Transcript and T-tests
B AD 6243: Applied Univariate Statistics Hypothesis Testing and the T-test Professor Laku Chidambaram Price College of Business University of Oklahoma Steps in Hypothesis Testing 1. 2. 3. 4. 5. 6. Determine hypotheses (null & alternative) Select significance level ( level/p level) Choose a sample size Calculate the value of the statistic Obtain critical value Compare results BAD 6243: Applied Univariate Statistics 2 Sample (“Trial”) Errors in Hypothesis Testing Decision When H0 is “true” When H0 is “false” Reject H0 Type I error (, significance level) Correct decision (1 - , confidence level) Fail to reject H0 Correct decision (1-, power level) Type II error () Population (“Truth”) BAD 6243: Applied Univariate Statistics 3 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 4 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 5 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 6 Standard Normal Distribution BAD 6243: Applied Univariate Statistics 7 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 8 Independent Samples t-test Group Statistics Starting Salary Gender Female Male N 469 631 Mean 24769.51 27026.51 Std. Deviation 6895.765 6870.097 Std. Error Mean 318.417 273.494 Independent Samples Test Levene's Test for Equality of Variances F Starting Salary Equal variances assumed Equal variances not assumed .034 Sig. .854 t-test for Equality of Means t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference Lower Upper -5.380 1098 .000 -2257.00 419.517 -3080.142 -1433.850 -5.377 1006.360 .000 -2257.00 419.748 -3080.678 -1433.314 BAD 6243: Applied Univariate Statistics 9 Independent Samples Error Bar 28000 27000 26000 25000 24000 23000 N= 469 631 Female Male Gender BAD 6243: Applied Univariate Statistics 10 T-test as a Regression Model Model Summary Model 1 R R Square .160 a .026 Adjus ted R Square .025 Std. Error of the Es timate 6881.049 a. Predictors : (Constant), Gender ANOVAb Model 1 Regress ion Res idual Total Sum of Squares 1.37E+09 5.20E+10 5.34E+10 df 1 1098 1099 Mean Square 1370474872 47348835.43 F 28.944 Sig. .000 a t 77.956 5.380 Sig. .000 .000 a. Predictors : (Constant), Gender b. Dependent Variable: Starting Salary Coefficientsa Model 1 Uns tandardized Coefficients B Std. Error (Cons tant) 24769.510 317.737 Gender 2256.996 419.517 Standardized Coefficients Beta .160 a. Dependent Variable: Starting Salary BAD 6243: Applied Univariate Statistics 11 Dependent Samples T-test Paired Samples Statistics Pair 1 Starting Salary Current Salary Mean 26064.20 27404.39 N 1100 1100 Std. Deviation 6967.982 7363.757 Std. Error Mean 210.093 222.026 Paired Samples Correlations N Pair 1 Starting Salary & Current Salary Correlation 1100 Sig. .994 .000 Paired Samples Test Paired Differences Mean Pair 1 Starting Salary Current Salary -1340.19 Std. Deviation Std. Error Mean 856.541 25.826 95% Confidence Interval of the Difference Lower Upper -1390.86 -1289.51 BAD 6243: Applied Univariate Statistics t -51.894 df 1099 Sig. (2-tailed) .000 12 Dependent Samples Error Bar 27600 27400 27200 27000 26800 26600 26400 95% CI 26200 26000 25800 N= 1100 1100 SAL1 SAL2 BAD 6243: Applied Univariate Statistics 13