Advanced Data Analysis

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Advanced Data Analysis Mean Comparisons

• Research Issues
• Common for marketers to need to compare an
  empirical mean to other means
• Theoretical some threshold level that has been
  established based on experience
• Laczniak Yogurt performs well financially when
  its customer satisfaction rating exceeds 5.0 (on
  a 7-point scale)
• Test to see if customer satisfaction gt 5.0
• Empirical derived via research in another time,
  with another sample, in a different place, etc.
• Laczniak Yogurt wants to continuously improve
  customer satisfaction is expected to increase
  each quarter
• Test to see if customer satisfaction this quarter
  gt C. S. last quarter

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Advanced Data Analysis Mean Comparisons

• Research Issues
• Common for marketers to need to compare an
  empirical percentage to other percentages
• Laczniak Yogurt will only introduce new flavors
  if they are deemed to be acceptable by 20 of
  its customers in a test market
• Test to see if Acceptance gt 20
• Such issues lend themselves to a specific set of
  analysis procedures which involve classical
  hypothesis testing procedures

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Advanced Data Analysis Mean Comparisons

• Hypothesis Test Procedures
• State Null and alternative hypotheses (Null
  always means no relationship reject it if you
  can)
• Specify the level of statistical significance (a)
• This is 1 - Confidence Interval
• According to the AMA
• .05 (in Marketing Research)
• Specify the critical region to be used
• Determine the critical value of the key statistic
  (t)
• Collect data and determine test statistic
  (computed t)
• Test hypothesis
• Reject or retain the null hypothesis

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Advanced Data Analysis Mean Comparisons

• t-test
• Used to test hypotheses that a mean is greater
  (less) than or equal to some theoretical value
• Laczniak Yogurt is test marketing new flavor
  (grape). History tells them that the new flavor
  will be successful if they sell, on average, more
  than 100 cartons in one month in each of the test
  markets.

5
Advanced Data Analysis Mean Comparisons
Store Sales (000)
1 86
2 97
3 114
4 108
5 123
6 93
7 132
8 116
9 105
10 120
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Advanced Data Analysis Mean Comparisons

• Steps in Hypothesis Testing
• State Null and alternative hypotheses (Null
  always means no relationship reject it if you
  can)
• Ho m 100
• Ha m gt100
• Specify the level of statistical significance (a)
• .05, obviously
• Specify the critical region to be used (Table 4
  P. 828)
• Critical t (df n-1 10-19) 1.83

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Advanced Data Analysis Mean Comparisons

• Collect data and determine test statistic
• For example
• n 10 (with SRS)
• mean 109.4
• s 14.40
• Test hypothesis -- reject or retain the null
  hypothesis
• Compute t
• Where t computed mean m/ v n
• 109.4 100/(14.4/v10)
• Computed t 2.07
• Computed t (?) Critical t
• 2.07 1.83 -- Reject the null hypothesis

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Advanced Data Analysis Mean Comparisons

• What if
• n 10 (with SRS)
• Mean 103.4
• s 10.0
• n 50 (with SRS)
• Mean 103.4
• s 10.0
• Importance of n and s

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Advanced Data Analysis Mean Comparisons

• Hypothesis Tests
• t-test
• Used to test hypotheses that a mean is greater
  (less) than or equal to a different empirically
  derived value
• For example, test the hypothesis is Mean1 gt Mean
  2

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Advanced Data Analysis Mean Comparisons

• Laczniak Yogurt Company is interested in using a
  new container design for its product. Two
  alternative designs (one red, the other orange)
  were chosen to test in 20 stores (ten for each
  design) in Iowa. Laczniak management wants to
  use the design that lead to the highest sales
  level in the test markets. Data for the stores
  are

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Advanced Data Analysis Mean Comparisons
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Advanced Data Analysis Mean Comparisons

• Here is a summary of the data
• Red
• Mean 403
• s 20.76
• Orange
• Mean 390.3
• s 15.26
• State Null and alternative hypotheses
• Ho m1 ? m2
• Ha m1 gt m2
• Compute t statistic (t 1.56) critical t (df
  n1 n2 2)
• Critical t 1.73
• Test ? If Computed t critical
• Is 1.56 1.73?
• NO -- CANNOT REJECT THE NULL

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Advanced Data Analysis Mean Comparisons

• What if the mean and standard deviation remained
  constant and the sample size for both containers
  were 25?
• What if the means remained the same and s for
  both containers was 10.00 (n 10)?

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Advanced Data Analysis Mean Comparisons

• Research Issues
• Common for marketers to need to compare an
  empirical percentage to a theoretical percentage
  (or standard)
• Laczniak Yogurt will only introduce new flavors
  if they are deemed to be acceptable by more
  than 20 of its customers in a test market
• Assume that Laczniak attempted to introduce a new
  plum flavored yogurt
• Had a sample of 625 randomly selected customers
  who participated in the test market 140
  indicated that they would buy the new flavor

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Advanced Data Analysis Mean Comparisons

• Steps in Hypothesis Testing
• State Null and alternative hypotheses (Null
  always means no relationship reject it if you
  can)
• Ho ? .20
• Ha ? gt 20
• Specify the level of statistical significance (a)
• .05, obviously
• Compute test statistic and test hypothesis
• z-statistic p - ?/sp where sp v ? (1 - ?)/ n

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Advanced Data Analysis Mean Comparisons

• Collect data and determine test statistic
• For example
• n 625 (with SRS)
• p 140/625 .23
• sp v .2 (.8)/625 .016
• Test hypothesis -- reject or retain the null
  hypothesis
• Compute z
• Where z p - ?/sp
• .23 .20/.016
• Computed z 1.88
• Computed z Critical z (1.645 for alpha .05)
• 1.88 1.645
• Reject the null hypothesis

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Advanced Data Analysis Mean Comparisons

• What if the same data were generated, but the
  sample size was 225?