8 - 1 © 1998 Prentice-Hall, Inc. Statistics for Managers Using Microsoft Excel, 1/e Statistics for Managers Using Microsoft Excel Two-Sample & c-Sample Tests with Numerical Data Chapter 8 n Distinguish parametric & nonparametric procedures n Test two or more populations using parametric & nonparametric procedures l Means l Medians l Variances

8 - 2 © 1998 Prentice-Hall, Inc. Statistics for Managers Using Microsoft Excel, 1/e Hypothesis Testing Procedures

8 - 3 © 1998 Prentice-Hall, Inc. Statistics for Managers Using Microsoft Excel, 1/e Parametric & non-Parametric Test Procedures n Parametric Test Procedures l Involve population parameters s Example: Population mean l Require interval scale or ratio scale s Whole numbers or fractions s Example: Height in inches: 72, 60.5, 54.7 l Have stringent assumptions s Example: Normal distribution l Examples: Z test, t test n Non-Parametric Test Procedures l Statistic does not depend on population distribution l Data may be nominally or ordinally scaled s Example: Male-female l May involve population parameters such as median l Example: Wilcoxon rank sum test

8 - 4 © 1998 Prentice-Hall, Inc. Statistics for Managers Using Microsoft Excel, 1/e Advantages & Disadvantages of Nonparametric Tests n Advantages l Used with all scales l Easier to compute s Developed before wide computer use l Make fewer assumptions l Need not involve population parameters l Results may be as exact as parametric procedures n Disadvantages n May waste information l If data permit using parametric procedures l Example: Converting data from ratio to ordinal scale n Difficult to compute by hand for large samples n Tables not widely available

8 - 5 © 1998 Prentice-Hall, Inc. Statistics for Managers Using Microsoft Excel, 1/e 2 & c-Sample Tests with Numerical Data

8 - 6 © 1998 Prentice-Hall, Inc. Statistics for Managers Using Microsoft Excel, 1/e t Pooled Variance t Test n Tests means of 2 independent populations having equal variances n Parametric test procedure n Assumptions l Both populations are normally distributed If not normal, can be approximated by normal distribution (n 1  30 & n 2  30 ) l Population variances are unknown but assumed equal

8 - 7 © 1998 Prentice-Hall, Inc. Statistics for Managers Using Microsoft Excel, 1/e Two Independent Populations Examples n An economist wishes to determine whether there is a difference in mean family income for households in 2 socioeconomic groups. n An admissions officer of a small liberal arts college wants to compare the mean SAT scores of applicants educated in rural high schools & in urban high schools.

8 - 8 © 1998 Prentice-Hall, Inc. Statistics for Managers Using Microsoft Excel, 1/e t Pooled Variance t Test Hypotheses

8 - 9 © 1998 Prentice-Hall, Inc. Statistics for Managers Using Microsoft Excel, 1/e Sampling Distribution

© 1998 Prentice-Hall, Inc. Statistics for Managers Using Microsoft Excel, 1/e t Pooled Variance t Test Test Statistic Hypothesized difference

© 1998 Prentice-Hall, Inc. Statistics for Managers Using Microsoft Excel, 1/e t Pooled Variance t Test Example You’re a financial analyst for Charles Schwab. You want to see if there a difference in dividend yield between stocks listed on the NYSE & NASDAQ. NYSE NASDAQ Number 2125 Mean Std. Dev Assuming equal variances, is there a difference in average yield (  =.05)? © T/Maker Co.

© 1998 Prentice-Hall, Inc. Statistics for Managers Using Microsoft Excel, 1/e H 0 :  1 -  2 = 0 (  1 =  2 ) H 1 :  1 -  2  0 (  1   2 )  .05 df  = 44 Critical Value(s): Test Statistic: Decision: Conclusion: Reject at  =.05 There is evidence of a difference in means t Pooled Variance t Test Solution

© 1998 Prentice-Hall, Inc. Statistics for Managers Using Microsoft Excel, 1/e Test Statistic Solution

© 1998 Prentice-Hall, Inc. Statistics for Managers Using Microsoft Excel, 1/e You’re a research analyst for General Motors. Assuming equal variances, is there a difference in the average miles per gallon (mpg) of two car models (  =.05)? You collect the following: Sedan Van Number1511 Mean Std Dev t Pooled Variance t Test Example

© 1998 Prentice-Hall, Inc. Statistics for Managers Using Microsoft Excel, 1/e H 0 :  1 -  2 = 0 (  1 =  2 ) H 1 :  1 -  2  0 (  1   2 )  .05 df  = 24 Critical Value(s): Test Statistic: Decision: Conclusion: Do not reject at  =.05 There is no evidence of a difference in means t Pooled Variance t Test Solution

© 1998 Prentice-Hall, Inc. Statistics for Managers Using Microsoft Excel, 1/e Test Statistic Solution*