1. Secondary Data, Measures, Hypothesis Formulation, Chi-Square Market Intelligence Julie Edell Britton Session 3 August 21, 2009

2. Today’s Agenda  Announcements  Secondary data quality  Measure types  Hypothesis Testing and Chi-Square

3. 3 National Insurance Case for Sat. 8/22 –Stephen will do a tutorial today, Friday, 8/21 from 1:00 -2:15 in the MBA PC Lab and be available tonight from 7 – 9 pm in the MBA PC Lab to answer questions –Submit slides by 8:00 am on Sat. 8/22 –2 slides with your conclusions – you may add Appendices to support you conclusions Announcements

4. Primary vs. Secondary Data  Primary -- collected anew for current purposes  Secondary -- exists already, was collected for some other purpose  Finding Secondary Data Online @ Fuqua  http://library.fuqua.duke.edu

5. Primary vs. Secondary Data

6. Evaluating Sources of Secondary Data  If you can’t find the source of a number, don’t use it. Look for further data.  Always give sources when writing a report.  Applies for Focus Group write-ups too  Be skeptical.

7. Secondary Data: Pros & Cons  Advantages  cheap  quick  often sufficient  there is a lot of data out there  Disadvantages  there is a lot of data out there  numbers sometimes conflict  categories may not fit your needs

8. Types of Secondary Data *IRI = Information Resources, Inc. (http://us.infores.com/)

9. Secondary Data Quality: KAD p. 120 & “What’s Behind the Numbers?”  Data consistent with other independent sources?  What are the classifications? Do they fit needs?  When were numbers collected? Obsolete?  Who collected the numbers? Bias, resources?  Why were the data collected? Self-interest?  How were the numbers generated?  Sample size  Sampling method  Measure type  Causality (MBA Marketing Timing & Internship)

10. It is Hard to Infer Causality from Secondary Data Took Core Marketing Got Desired Marketing Internship Did Not Get Desired Marketing Internship Term 176%24% Term 351%49%

11. Today’s Agenda  Announcements  Secondary data quality  Measure types  Hypothesis Testing and Chi-Square

12. Measure Types  Nominal: Unordered Categories  Male=1; Female = 2;  Ordinal: Ordered Categories, intervals can’t be assumed to be equal.  I-95 is east of I-85; I-80 is north of I-40; Preference data  Interval: Equally spaced categories, 0 is arbitrary and units arbitrary.  Fahrenheit temperature – each degree is equal, Attitudes  Ratio: Equally spaced categories, 0 on scale means 0 of underlying quantity.  $ Sales, Market Share

13. Meaningful Statistics & Permissible Transformations

14. Means and Medians with Ordinal Data GenderMeasure 1Measure 2Means M 11Measure 1 M 22M=5.4 < F=5.6 F 33Measure 2 F 44M=65.4 > F=25.6 F 55 F 66Medians M 7107Measure 1 M 8108M=7 > F=5 M 9109Measure 2 F10110M=107 > F=5

15. Ratio Scales & Index Numbers

16. Today’s Agenda  Announcements  Southwestern Conquistador Beer Case  Backward Market Research  Secondary data quality  Measure types  Hypothesis Testing and Chi-Square

17. Cross Tabs of MBA Acceptance by Gender A. Raw FrequenciesB. Cell Percentages

18. C. Row Percentages D. Column Percentages

19. Rule of Thumb  If a potential causal interpretation exists, make numbers add up to 100% at each level of the causal factor.  Above: it is possible that gender (row) causes or influences acceptance (column), but not that acceptance influences gender. Hence, row percentages (format C) would be desirable.

20. Hypothesis Formulation and Testing Hypothesis: What you believe the relationship is between the measures. Theory Empirical Evidence Beliefs Experience Here: Believe that acceptance is related to gender Null Hypothesis: Acceptance is not related to gender Logic of hypothesis testing: Negative Inference The null hypothesis will be rejected by showing that a given observation would be quite improbable, if the hypothesis was true. Want to see if we can reject the null.

