Types of Data in FCS Survey

1. Types of Data in FCS Survey • Nominal Scale • Labels and categories (branch, farming operation) • Ordinal Scale • Order and rank (expectations, future plans, age and other classification measures) • Interval Scale • Differences in numbers equal to differences in level (Satisfaction item, importance items)

2. Appropriate Analyses • Nominal Scale • Counts, proportions, serve to uniquely classify • SPSS Frequencies and Crosstabs • Ordinal Scale • Relative proportions—relative performance • SPSS Frequencies and Crosstabs • Confidence intervals and t-tests for proportions • Interval Scale • Computation of means, comparisons of means • SPSS t-tests procedure

3. Examining Differences Between Groups Introduction to t-Tests

4. Overview • Interpretations • t-Tests Comparing Group Means (SPSS) • One sample • Independent samples • Paired samples • Interpretations

5. Marketing Surveys and Comparisons • What are the important differences… • Among our different customer groups? • In preferences within our core customers? • Are the differences statistically significant, i.e., are they significantly different from sample-to-sample variation? • Does the difference justify a different marketing action, a unique marketing mix?

6. Importance of Sample Mean • Is an efficient statistic. • Appropriate for survey items that have interval or ratio properties. • Likert items • Semantic differential • Appropriate for data that we believe to be continuous in nature, i.e., possible values lie on a uniform continuum.

7. One Sample t-Test

8. Null Hypothesis • A testable statement, either can be rejected (as false), or we can “fail to reject,” in other words, the statement will be accepted until rejected. • In a one-sample test, “There is no difference between a sample mean and a population mean of 3.0.” • If respondents chose at random or • If the average response was “neutral”

9. Statistical Significance • Significance levels are reported with t statistics indicating the probability of incorrectly rejecting the null hypothesis, or alpha () error. • Similarly, a 95% statistical confidence level means that we would incorrectly reject the null hypothesis 5% (.05) of the time. • Significance levels reported in output are  probabilities, whereas <.05 is regarded as highly significant, corresponding to t-statistics of 1.96 (2.0) or greater magnitude.

10. One sample t-test, where H is 3, n=32 Hypothesized population mean (and sampling distribution) 4.78 1 Not Important 2 3 4 5 Very Important

11. Standard t-Test Statistic

12. Independent Samples • The most typical application of t-tests in survey research. • Comparisons on the same measure between different groups. • Important uses for marketers: • Significant differences are important in segmentation analysis and targeting. • Determining significant differences between marketing inputs, such as in test markets and advertising studies.

13. Null Hypothesis in Independent Samples t-Test • “There is no difference between groups on this questionnaire item.” • Stated differently, the mean of Group 1 minus the mean of Group 2 equals zero. • Rejection of the null hypothesis means that a difference exists.

14. Independent samples t-test, testing mean of Branson is equal to the mean of Grandville “Grandville” “Branson” 3.70 4.78 1 Not Important 2 3 4 5 Very Important “How important is the Patronage Refund Program to you as a member/borrower with FCS?

15. Independent samples t-test, testing mean of Branson is equal to the mean of Grandville

16. Interpreting t-Tests • Define the groups—What formed groups 1 and 2? • What is measured by the magnitude of the sample means? • What were the respective groups’ sample means? • Is the difference statistically significant? (Versus random sampling error.)

17. Example • The t-test compares the mean response of Grandville (Grp. 1) to the mean response of Branson (Grp. 2) • … on their ratings of the importance of the refund, whereas a higher score indicates the respondent felt it was “very important.” • The mean for Grandville was higher (4.78) than the mean for Branson (3.70). • The difference is statistically significant, t=-2.24, with a two-tailed significance level <.05.

18. Sample Size in t-Tests • Standard error of group means increases with smaller sample sizes • Pooled standard error (Std. Error of difference) increases with smaller samples sizes • Sensitivity of statistical tests of group differences in means decreases with smaller sample sizes.

19. Confidence Interval Interpretation • 95% confidence level = 95% of all sample proportions will fall within +/- 1.96 units of standard error (s.e.) from the population proportion. • Conversely, the population proportion will lie within +/-1.96 units of s.e. from the sample proportion in 95% of all samples taken. • A 99% confidence level implies all sample proportions will fall within +/-2.58 s.e. units of the population proportion.

20. Interpretation • Values for the t-test greater than +/-1.96 are significant at the 95% confidence level +/-1.65 for the 90% confidence level +/-2.58 for the 99% confidence level • These confidence level can be interpreted as “there is 5% chance we would be incorrectly rejecting the null hypothesis…”

21. Paired Samples t-Tests • Permits the comparison on separate questionnaire items from the same group of respondents • Allows hypothesis tests that responses to two different questions were identical. • Identifies varying levels of like/dislike, or importance/unimportance to be determined on identically coded questions.

22. Paired t-Test Statistic

23. Paired samples t-test, testing means of refund importance items. “Member/borrower” “FCS vs. competitors” 4.02 4.24 1 Not Important 2 3 4 5 Very Important