Comparing Groups

1
Comparing Groups Looking at Distributions

• EDLD 6333 Statistical Reasoning

2
The MEANS Procedure

• To compare summary statistics (means) over groups
  of cases
• Independent variable grouping variable
• Dependent variable interval/ratio
• Graphs to display means for groups
• Layers More than one subgrouping variable

3
Education and Job Satisfaction
ANALYZE?COMPARE MEANS?MEANS
4
MEANS Output
What exactly does this mean? N 747 M 14.04
SD 2.7 But now for I.V.s groups.
5
Seeing it Graphically
In Output Window, click on GRAPHS?BAR? Then
select Simple and Summaries for groups of cases
as shown to the right.
6
Bar Chart Dialog Box
To view years of education by the I.V. groups,
select options shown here.
7
Bar Chart of Educ by Satjob
Much easier to see differences in the mean years
of education for each group graphically. Later,
well be testing to see if there are
statistically significant differences.
8
More Than One Layer

• To see if the relationship between job
  satisfaction and education is similar for another
  layer of groups (male, female)
• Subdivide the rows and summary statistics further
• 1st subdivide by jobsat
• 2nd subdivide by sex

9
Education by jobsat sex
Click on NEXT to add variable sex as the second
layer
10
Output for 2 Subgroups
You can make multiple comparisons. Be careful of
sample size shrinkage in subgroups!
11
Seeing it Graphically
In Output Window, click on GRAPHS?BAR? Then
select Clustered and Summaries for groups of
cases as shown here.
12
Clustered Bar Dialog Box
Select educ for bars, Category Axis should be
satjob, and define clusters by sex.
13
Bar Chart of educ by satjob and sex
For which job category do you find the greatest
difference in years of education for males and
females?
14
Bar Chart of educ by sex and satjob
Here you can definitely see that the relationship
b/w jobsat and educ is NOT the same for men and
women.
To transpose the chart like this, in the Chart
Editor window select SERIES? TRANSPOSE DATA
15
What else can we do?

• The EXPLORE procedure
• Examining the relationship between groups of
  cases in more detail
• More descriptive statistics
• Stem-and-leaf plots
• Boxplots

16
Age and Job Satisfaction

• ANALYZE?DESCRIPTIVE STATISTICS?EXPLORE

17
EXPLORE Output
18
Terms in Output

• Mean average
• 5 Trimmed Mean excludes the 5 largest and 5
  smallest values
• Less sensitive to outliers
• Based on 90 center
• Only very different if you have extreme outliers
• Median
• Standard Dev., Min., Max., Range, IQR

19
Extreme Values

• Ask for Outliers in the Statistics subdialog box

Check suspicious values for errors in recording
or entry. If there are extreme values and they
are correct, use an appropriate summary measure
that wont be too affected.
20
Percentiles

• Ask for percentiles in the Statistics subdialog
  box

You will get two types of percentiles, Weighted
Average and Tukeys Hinges. They are different
b/c the calculations are different-one based on
intervals, another on first value.
21
Graphical Displays for EXPLORE

• Histogram
• Look for extreme values, symmetry, separate
  clumps of data
• Stem-and-Leaf Plots
• Like histograms, w/ more information
• Boxplots
• To help visualize the distribution
• Gives median, IQR, and range

22
To Get Different Plots
In the Plots subdialog box, select the displays
you want. For Boxplot, select Factor levels
together, b/c you want to compare groups.
23
Histogram
24
Stem-and-Leaf Plot
Age of Respondent Stem-and-Leaf Plot for SATJOB
Very satisfied Frequency Stem Leaf
1.00 1 . 16.00 2 .
01333344 29.00 2 . 5555667778899
44.00 3 . 00001111222333334444 68.00
3 . 555555555666677778888888899999999
51.00 4 . 000001111122223333333344
38.00 4 . 55555666777789999 30.00
5 . 0000111123344 29.00 5 .
5557777888889 9.00 6 . 0123
4.00 6 . 6.00 Extremes (gt72)
Stem width 10 Each leaf 2 case(s)
denotes fractional leaves.
Multiply Stem and Stem width and add leaf values
to get data values.
25
Boxplot
26
Terms

• Outlier values b/w 1.5 and 3 IQRs
• Extreme Value more than 3 IQRs
• Skewness
• Median low, mean high Positive
• Median high, mean low Negative
• Remember, you can only look at means and
  variances for variables of interval/ratio scale

27
Green Book

• Exporting data and charts
• Ranking, sorting, transposing
• Splitting/Merging files
• Modifying Charts
• Modifying data values

28
Next Weeks Assignment

• See website