The homework problems on comparing central tendency and variability extend the focus central tendenc

1

• The homework problems on comparing central
  tendency and variability extend the focus central
  tendency and variability to a comparison of the
  central tendency and variability for two or more
  groups.
• The goal of comparing central tendency is to make
  a statement about which group tends to have
  higher scores than the other.
• The goal of comparing variability is to identify
  which group is more diverse, i.e. is more spread
  out around the measure of central tendency.
• As we did with the previous assignment, our first
  task is to examine the skewness of the variable
  we want to compare for all groups in the
  distribution.
• Based on our appraisal of skewness, we will
  determine that the mean/standard deviation or
  median/interquartile range are more appropriate
  measures.

2

• Using the appropriate statistic, we will compare
  the measures of central tendency for each group
  to determine which group had the higher or lower
  score, implying that they had more or less of the
  characteristic measured by the variable we are
  analyzing.
• Using the appropriate statistic, we will compare
  the measures of variability for each group to
  determine which group had more diverse scores,
  i.e. the larger measure of dispersion.

3

• The introductory statement in the question
  indicates
• The data set to use (GSS200R)
• The statistic to use (central tendency and
  dispersion) for two or more groups
• The variables to use in the analysis sex
  sexto form the groups for a comparison of age
  when first child was born agekdbrn.

4
The first statement for us to evaluate concerns
the number of valid and missing cases. To answer
this question, we produce the descriptive
statistics using the SPSS Explore procedure.
5
To compute the measures of central tendency and
dispersion in SPSS, select the Descriptive
Statistics Explore command from the Analyze
menu.
6
Move the variable for the analysis agekdbrn to
the Dependent List list box..
Click on the Statistics button to select
optional statistics.
7
The check box for Descriptives is already marked
by default.
Mark the Percentiles check box. This will
provided the upper and lower bounds for the
interquartile range.
Click on Continue button to close the dialog box.
8
After returning to the Explore dialog box, click
on the OK button to produce the output.
9
The SPSS output provides us with the answer to
the question on sample size.
The 'Case Processing Summary' in the SPSS output
showed the total number of valid cases to be 193
and the number of missing cases to be 77.
10
The 'Case Processing Summary' in the SPSS output
showed the total number of valid cases to be 193
and the number of missing cases to be 77. Click
on the check box to mark the statement as correct.
11
The next pair of statements asks us to identify
the direction of the skewing in the distribution
of the variable.
12
The skewness for the distribution of "age when
first child was born" agekdbrn is 1.09. Since
this is greater than zero, we characterize it as
positive skewing or skewing to the right. If it
were less than zero, it would be negative skewing
or skewing to the left.
13
The skewness for the distribution of "age when
first child was born" agekdbrn is 1.09. Since
this is greater than zero, we characterize it as
positive skewing or skewing to the right. We
mark the check box for the statement with the
correct response.
14
The next pair of statements asks us to identify
which measure of center and spread should be
reported for the variable.
15
When the distribution is symmetric, the mean and
standard deviation are better indicators of the
center and spread of the distribution. When the
distribution is badly skewed, the median and
interquartile range are the preferred indicators.
Using the rule of thumb that skewness between
-1.0 and 1.0 is acceptable, the skewness of
this distribution (1.09) is excessive making the
median and interquartile range the preferred
measures of center and spread.
16
Using the rule of thumb that skewness between
-1.0 and 1.0 is acceptable, the skewness of
this distribution (1.09) is excessive making the
median and interquartile range the preferred
measures of center and spread. The check box for
the second statement is marked.
17
Having decided to use the median and
interquartile range to represent the center and
spread of the distribution, the next pair of
questions ask us to compare the medians of the
two groups. To compare the groups, we need to
add the grouping variable to the analysis.
18
Click on the Dialog Recall button on the tool
bar. This button enables us to modify the
specifications for previously completed analyses.
19
When we click on the Dialog Recall button, a drop
down menu of recently conducted analyses appears.
We click on the Explore menu option to amend
the analysis which we just completed.
20
Second, click on the OK button to produce the
output.
First, move the grouping variable sex to the
Factor List list box. Descriptive statistics will
be computed for each category of the factor.
21
Since the distribution of "age when first child
was born" agekdbrn was badly skewed (1.09),
the comparison of the central tendency of the
groups is based on the median. ct.
The median for survey respondents who were male
(25) is larger than the median for survey
respondents who were female (22).
The statement that "survey respondents who were
male were older when first child was born than
survey respondents who were female" is correct.
22
Since the distribution of "age when first child
was born" agekdbrn was badly skewed (1.09),
the comparison of the central tendency of the
groups is based on the median. The median for
survey respondents who were male (25) is larger
than the median for survey respondents who were
female (22).
The statement that "survey respondents who were
male were older when first child was born than
survey respondents who were female" is correct
and is marked.
23
The next pair of questions ask us to compare the
interquartile ranges of the two groups.
24
Since the distribution of "age when first child
was born" agekdbrn was badly skewed (1.09),
the comparison of the spread or variability of
the groups is based on the interquartile range.
The interquartile range for survey respondents
who were male (7) is the same as the
interquartile range for survey respondents who
were female (7).
Each of the statements about the spread of the
distribution imply that one group is more diverse
than the other. Since both groups have the same
interquartile range, neither statement is correct.
25
Since the distribution of "age when first child
was born" agekdbrn was badly skewed (1.09),
the comparison of the spread or variability of
the groups is based on the interquartile range.
The interquartile range for survey respondents
who were male (7) is the same as the
interquartile range for survey respondents who
were female (7). Since both statements imply a
difference in the interquartile range, neither is
correct and neither one is marked.