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