
Intensity 4.67 3.02 4.22 1.99 2.37 .98
Redeemed 25.74 33.03 20.00 45.31 71.28 20.00
Voucher 2.02 26.37 .00 .08 4.37 .00
Net Loss 25.05 33.09 15.00 45.31 71.28 20.00
%Loss 96.63 17.67 100.00 99.97 1.82 100.00
Descriptive Statistics: Cluster 1 Sessions (Normal v. Outliers)
Normal Outlier
Mean SD Median Count Mean SD Median Count
Duration 23.89 16.98 10815 130.20 67.56 3028
Bets 93 93 62 224 292 116
Intensity 4.67 3.02 4.22 1.99 2.37 .98
Redeemed 25.74 33.03 20.00 45.31 71.28 20.00
Voucher 2.02 26.37 .00 .08 4.37 .00
Net Loss 25.05 33.09 15.00 45.31 71.28 20.00
%Loss 96.63 17.67 100.00 99.97 1.82 100.00
Table 12.  Cluster 2 Sessions (Normal v. Outliers)
Descriptive Statistics: Cluster 2 Sessions (Normal v. Outliers)
Normal Outlier
Mean SD Median Count Mean SD Median Count
Duration 12.64 11.73 14198 95.54 34.68 298
Bets 218 209 149 1599 622 1461
Intensity 17.27 3.18 17.84 16.80 2.95 16.99
Redeemed 51.40 81.72 25.00 225.45 292.33 150.00
Voucher 44.46 415.10 .20 24.98 281.31 .00
Net Loss 39.02 76.65 19.65 219.91 294.73 147.50
%Loss 71.28 43.23 99.10 94.85 21.61 100.00
Descriptive Statistics: Cluster 2 Sessions (Normal v. Outliers)
Normal Outlier
Mean SD Median Count Mean SD Median Count
Duration 12.64 11.73 14198 95.54 34.68 298
Bets 218 209 149 1599 622 1461
Intensity 17.27 3.18 17.84 16.80 2.95 16.99
Redeemed 51.40 81.72 25.00 225.45 292.33 150.00
Voucher 44.46 415.10 .20 24.98 281.31 .00
Net Loss 39.02 76.65 19.65 219.91 294.73 147.50
%Loss 71.28 43.23 99.10 94.85 21.61 100.00
Table 13.  Cluster 4 Sessions (Normal v. Outliers)
Descriptive Statistics: Cluster 4 Sessions (Normal v. Outliers)
Normal Outlier
Mean SD Median Count Mean SD Median Count
Duration 23.04 21.79 16907 162.67 49.02 346
Bets 609 603 401 4519 1656 4071
Bets per Minute 26.09 3.99 25.32 27.65 4.58 26.88
Redeemed 106.51 173.11 50.00 623.16 805.07 350.00
Voucher 94.80 496.65 .45 224.20 598.56 .20
Net Loss 69.34 151.70 19.85 504.17 746.68 259.93
%Loss 59.55 45.81 97.00 72.47 40.45 99.97
Descriptive Statistics: Cluster 4 Sessions (Normal v. Outliers)
Normal Outlier
Mean SD Median Count Mean SD Median Count
Duration 23.04 21.79 16907 162.67 49.02 346
Bets 609 603 401 4519 1656 4071
Bets per Minute 26.09 3.99 25.32 27.65 4.58 26.88
Redeemed 106.51 173.11 50.00 623.16 805.07 350.00
Voucher 94.80 496.65 .45 224.20 598.56 .20
Net Loss 69.34 151.70 19.85 504.17 746.68 259.93
%Loss 59.55 45.81 97.00 72.47 40.45 99.97
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