Types of Data in FCS Survey
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Transcript of Types of Data in FCS Survey
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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mean theoferror standard
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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.
4.78
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One sample t-test, where H is 3, n=32
Hypothesizedpopulation mean (andsampling distribution)
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
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Independent samples t-test, testing mean of Branson is equal to the mean of Grandville
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3.70
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“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
difference theoferror standard
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statistic test
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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”