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Analyzing Data: Comparing Means

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Analyzing Data: Comparing Means. Chapter 8. Are there differences? ... Really for comparison purposes. Select: Stat Basic Statistics 1-Sample t ... – PowerPoint PPT presentation

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Title: Analyzing Data: Comparing Means


1
Analyzing Data Comparing Means
  • Chapter 8

2
Are there differences?
  • One of the fundament questions of survey research
    is if there is a difference among respondents
  • When seeking to evaluate differences in means, we
    can use t-test or ANOVA analysis of variance

3
t-test
  • 2-Sample t (independent) performs a hypothesis
    test of the difference between two population
    means when standard deviation's are unknown and
    samples are drawn independently from each other.
  • It is based upon the t-distribution
  • If the sample is small, it works best if data
    were drawn from distributions that are normal or
    close to normal.
  • Select Stat gt Basic Statistics gt 2-Sample t

4
Equal Variances?
  • Many statistical procedures assume that although
    different samples may come from populations with
    different means, they have the same variance.
  • We can test for this
  • use Bartlett's and Levene's tests.
  • Select Stat gt ANOVA gt Test for Equal Variances

5
t-test
  • Paired t performs a hypothesis test of the
    difference between two population means when
    observations are paired (matched).
  • When data are paired, as with before-and-after
    measurements, the paired t-procedure results in a
    smaller variance and greater power of detecting
    differences than the 2-sample t.
  • Select Stat gt Basic Statistics gt Paired t

6
One-Sample t
  • 1-Sample t performs a hypothesis test of the
    mean.
  • We use this in survey research, when testing
    known values of the population or another group
    values
  • Really for comparison purposes
  • Select Stat gt Basic Statistics gt 1-Sample t

7
ANOVA Analysis of Variance
  • ANOVA is similar to regression in that it is used
    to investigate and model the relationship between
    a dependent (response) variable and one or more
    independent (explanatory) variables.
  • It is different
  • the independent variables are qualitative
    (categorical)
  • no assumption is made about the nature of the
    relationship
  • ANOVA really extends the two-sample t-test for
    testing the equality of two population means to a
    more general null hypothesis of comparing the
    equality of more than two means, versus them not
    all being equal.

8
One-way ANOVA
  • Select Stat gt ANOVA gt One-way
  • Performs an one-way ANOVA, with the dependent
    variable in one column, subscripts in another.
  • Select Stat gt ANOVA gt One-Way (Unstacked)
  • Performs a one-way ANOVA, with each group entered
    in its own column
  • Response Select the column containing the
    response
  • Factor Select the column containing the factor
    levels

9
Two-Way ANOVA
  • Select Stat gt ANOVA gt Two-way
  • A two-way ANOVA tests the equality of populations
    means when classification of treatments is by two
    variables or factors.
  • All cells must have the same number of
    observations
  • Factors must be fixed
  • If your data are unbalanced or if you wish to
    compare means using multiple comparisons, utilize
    General Linear Model
  • Response Enter the column containing the
    response variable
  • Row Factor Enter one of the factor level columns
  • Column factor Enter the other factor level column

10
Differences
  • Both the t and F-test tell us if a difference
    exists, but it does not tell us any thing about
    the strength
  • Sometimes there is a need to utilize several
    statistical techniques
  • Your job is to choose the best stats for your
    purpose and objectives
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