21. Steps in Hypothesis Testing 1.State the hypothesis in Null and Alternative Form –Ho: There is no relationship between gender and MBA acceptance –Ha1: Gender and Acceptance are related (2-sided) –Ha2: Fewer Women are Accepted (1-sided) 2.Choose a test statistic 3.Construct a decision rule

22. Chi-Square Test  Used for nominal data, to compare the observed frequency of responses to what would be “expected” under the null hypothesis.  Two types of tests  Contingency (or Relationship) – tests if the variables are independent – i.e., no significant relationship exists between the two variables  Goodness of fit test – Compare whether the data sampled is proportionate to some standard

23. Chi-Square Test With (r-1)*(c-1) degrees of freedom Observed number in cell i Expected number in cell i under independence number of cellsnumber of rows number of columns = Column Proportion * Row Proportion * total number observed

24. MBA Acceptance Data Contingency A. Observed Frequencies B. Cell Percentages AcceptReject M.111*.556*1800=111.889*.556*1800=890 F.111*.444*1800= 89.889*.444*1800=710 C. Expected Frequencies

25. Chi-Square Test With (r-1)*(c-1) degrees of freedom =(140-111) 2 /111 + (860-890) 2 /890 + (60-89) 2 /89 + (740-710) 2 /710 = 19.30 So? 3. Construct a decision rule

26. Decision Rule 1.Significance Level - 2.Degrees of freedom - number of unconstrained data used in calculating a test statistic - for Chi Square it is (r-1)*(c-1), so here that would be 1. When the number of cells is larger, we need a larger test statistic to reject the null. 3.Two-tailed or One-tailed test – Significance tables are (unless otherwise specified) two tailed tables. Chi-Sq is on pg 517 Ha1: Gender and Acceptance are related (2-sided) Critical Value = 3.84 Ha2: Fewer Women are Accepted (1-sided) Critical Value = 2.71 4. Decision Rule: Reject the Ho if calculated Chi-sq value (19.3) > the test critical value (3.84) for Ha1 or (2.71) for Ha2 Probability of rejecting the Null Hypothesis, when it is true

27. Chi-Square Table

28. Chi-Square Test  Used for nominal data, to compare the observed frequency of responses to what would be “expected” under some specific null hypothesis.  Two types of tests  Contingency (or Relationship) – tests if the variables are independent – i.e., no significant relationship exists  Goodness of fit test – Compare whether the data sampled is proportionate to some standard

29. Goodness of fit – Chi-Square Ho: Car Color Preferences have not shifted Ha: Car color Preferences have shifted Data Historic Distribution Expected # = Prob*n Red 68030% 750 Green 52025%625 Black 67525%625 White 62520%500 Tot (n)2500 Do we observe what we expected?

30. Chi-Square Test With (k-1) degrees of freedom =(680-750) 2 /750 + (520-625) 2 /625 + (675-625) 2 /625 + (625-500) 2 /500 = 59.42 So? 3. Construct a decision rule

31. Decision Rule 1.Significance Level - 2.Degrees of freedom - number of unconstrained data used in calculating a test statistic - for Chi Square it is (k-1), so here that would be 3. When the number of cells is larger, we need a larger test statistic to reject the null. 3.Two-tailed or One-tailed test – Significance tables are (unless otherwise specified) two tailed tables. Chi-Sq is on pg 517 Ha: Preference have changed (2-sided) Critical Value = 7.81 4. Decision Rule: Reject the Ho if calculated Chi-sq value (59.42) > the test critical value (7.81). Probability of rejecting the Null Hypothesis, when it is true

32. Chi-Square Table

33. Recap  Finding & Evaluating Secondary Data  Measure Types  permissible transformations  Meaningful statistics  Index #s  Crosstabs  Casting right direction  Chi-square statistic  Contingency Test  Goodness of Fit Test