BIVARIATE

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BIVARIATE

• Glenda Gamboa
• Nicholas Gallagher
• Gina Hass
• Linda Isaac
• Sheila Purcell

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Statistical Hypothesis Testing

• Hypothesis tests are tools used to apply
  statistics to real life problems
• They are based on contradictions, by forming a
  null hypothesis and then testing it with sample
  data.

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Statistical Hypothesis Testing
NULL HYPOTHESIS (Hø) a plausible hypothesis,
which may explain a given set of data, unless
statistical evidence indicates otherwise (in
which case, the null hypothesis is REJECTED and
an Alternative Hypothesis (Ha) can be devised).
If the null hypothesis explains the data, it is
ACCEPTED due to a lack of evidence, and no
further tests are necessary.
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EXAMPLE

• Hypothesis
• Children raised by parents with degrees are more
  likely to go to college
• Independent Variable Being raised by parents
  with degrees
• Dependent Variable Going to college

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ERRORS
TYPE 1 ERRORS reject the null hypothesis when it
is really true. TYPE 2 ERRORS fail to reject
the null hypothesis when it is really false.
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MEASUREMENTS OF RELATIONSHIP

• Nominal "involves naming or labeling...placing
  cases into categories and counting their
  frequency of occurence" (Levin Fox 2004, 5)
• Ordinal at this level, the researcher "seeks to
  order her/his cases in terms of the degree to
  which they have any given characteristic...but
  does not indicate the magnitude of difference
  between numbers" (Levin Fox 2004, 5)
• Interval "not only tells us about the ordering
  of categories but also indicates the exact
  distance between them" (Levin Fox 2004, 5)

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ORGANIZING THE DATA IN GRAPHIC FORM
Pie Charts "one of the simplest methods of
graphical presentation. Pie
charts are particularly

useful for showing the differences in
frequencies and
precentages among
categories of nominal-level variable."
(Levin
Fox 2004, 38) Bar Graphs "can
accommodate any number of categories at
any level of
measurement." (Levin Fox
2004, 38)
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More Graphic Presentations
Frequency Polygon "tends to stress continuity
rather than differentness therefore, it is
particularly useful for depicting ordinal and
interval data. This is because frequencies
are indicated by a series of points placed
over the score values or midpoints of each
class interval...The height of each point or dot

indicates
frequency or percentage of occurrence."
(Levin Fox 2004, 40) Shape of Frequency
Distribution
"Frequency polygons can help us
visualize
the variety of shapes and forms
taken
by
frequency distributions." (Levin Fox 2004,
41)
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Still not tired of graphic presentations?
Kurtosis "A shape characteristic of a frequency
distribution that reflects the sharpness of the
peak (for a unimodal distribution) and the
shortness of the tails..."(Oxford English
Dictionary) 
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Nominal Measures of Relationship

• Classifies objects into categories based on some
  characteristic of the object
• Gender
• Marital status
• Race
• College major
• Religious affiliation
• Categories are mutually exclusive
• The order is not important

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Nominal Measures ofRelationship

• The mode is the most appropriate measure to use.

1996 Party Identification Among Nonsouthern
Whites (Hypothetical Data) _______________________
_____________________________ Party
Identification f _____________________________
_______________________ Democrat 126 Independe
nt 78 Republican 96 ___ Total
300 (Frankfort-Nachmias and David
Nachmias. 2000. Bivariate analysis. In Research
Methods in the Social Sciences 351 - 384. New
York Worth. )
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Nominal Measures ofRelationship

• Chi-square test
• Fishers exact test
• Lambda (Guttman coefficient of predictability)

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Ordinal Measures of Relationship

• Objects represent the rank order
• Categories are mutually exclusive
• Categories have logical order

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Ordinal Measures of Relationship

• The central tendency of an ordinally measured
  variable can be represented by its mode or its
  median
• Sign Test
• Runs Test
• Gamma

