Educational Research: Educational Research: Correlational StudiesCorrelational Studies

EDU 8603

Educational Research

Richard M. Jacobs, OSA, Ph.D.

Research...Research...

The systematic application of a family of methods employed to provide trustworthy information about problems…an ongoing process based on many accumulated

understandings and explanations that, when taken together lead to generalizations about problems and the development of theories

The basic steps of research...The basic steps of research...

Scientific and disciplined inquiry is an orderly process, involving:

description and execution of procedures to collection information (“methodmethod”)

objective data analysisanalysis statement of findings (“resultsresults”)

recognition and identification of a topic to be studied (“problemproblem”)

Research methods...Research methods...

QuantitativeQuantitative……collects and analyzes numerical datadata

obtained from formal instrumentsinstruments

Quantitative methods...Quantitative methods...

descriptive research (“survey research”)correlational researchcausal-comparative research (“ex post facto research”)

experimental research

correlational researchcorrelational research…determines whether and to what

degree a relationship exists between two or more quantifiable variablesvariables

…the degree of the relationship is expressed as a coefficient of correlation

…the presence of a correlation does not indicate a cause-effect relationship primarily because of the possibility of multiple confounding factorsconfounding factors

A correlation study…A correlation study…

…a study providing a numerical estimatethe correlation coefficientcorrelation coefficientabout the relationship between two or more variables

Types of correlation studies…Types of correlation studies…

relationship studies……attempt to gain insight into variables that are related to more complex

variables

prediction studies……conducted to facilitate decisions about individuals, to aid in various types of selection, to test variables

believed to be good predictors of a criterion, or to determine predictive validity of measuring instruments

Conducting a correlational study…Conducting a correlational study…

1. select the problem2. select participants and instrument

3. design and procedure

4. data analysis and interpretation

1. select the problem……the variables to be correlated should

be selected on the basis of some rationale

…a shotgunshotgun or fishingfishing approach is discouraged

2. select participants and instrument……using an acceptable sampling

methodology, a minimum of 30 participants is acceptable

…larger samples are used if validity and reliability are important because error measurement may mask the true relationship

3. design and procedure……two or more scores are obtained for each member

of the sample, one score for each variable of interest, and the paired scores are then correlated

…the result is expressed as a correlation coefficientcorrelation coefficient

4. data analysis and interpretation……the two or more scores are obtained for each member

of the sample, one score for each variable of interest, and the paired scores are then correlated

…the correlation coefficient indicates the degree of relationship between the variables of interest

Correlation coefficient…Correlation coefficient…

-1.00 +1.00

strong negative strong positive

0.00

no relationship

A positive correlation…A positive correlation…

y

x

A negative correlation…A negative correlation…

y

x

No correlation…No correlation…

y

x

No correlation…No correlation…

y

x

statistical significancestatistical significance……a statement that the relationship between

the variables, at a given level of probability (α, alpha), are truly related

…is dependent upon the sample size

Conducting relationship studies…Conducting relationship studies…

Follows the procedure for correlational studies with two adaptations…

1. data collection

2. data analysis and interpretation

relationship studies……attempt to gain insight into variables that are related to complex variables

…indicate whether causal-comparative and experimental studies may determine a causal connection between the variables

1. select the problem……the variables to be correlated should

be selected on the basis of some rationale

…identify an appropriate population of participants from which to sample

…if needed, administer instrument to collect data

2. data analysis and interpretation……the scores for one variable are correlated with

the scores for another variable and expressed in the form of a correlation coefficient

The method for computing a correlation coefficient…

…depends upon the type of data represented by each variable

…types of data:nominal nominal (dichotomous)

ordinal ordinal (rank)

interval interval (continuous)

ratio ratio (continuous)

with continuous data……use the product moment correlation,

Pearson r (ρ, rho) with rank data…

…use the rank difference correlation, Spearman r (ρ, rho)

with dichotomous data…

…use the phi correlation (ψ) with curvilinear data…

…use the eta correlation (η)

Conducting prediction studies…Conducting prediction studies…

Follows the procedure for correlational studies with two adaptations…

1. data collection

2. data analysis and interpretation

predictive studies……when two variables are highly related,

scores on one variable can be used to predict scores on the other variable

…facilitate decisions about individuals or to aid in various types of selection

predictor variablepredictor variable……the variable used to predict

criterion variablecriterion variable……the variable predicted

1. data collection……valid measuring instruments should

be carefully selected to represent the variables of interest

…it is especially important that the measure used as the criterion variable be valid

2. data analysis and interpretation……single prediction studies single prediction studies use one

predictor

…multiple prediction studiesmultiple prediction studies use more than one predictor

