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)

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)

ORGANIZING THE DATA IN GRAPHIC FORM:

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 exclusiveThe order is not important

Nominal Measures ofRelationship

The mode is the most appropriate measure to use.

1996 Party Identification Among Nonsouthern Whites(Hypothetical Data)

____________________________________________________Party Identification f____________________________________________________Democrat 126Independent 78Republican 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 ofRelationship

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 medianSign TestRuns TestGamma

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 relationshipWhen 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 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.

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 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.

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/