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Management of Design Systems TTMG 5004 “Introduction to stats” May 17, 2004 John Callahan, PhD

Management of Design Systems TTMG 5004 “Introduction to stats” May 17, 2004 John Callahan, PhD. Upon completion of this class. You will know about: The Normal and t distributions Sampling distributions for sample means Hypothesis testing using the Normal and t distributions

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Management of Design Systems TTMG 5004 “Introduction to stats” May 17, 2004 John Callahan, PhD

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  1. Management of Design SystemsTTMG 5004“Introduction to stats”May 17, 2004John Callahan, PhD

  2. Upon completion of this class You will know about: • The Normal and t distributions • Sampling distributions for sample means • Hypothesis testing using the Normal and t distributions You will be able to: • Formulate hypotheses for population means • Test these hypotheses Management of Design Systems

  3. Agenda • Normal distribution • Sampling distribution of a sample mean • Hypothesis testing • t distribution Management of Design Systems

  4. The Normal distribution has 2 parameters and is symmetric Management of Design Systems

  5. Many variables have a Normal distribution:example – Figure 11.3 from Norusis Management of Design Systems

  6. Critical values for the Normal distribution • http://www.statsoftinc.com/textbook/sttable.html • 90%: 1.64 standard deviations • 95%: 1.96 standard deviations • 99%: 2.58 standard deviations Management of Design Systems

  7. Agenda • Normal distribution • Sampling distribution of a sample mean • Hypothesis testing • t distribution Management of Design Systems

  8. Sampling distributions are often Normal:example – distribution of sample mean • Sampling distributions • http://www.ruf.rice.edu/~lane/stat_sim/ • Central Limit Theorem • http://www.intuitor.com/statistics/CentralLim.html • Theory • Sample mean is average of n independent random variables, the sample values • If sample values are drawn from population with a Normal distribution then sample mean is Normal • If not, sample mean still approximately Normal via the Central Limit Theorem • Variance of sample mean is 1/n times the variance of population • Standard deviation of sample mean is 1/n of population standard deviation, that is /n Management of Design Systems

  9. Agenda • Normal distribution • Sampling distribution of a sample mean • Hypothesis testing • t distribution Management of Design Systems

  10. Under English common law, a defendant is innocent until proven guilty • http://www.intuitor.com/statistics/T1T2Errors.html Management of Design Systems

  11. Population, sampling frame, sample- the inference process • Sampling Terminology • http://trochim.human.cornell.edu/kb/sampterm.htm • Sample from the population, use sample properties (e.g., statistics) to make inferences about the population (e.g., parameters) Population Sample x1 x2 sampling process xn Sampling frame inference Management of Design Systems

  12. Example universes, sampling frames and samples • Eytan Lasry (2000) • Jian Wu (2004) • Chris Fang (2004) • Alex Li (2004) • Edward Qin (2004) Management of Design Systems

  13. Test if the mean number of hours worked by college grads (generally) is 40 hours H0:  = 40 Ha:   40 Is it likely that  = 40? (47.00 – 40) / 0.49 = 14.3 reject H0 accept Ha Management of Design Systems

  14. Agenda • Normal distribution • Sampling distribution of a sample mean • Hypothesis testing • t distribution Management of Design Systems

  15. Return to the test if the mean number of hours worked by college grads - I cheated! • How did I get the standard error – the standard deviation of the sample mean? • The standard error is /n, but I do not know  • We used s, the estimate of , instead of  • s = {SUMi[hrsi – av(hrs)]2/n-1} = 10.21 • Should use t distribution rather than the Normal distribution for the distribution of the sample mean • t distribution has fatter tails because of the uncertainty about /n • http://www-stat.stanford.edu/~naras/jsm/TDensity/TDensity.html • For critical t values, see • http://www.psychstat.smsu.edu/introbook/tdist.htm Management of Design Systems

  16. Test if the mean number of hours worked by college grads is 40 hours – correctly! Management of Design Systems

  17. Next class – Wed. May 19 • Philosophy of research • http://trochim.human.cornell.edu/kb/philosophy.htm • Structure of research • Deduction and induction • Positivism & post-positivism • Introduction to validity • Christensen et al. (2002) • Hypothesis testing • Zirger and Maidique (1990) Management of Design Systems

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