Generalizing a Samples Findings to its Population and Testing Hypotheses about Percents and Means an

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Generalizing a Samples Findings to its
Population and Testing Hypotheses about Percents
and Means and Testing for Differences

• Dr. John T. Drea
• Professor of Marketing
• Western Illinois University

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Basic terms in inferential statistics

• Statistical inference
• Sample statistics are used to make estimates of
  population parameters.
• To do this, you should have drawn the sample
  using a probability sampling procedure
• Sample Statistic
• A statistic drawn from the sample that represents
  the sample.
• Hypothesis testing
• Comparing a sample statistic with a predefined
  level.
• Confidence Interval
• A range to either side of a mean/percentage. It
  contains a specific degree of accuracy (typically
  95)

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How do I get the std. error of the mean in SPSS?
Step 1
Step 3
Be sure to select S.E. mean as an option.
Step 2
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Testing Hypothesized Population Parameter Values
You can get std. error of the mean from SPSS
Z sample mean hypothesized mean std. error
of the mean
The std. error of the mean is typically written
in scientific notation In this example,
2.788E-02 can also be expressed as .02788
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Testing Hypothesized Population Parameter Values
Assume we wanted to test the hypothesis that the
average Amtrak rider would have an Aamtrak of 5
on a 1-7 scale.
Z sample mean hypothesized mean std. error
of the mean
5.8081 5 28.985 .02788
Since this is greater than the z value for a 95
level of confidence, we would reject the null
hypothesis that there is no difference between
the sample mean and the hypothesized mean.
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Computing a t-test in SPSS
Step 1
Step 2
Be sure to specify the test value (i.e., what
your hypothesis is)
Produces these results
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Computing a t-test in SPSS
Results
The t-value is greater than 1.96 (i.e, 28.988 gt
1.96) Therefore, we would reject the null
hypothesis than the hypothesized mean and the
sample mean are the same. This is also indicated
by the significance value if it is below .05,
we reject the null hypothesis. Also, note the
similarity between the t-value and the z-score
we computed earlier!
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Directional Hypotheses
mean

• Population Parameter Hypothesis
• The mean Aamtrak will be a 5 on a 1-7 scale.
• Directional Hypothesis
• The mean Aamtrak will be less than 5 on a 1-7
  scale. or
• The mean Aamtrak will be greater than 5 on a 1-7
  scale.
• When computing z for a directional hypothesis,
  you would compare your t or z value to 1.64, not
  1.96, since you are only looking at one tail of
  the distribution.

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Testing for Differences Between Two Groups for
the Same Variable
Step 1
Step 2
In Step 2, select your test variable(s) and
then select a grouping variable. In the
present example, I wanted to test whether there
is a difference between men and women for
Aamtrak, so Ive selected gender as the
grouping variable and then clicked define
groups, with a 1 and a 2 as the values to
compare. (1 is male, 2 is female)
Step 3
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Testing for Differences Between Two Groups for
the Same Variable

• 1. The Levenes test tell you whether you can
  assume equal variances if the significance
  value is .05 or greater, you assume equal
  variances.
• The t-value is greater than 1.96 (it is 2.990),
  so we reject the null hypothesis that there is no
  difference between the mean scores for men and
  women. This is further evidence by the
  significance value of .003.

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Testing for differences in more than two groups
ANOVA(or ANOVA is not an old Chevy)

• ANOVA will tell you if the means of two or more
  groups are statistically the same, such as the
  difference between three groups of customers (A,
  B, and C.)
• ANOVA will not tell you whether Group A is bigger
  than Group B, or if Group C is bigger than Group
  A.
• AVOVA tests the null hypothesis that each of the
  groups are the same, that is A B C.
• ANOVA does this by taking the variation between
  groups and dividing it by the variation within
  the groups.

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Computing One-Way ANOVA in SPSS
Step 1
This ANOVA is to determine if the mean score for
Aamtrak is the same for each for four corridors
(sets of tracks, such as Chicago to St. Louis,
Chicago to Quincy, etc.) Thus, Aamtrak is the
dependent variable and corridor is the factor Be
sure to click on options and choose
descriptives. Also, click on post-hoc and
select a Duncan post-hoc test to determine
which means are different from each other.
Step 2
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Computing One-Way ANOVA in SPSS
The ANOVA results indicate that you would reject
the null hypothesis that there are no differences
between the means of the four groups, since the
F-ratio is significant (below the .05 level)
This is the results of a Duncan post-hoc test
this test groups means together that are
statistically the same. In this case, each of
the means are different from one another EXCEPT
St. Louis and Milwaukee SPSS and the Duncan
test have grouped them together.