Educational Research: Correlational Studies EDU 8603 Educational Research Richard M. Jacobs, OSA, Ph.D.

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... Scientific and disciplined inquiry is an orderly process, involving: method description and execution of procedures to collection information (“method”) analysis objective data analysis results statement of findings (“results”) problem recognition and identification of a topic to be studied (“problem”)

Research methods... Quantitative Quantitative… data instruments …collects and analyzes numerical data obtained from formal instruments

Quantitative methods... descriptive research (“survey research”) correlational research causal-comparative research (“ex post facto research”) experimental research

correlational research correlational research variables …determines whether and to what degree a relationship exists between two or more quantifiable variables …the degree of the relationship is expressed as a coefficient of correlation

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

A correlation study… correlation coefficient …a study providing a numerical estimate  the correlation coefficient  about the relationship between two or more variables

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… 1. select the problem 2. 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 shotgunfishing …a shotgun or fishing 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 correlation coefficient …the result is expressed as a correlation 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… strong negative strong positive 0.00 no relationship

A positive correlation… y x

A negative correlation… y x

No correlation… y x

y x

statistical significance statistical 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… 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… 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 variable predictor variable… …the variable used to predict criterion variable criterion 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 studies …multiple 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 + bX Where 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 + bX 1 + bX 2 + … + bX n Where Y = predictor criterion X n = 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 analysis discriminant function analysis …similar to multiple regression analysis but a continuous predictor variable is used to predict a categorical variable

path analysis path analysis …studies relationships and patterns among a number of variables, yielding a diagram showing the direct or indirect relationships between the variables

structural equation modeling structural 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 correlation canonical 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… 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... …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......which attempt to determine the cause, or reasons for pre-existing differences in groups of individuals causal-comparative studies