B AD 6243: Applied Univariate Statistics Hypothesis Testing and the T-test Professor Laku Chidambaram Price College of Business University of Oklahoma

BAD 6243: Applied Univariate Statistics 2 Steps in Hypothesis Testing 1.Determine hypotheses (null & alternative) 2.Select significance level (  level/p level) 3.Choose a sample size 4.Calculate the value of the statistic 5.Obtain critical value 6.Compare results

BAD 6243: Applied Univariate Statistics 3 Errors in Hypothesis Testing DecisionWhen H 0 is “true” When H 0 is “false” Reject H 0 Type I error ( , significance level) Correct decision (1 - , confidence level) Fail to reject H 0 Correct decision (1- , power level) Type II error (  ) Population (“Truth”) Sample (“Trial”)

BAD 6243: Applied Univariate Statistics 4 MAXMINCON Principle Maximize experimental variance –Design, plan and conduct research so that the experimental conditions are as different as possible Minimize error variance –Reduce error through controlling experimental conditions –Reduce error by increasing reliability of measures Control extraneous variance –Randomization: Groups can be considered statistically equal in all possible ways –Selection: To eliminate the effect of an extraneous variable on a dependent variable, choose subjects so that they are as homogenous as possible (on that variable) –Addition: To control the effect of an extraneous variable, build it into the research design, so as to measure its effect on the dependent variable

BAD 6243: Applied Univariate Statistics 5 Differences between Groups Randomized groups –Random sampling; random assignment –Simple vs. factorial designs –Concerns: (Pre-experimental) equality of groups Unequal cell sizes Correlated group(s) –Use same units in different treatments –Single vs. multi-group designs –Concerns: History, maturation and sensitization

BAD 6243: Applied Univariate Statistics 6 Concepts Related to the T-test Degrees of freedom T-distribution vs. standard normal distribution Level of significance Between subjects design: –Equal sample sizes –Equal variance Within subjects design

BAD 6243: Applied Univariate Statistics 7 Standard Normal Distribution

BAD 6243: Applied Univariate Statistics 8 t Distributions t-distributions refer to a family of distributions, which like normal distributions, are bell-shaped, but whose shape changes with the sample size; smaller sample sizes have flatter distributions, while larger sizes approximate normal distributions

BAD 6243: Applied Univariate Statistics 9 Independent Samples t-test

BAD 6243: Applied Univariate Statistics 10 Independent Samples Error Bar

BAD 6243: Applied Univariate Statistics 11 T-test as a Regression Model

BAD 6243: Applied Univariate Statistics 12 Dependent Samples T-test

BAD 6243: Applied Univariate Statistics 13 Dependent Samples Error Bar