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.

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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.

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Standard t-Test Statistic

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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.

4.78

1Not

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2 3 4 5Very

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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?

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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 +/- 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.

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

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Paired samples t-test, testing means of refund importance items.

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“FCS vs. competitors”“Member/borrower”