Quantitative Data Analysis

The purpose of conducting a statistical test is to determine statistical significance:

The conclusion that the results are unlikely to have occurred by chance.  An observed relationship or difference probably exists in the population.

•	Probability of .05 (p = .05) or less 
•	Referred to as the ".05 level of significance"
•	Outcome will occur by chance less than 5 times in 100

•	More stringent level of significance (p = .01)
•	Outcome will occur by chance less than 1 time in 100

Statistical tests are generally used to:

1.	Determine the strength of a relationship
or
2.	Determine whether there is a difference between groups

Common Statistical Tests for Calculating Difference

t test for independent means: 
Used to compare the means of two samples to see whether there is a statistical difference between the groups.
•	Produces a value called an obtained t 

Analysis of Variance (ANOVA):
Used to compare the means of two or more groups to see whether statistical differences exist between the groups.  To know where the significant difference are, a post hoc analysis is necessary.
•	F value

Analysis of Covariance (ANCOVA):
Used for equating groups on one or more variables.  It adjusts scores on a dependent variable for initial differences on other variables, such as a pretest score.
•	F value

Multivariate Analysis of Variance (MANOVA):
An extension of ANOVA which incorporates two or more dependent variables in the same analysis.  Used only when researcher has reason to believe relationships exist between the dependent variables.
•	Value is called Wilk's lambda

Chi-Square Test:
Used to analyze data that are reported in categories such as gender.
•	(X2)
Common Statistical Tests for Calculating Relationship

Pearson Product Moment Correlation:
Used to compare groups when data in interval (percentage) or ratio (frequency) scales.  Determines degree of relationship between variables in a group.  Produces a correlation coefficient to describe the strength of relationship.
•	r

Magnitude of r
	Interpretation	
.00 - .40
	Of little practical importance.  Possible to use for theoretical purposes.
	
.41 - .60
	Large enough to be of practical and theoretical use.	
.61 - .80
	Strong relationship, may have predictive value.	
.81 or above	Very sizable relationship.  Highest predictive use.

Effect Size (ES):
Used to assess the magnitude of a difference between groups.  Used when researchers look at the outcomes of many studies that measure the same variable (meta-analysis).  May also be used with in a study.
•	ES of .50 or higher is considered to be an important finding
•	(Δ)

 

Common Statistical Tests for Calculating Prediction

Multiple Regression:
Analysis used to determine a correlation (relationship) between a criterion variable and the best combination of two or more predictor variables.
•	r
•	Verbal score on SAT and high school GPA (predictor variables) have a high positive correlation (r = +.68) for first-semester college GPA (criterion variable).
•	Strength of correlation is symbolized by R
•	R of .70 - .80 are considered quite high
•	⇧ R  =  more reliable prediction

Path Analysis:
Used to test the possibility of a causal connection among three or more variables.  Identifying causal variables could explain why a phenomenon occurs.
•	r
•	Example hypothesis:  Students who feel alienated at school …
relevance of coursework ⇨ school enjoyment ⇨ number of friends

Research Definitions
Abstract:
Summary of the study that describes the most important aspects, including major findings and conclusions.

Variable:
A characteristic that can assume any one of several values, such as ethnicity, height, or teaching method.

Dependent Variable:
A variable expected to be affected by the independent variable.  Sometimes called the criterion or outcome variable.  Effect of method of instruction on history test score; the dependent variable is the test score (represented on y axis).

Independent Variable:
A variable that is presumed to affect the dependent variable.  Sometimes called the experimental or treatment variable (represented on the x axis), such as method of instruction.

Triangulation:
Cross checking of data using multiple data sources or multiple data collection procedures.  For example, using both quantitative and qualitative methods to collect information on the effects of teaching methods on final exam scores, student motivation in the class, and teacher enthusiasm.

Reference
Fraenkel, J. R. & Wallen, N. E. (1993).  How to design and evaluate research
in education (2nd edition).  New York: McGraw-Hill.