1. Slide 1 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 1 Analysis of frequency data n Learning Objectives –Understand the meaning of a categorical variable –Understand the difference between a single variable problem and a two variable problem –Construct a table for a single variable problem –Construct a contingency table for a two variable problem –Analyse single variable data –Analyse two variable data Chapter S13

2. Slide 2 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 2 Categorical data non-numeric n Data are often non-numeric—each individual observation is a description rather than a number n Averages cannot be used in these circumstances n Systems where observations are descriptive (rather than numerical) are described as categorical n Systems where observations are descriptive (rather than numerical) are described as categorical (e.g. ‘what gender are you?’, ‘what colour are your eyes?’)

3. Slide 3 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 3 Presentation of single variable categorical data n Frequency table—table in which the number of occurrences of each category is recorded Table S13.1 Outcomes of 60 rolls of a fair six-sided die in Example S13.4 Category 123456Total Frequency 87121351560

4. Slide 4 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 4 Contingency tables n Two-dimensional table n Two-dimensional table—where one variable is presented along the rows and the other variable down the columns Table S13.3 A typical contingency table for the Internet survey in Example S13.6 Live Yes52 47 105 34 238 No28 63 35 36 162 InternetNorth South East West Total Total80 110 140 70 400

5. Slide 5 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 5 Analysis of single variable problems n There is only a single variable n Objective—determine whether an observed set of categorical data is reasonably consistent with what was expected by some prior line of reasoning n Analysis of single variable problems. The steps involved are known as a goodness-of-fit test chi-square test statistic n Use the chi-square test statistic as a basis for the goodness-of-fit test

6. Slide 6 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 6 Analysis of contingency tables n Two variables involved n The data will be in the form of a contingency table n Objective—determine whether the discrepancy between the observed and expected frequencies is merely a natural one due to chance fluctuations n Use the chi-square test statistic as a basis for a test on degrees of freedom

7. Slide 7 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 7 Steps involved in the analysis of contingency tables 1.Construct the null hypothesis for the problem 2.The observed frequencies come from the data of the problem 3.The expected frequencies are those that we might ‘expect’ to occur if H 0 were true 4.Use the chi-square statistic 5.Associated with the test statistic are degrees of freedom 6.The calculated value of the chi-square test statistic must be compared with a critical value 7.Compare the value of that you calculated with the critical value 8.Based on this outcome a conclusion can be drawn