EDUC 607 - Murillo

Summary of Selected Statistical Procedures

The following material is based on the assumption that the widespread use of statistical computer software has diminished the need for introductory students to memorize mathematical formula. It presents information about some of the most commonly used quantitative summary procedures: Name, Reference (from the McMillan and Schumacher text), Function, an Example of how it can be used, Relevant Terms, and Attributes. See also Locke, L. F., Silverman, S. J., & Spirduso, W.W. (1998) Table 6.1, pp. 126 - 127.

     Procedure / Name / Reference                             Function                 Example of What it Can be Used to Study

t-test, 

pp. 363-368
To compare the means of two groups
Attitudes of 4th and 6th graders, pre and posttest scores, etc.

 

 

Chi-Square,

pp. 379-382
To compare observed frequencies with expected frequencies, especially when the independent variable is subdivided
The number of students who used counseling center services, according to grade level

 

 

 

 

Analysis of Variance (ANOVA) 

pp. 368-370
  To compare two or more sample groups with one independent variable 

The effects of three different treatments on posttest achievement

 

 

 

Factorial Analysis of  Variance,

pp. 371-376
  
To compare two or more sample groups with two or more independent variables 
Whether type of treatment and level of anxiety improve achievement

                                        
 

 

Analysis of Co-Variance (ANCOVA),

pp. 376-378

1) To adjust initial, uncontrolled groupdifferences related to the dependent variable, or

2) To increase the likelihood of finding a difference in the means of small groups
1) When two groups have different pre test means, ANCOVA can help

identify the significance of pre/posttest contrasts

2) When intact groups are used with randomization--however,

ANCOVA cannot “equalize” them (cannot match or randomize)

                                        
                                         

                                                                                                                                       

                                    
                                                      

 

Multivariate Analysis of Variance (MANOVA),

pp. 380-384
In the generic sense appropriate to introductory research, for comparisons in studies with many variables
 

Whether the effect of many specific component attitudes toward science

affect a general attitude (enjoyment,

appreciation of physics, respect for chemistry, opinion of dissection, benefits of field trips, and so forth)

                                                                       
                                                          

                                               
                                 

 

Multiple CorrelationTests (Multiple Regression) pp. 226-29, 290
To add together the predictive power of several independent variables, and express each so they can be compared and contrasted   
The predictive value on teacher effectiveness of 1) teacher evaluation scores, 2) college GPA, 3) ratings by references, 4) interview ratings, and 5) written self-report by teacher

 

 

 

Wilcoxon Rank Sum

To check whether two populations have the same medians, especially when it is necessary to compare data from one population withsensitive data from another sample

Is student achievement greater in a sampleof independent schools, or in the population of schools in statewide school districts

Note: Rank sum procedures are not to extreme outlying

 

 

                                     
 

                                                           

Meta-Analysis,

pp. 147-148 
To statistically summarize results of prior independent studies
Review of 282 studies to identify strategies that can help reducerecidivism (“What works?”)



 

 

                                                                  
                                                                                                                                

Relevant Terms

INDEPENDENT VARIABLE: (AKA experimental or manipulated variable.) The measured data that precedes, or is antecedent to, the dependent variable; the cause--time directed to study, motivation, voluntary enrollment, etc...

DEPENDENT VARIABLE: The measured data that is the consequence of another measured variable; the effect--achievement scores, grade point average (GPA), diminished disciplinary reports, numbers of objectives attained, etc...

UNIVARIATE DATA: Measured data that involve only one variable within a population, with all variables held constant except the one studied.

MULTIVARIATE DATA: In the generic sense, measured data that involve more than one variable within a population.

PARAMETRIC TESTS: Statistical procedures that are based on the assumption of normality (the “bell-shaped curve”--homogeneity of score dispersion).

NONPARAMETRIC TESTS: Statistical procedures that do not require normality.

 

 

 

Attributes of the Procedures Outlined in this Summary
Note 1: Inferential procedure names are underlined.
Note 2: Asterisked (*) procedures are based dispersion or variance.

                                                     VARIABLES                 |                       NORMALITY
Name of Procedure                   Univariate Multivariate        |            Parametric         Nonparametric
                                                                                           |
t-test                                              X                                   |                X
Chi-Square                                    X                                   |                                            X
ANOVA*                                     X                                   |                 X
Factorial ANOVA*                                         X                 |                 X
ANCOVA*                                   X                                   |                X
MANOVA*                                                    X                 |                X
Multiple Correlation Tests                                X                  |                X        (either)      X
Wilcoxon Rank Sum                       X                                   |                                            X
Meta-Analysis                                X   (both)  X                  |                X         (both)       X