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Interval Measures of Relationship Spatial
measurement which is used to show the distance
between values.  Dates and temperature (not
Kelvin) are good examples of interval
measurement. The difference between 30 and 40
degrees Fahrenheit is the same as the difference
between 70 and 80 degrees. Distance between units
matters most, but  because there is no natural
zero one cannot say that 80 degrees is twice as
hot as 40 degrees. Ratio measurement is like
interval measurement but ratios rely a natural
zero (i.e. weight, height, age...). 
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Interval Measures of Relationship Spatial
measurement is good for determining correlation
(linear dependence) without doing any
calculations.  Pearson's Product-Moment
Correlation Coefficient rWhen r 1, there is
a perfect positive relationshipWhen r -1,
there is a perfect negative relationshipWhen r
0, there is no relationship 
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Interval Measures of Relationship ?
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Interval Measures of Relationship  Numerical
example of Pearson's Correlation here.
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LITERATURE REVIEW
I couldn't find any peer reviewed articles using
bivariate analysis for   research in our field
from the last 10 years!  Well, there was one
but   the Bivariate group from last year used
it...    Online Workplace  Training in
Libraries"    By Connie K Haley  
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Real Fast...

• Studied people's preferences for online or
  in-person training in correlation with their
  demographic data, experience, and other variables
  in order to identify possible relationships.   
• The methodology was quantitative using
  demographic characteristics and the Likert-scale
  assessment of training preferences as well as
  qualitative using open-ended questions.
• A summary of the deductive theories were that
  younger and or better educated/trained people
  would prefer online training.
• The data did not support the original assumptions
  and only established a relationship between a
  preference for online training and the training
  providers as well as the training location.

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Highlighting the Bivariate Analysis!
  Looking for statistically significant
relationships between Variables and Preference
for online training
Insignificant relationship
Significant relationships
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A Snapshot of Community-Based, Research
InCanada Who? What? Why? How?

• Studied the context Community-Based Research (as
  opposed to "outside-expert driven research") in
  Canada by comparing the levels of involvement by
  organization type and other descriptive variables
  of participants.
• A 25 question survey reviewed by the University
  of Toronto was produced and emailed to 2,000
  appropriate potential participants with 308
  returning completed surveys.  The data was
  analyzed using univariate and bivariate stats
  tests.    
• Academic and Non-profit organization were most
  actively pursuing Community-Based Research with a
  high level of satisfaction also impacting policy
  and programing on a noticeable level.

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Highlighting the Bivariate Analysis!
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Advantages of Bivariate Models
Bivariate models are easy to create and
interpret.   It is convenient to quantify
variables and have a mathematical expression for
a relationship.   They can provide a good
starting-off point. For example, a bivariate
model shows that taller people tend to make more
money than shorter people. Now that a
relationship has been defined, a study can be
done to explain why this is true.    
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Disadvantages ofBivariate Models
  They may be oversimplified and cannot always be
taken at face value.   An analysis of income vs.
gender is informative, but the additional
variable for race gives us a better picture. Men
earn more than women, but white women earn more
than black men.
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Even More Disadvantages ofBivariate Models
 
  Relationships may be indirect.   People with
historically African-American names tend to earn
less than people with white names, but giving
your child a white-sounding name will not
necessarily make him more successful.
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Even More Disadvantages ofBivariate Models
 
  Correlation is not causation.   If I have a
rock and no tigers show up for a week, one should
not conclude that my rock is a tiger
repellent.      
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REFERENCES 

• Bartlett II, James E., Joe W. Kotrlik and
  Chadwick C. Higgins. Organizational research
  Determining appropriate sample size in survey
  research. Information Technology, Learning, and
  Performance Journal 19, no.1Spring 43 - 50.
• Frankfort-Nachmias and David Nachmias. 2000.
  Bivariate analysis. In Research Methods in the
  Social Sciences 351 - 384. New York Worth.
•  
• Haley, Connie K. 2008. Online workplace training
  in libraries. Information Technology and
  Libraries 27, no.1March33 - 40.
•  
• Levin, Jack and James Alan Fox. 2004. Elementary
  statistics in social research. Boston Allyn and
  Bacon.
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• Oxford English Dictionary. http//dictionary.oed.c
  om/
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