…in both, a continuous predictor variable is used to predict a continuous criterion variable

single prediction studies… Y = a + bXWhere Y = predictor criterion X = an individual’s score on the predictor variable a = a constant calculated from the scores of all participants b = the coefficient indicating the contribution of the predictor to the criterion

multiple prediction studies……use multiple predictors Y = a + bX1 + bX2 + … + bXn

Where Y = predictor criterion Xn = an individual’s score on the predictor variable a = a constant calculated from the scores of all participants b = the coefficient indicating the contribution of the predictor to the criterion

discriminant function analysisdiscriminant function analysis…similar to multiple regression analysis but a continuous predictor

variable is used to predict a categorical variable

path analysispath analysis…studies relationships and patterns among a number of variables, yielding a

diagram showing the direct or indirect relationships between the variables

structural equation modelingstructural equation modeling…a sophisticated form of path analysis providing greater theoretical validity and statistical precision

clarifying the direct or indirect interrelationships among variables relative to a given variable

canonical correlationcanonical correlation…an extension of multiple regression analysis that produces a correlation

based on a group of predictor variables and a group of criterion variables

factor analysis (FANOVA)factor analysis (FANOVA)…a statistical method for making sense of a large number of variables

…approach: group a larger number of variables into a smaller number of clusters; derive factors by finding groups of variables that are highly among each other, but lowly with other variables; use factors as variables

Mini-Quiz…Mini-Quiz…

True and false…

…a high degree of correlation between two variables implies that one causes the other

False

…the existence of a high negative correlation permits prediction

True

…the correlation coefficient indicates the percentage of relationship between the variables

False

…the correlation coefficient indicates the amount of common variance shared by the variables

True

…common, or shared, variance indicates the extent to which variables vary in a systematic way

True

…the more systematically two variables vary, the lower the correlation coefficient

False

…the amount common, or shared, variance is much less than the numerical value of the correlation coefficient

True

…for a given sample size, the value of the correlation coefficient needed for significance increases as the level of confidence increases

True

…the level of significance indicates the probability that a given relationship is a true one, regardless of whether it is a strong or weak relationship

True

…a statistically significant correlation coefficient establishes a cause-effect relationship

False

…relationship studies that have not uncovered useful relationships have at least identified variables that can be excluded from future studies, which is a necessary step in science

True

…the more correlation coefficients computed at one time, the more likely it is that some wrong conclusions about the existence of a relationship will be reached

True

…an appropriate population is one for which the data on each of the identified variables can be collected

True

…an artificial dichotomy is one where ordinal, interval, or ratio data are artificially turned into nominal data

True

…most correlational techniques assume that the relationship being investigated is linear

True

…a correction for unreliability should be used in prediction studies

False

…the greater the variability there is in each set of scores being correlated, the higher the correlation coefficient is likely to be

True

…in a prediction study, it is especially important that the measure used as the criterion be reliable

False

…one reason for shrinkage is that an initial predictor equation may be the result of chance relationship that will not be found again with another group of participants

True

…the mathematical expression of the degree of relationship between variables

correlation coefficient

…a research strategy in which the researcher correlates all sorts of variables to discover relationships

shotgun or fishing approach

Fill in the blank…

…indicates that an obtained correlation coefficient is really different from a correlation of zero, or no relation, usually stated at a given level of probability

statistical significance

…a type of study in which a researcher identifies variables that are correlated with the dependent variable and removes their influence so that they will not be confused with that of the independent variable

relationship study

…a chart on which the variables to be correlated are placed which provides a visual representation of their relationship

scatter plot

…a relationship between variables in which an increase in one variable is associated with a corresponding increase in another variable up to a point, at which further increases in the first variable result in corresponding decreases in the other variable (or vice versa)

curvilinear

…the fact that correlation coefficients tend to be lowered if the measures being correlated have low reliability

attenuation

…the variable used to predict

predictor

…the variable that is predicted

criterion

…the tendency of a prediction equation to become less accurate when used with a group other than the one on which the equation was originally developed

shrinkage

…the procedure by which a prediction equation is validated with at least one other group and the variables no longer found to be related to the criterion measure are removed from the equation

cross-validation

…the equation used in a multiple prediction study

multiple regression equation

This module has focused on...This module has focused on...

…which involve collecting data in order to determine whether, and to what degree, a relationship exists between two or more quantifiable variables

correlational studies

The next module will focus on...The next module will focus on...

...which attempt to determine the cause, or reasons for pre-existing differences in groups of individuals

causal-comparative studies