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)

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

Examining Differences Between Groups Introduction to t-Tests

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

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?

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.

One Sample t-Test

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”

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.

Not Important 2345 Very Important One sample t-test, where  H is 3, n=32 Hypothesized population mean (and sampling distribution)

Standard t-Test Statistic

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.

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.

Not Important 2345 Very Important Independent samples t-test, testing mean of Branson is equal to the mean of Grandville “Grandville” 3.70 “Branson” “How important is the Patronage Refund Program to you as a member/borrower with FCS?

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

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.)

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.

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.

Confidence Interval Interpretation 95% confidence level = 95% of all sample proportions will fall within +/ 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.

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…”

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.

Paired t-Test Statistic

Not Important 2345 Very Important Paired samples t-test, testing means of refund importance items “FCS vs. competitors” “Member/borrower”