Transcript Document

BIVARIATE
Glenda Gamboa
Nicholas Gallagher
Gina Hass
Linda Isaac
Sheila Purcell
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.
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.
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
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.
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)
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)
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)
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)
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
Nominal Measures of
Relationship
The mode is the most appropriate measure
to use.
1996 Party Identification Among Nonsouthern Whites
(Hypothetical Data)
____________________________________________________
Party Identification
f
____________________________________________________
Democrat
126
Independent
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. )
Nominal Measures of
Relationship
Chi-square test
Fisher’s exact test
Lambda (Guttman coefficient of
predictability)
Ordinal Measures of
Relationship
Objects represent the rank order
Categories are mutually exclusive
Categories have logical order
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
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...).
Interval Measures of
Relationship
Spatial measurement is good for determining
correlation (linear dependence) without doing
any calculations.
Pearson's Product-Moment Correlation Coefficient =
r
When r = 1, there is a perfect positive relationship
When r = -1, there is a perfect negative relationship
When r = 0, there is no relationship
Interval Measures of
Relationship

Interval Measures of
Relationship
Numerical
example of
Pearson's
Correlation here.
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
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.
Highlighting the Bivariate
Analysis!
Looking for statistically significant
relationships between Variables and
Preference for online training
Insignificant relationship
Significant relationships
A Snapshot of Community-Based, Research In
Canada: 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.
Highlighting the Bivariate
Analysis!
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.
Disadvantages of
Bivariate 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.
Even More Disadvantages
of
Bivariate 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.
Even More Disadvantages
of
Bivariate 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.
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.1[Spring]: 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.1[March]:33 - 40.
Levin, Jack and James Alan Fox. 2004. Elementary statistics in
social research. Boston: Allyn and Bacon.
Oxford English Dictionary. http://dictionary.oed.com/