involves collecting data to determine whether, and to what degree, a relationship exists between two or more quantifiable variables.

Pupose of Correlational Research

1.       To determine relations among variables (i.e. relationship study)

2.       To use these relations to make a prediction (i.e. prediction study

3.       Used to determine various types of validity and reliability.

-          High correlation between two variables does not imply that one causes the other. You should not infer causal relations on the basis of data from a correlational study.  However high correlation permits predictions.

What are the major steps invovled in correlational research?

What is an acceptable sample size?

1.       Problem selection: correlational studies are designed to either determine how a set of variables are related or test a hypothesis regarding expected relationships.  You have to make this decision

2.       Participants and Instrument selection: if instruments do not accurately reflect the intended variables, the resulting correlation coefficient will not accurately indicate the degree of relationship.  Minimum sample size is generally 30 participants

3.       Design and procedure: Scores for two (or more) variables of interest are obtained for each member of the sample, and the paired scores are then correlated.  The result is the expressed as a correlational coefficient that indicated the degree of relation between two variables.

4.       Data analysis and interpretation: correlational coefficient is a decimal number ranging from -1.00 to +1.00.  It indicates the size and direction of relation between the two variables.  A coefficient close to +1.00 has a high correlation.  If a person has a score on one then they are likely to have a high score on the other, and vice versa.  If the coefficient is near .00 the variables are not related.

Correlational Coefficient

correlational coefficient: is a decimal number ranging from -1.00 to +1.00.  It indicates the size and direction of relation between the two variables. 

- A coefficient close to +1.00 has a high correlation.  If a person has a score on one then they are likely to have a high score on the other, and vice versa.  If the coefficient is near .00 the variables are not related.

Positive Correlation

Negative Correlation

Curvilinear Correlation

Positive correlations: correlation coefficient near +1.00 indicates that the variables are strongly and positively related.  A person with a high score on one is likely to have a high score on the other variable and vice versa. An increase on one variable is associated with an increase on the other. (e.g. IQ score and GPA)

Negative correlations: correlation coefficient near -1.00 are strongly negative correlations or inversely related. A person with a high score on one variable will have a low score on the other variable.  An increase on one variable is associated with a decrease on the other variable. (e.g. IQ score and errors)

Curvilinear correlations: an increase in one variable is associated with an increase in another up to a point, at which further increase  in the first variable results in a corresponding decrease in other variable (or vice versa). (e.g. age and agility)

Scatterplot

Visual displays of data from all the case study sites based on diminsions or themes of interest that appear to be related to each other.

Low, moderate, and high correlational coefficients

Low correlation: a low correlation represents a low degree of association between the variables.        Correlational coefficient much lower than .50 is generally not useful for group prediction or individual prediction

Moderate correlation: .60’s and .70’s adequate for group prediction purposes

High correlation: .90’s

Common variance (shared variable)

 indicates the extent to which variables vary in a systematic way; it is computed by squaring the correlation coefficient.  The higher the common variance, the higher the correlation. (e.g. correlational coefficient of .80 indicates (.80)squared or .64, or 64% common variance

-          the extent to which variables vary in a systematic manner

-          the percentage of variance in the criterion variable explained by the predictor variable

Statistical Significance

 refers to the probability that the results (i.e. correlation of this size) would have occurred simply due to chance.

-          To be statistically significant the obtained correlational coefficient must reflect a true statistical relation, not a chance one.

-          “Significant” does not mean “important”; rather, it is a statistical term indication the probability that a given result is due to chance.

-          To determine whether a correlation is statistically significant, researchers set a standard (e.g., 95% confident, or probability of chance =.05) then compare the obtained correlation to a table that shows correlation coefficient values for particular significance levels and sample sizes.

Relationship study is conducted to gain insight into the variable or factors that are related to a complex variable, such as academic achievement, motivation, or self-concept. 

-          Such studies give direction to subsequent causal-comparative and experimental studies.

-          For data collection in relationship studies, the researcher first identifies the variables to be related.

-          In data analysis and interpretation of relationship studies, the scores for one variable are correlated with the scores for another variable, or the scores for a number of variables are correlated with some particular variable of primary interest.

-          One advantage of relationship study is that all the data may be collected within relatively short time period.

Prediction Study

Prediction study is an attempt to determine which of a number of variables are most highly related to the criterion variable.

-          Prediction studies are often conducted to facilitate decision making about individuals or to aid in the selection of individuals.

-          The variable used to predict is called the predictor, and the variable that is predicted is a complex variable called the criterion.

What is the Differense between

Relationship study and Prediction Study

The difference in data collection procedures for a prediction study and a relationship study is that in a prediction study the predictor variables are generally obtained earlier than the criterion variables, whereas in a relationship study all variables are collected within a relatively short period of time. 

What are the different types of correlational coefficients used in "continous" (interval and ration) and "ordinal" data.

Continuous data (i.e. interval and ration): used in Pearson r.  Most scores from instruments used in education, such as achievement measures and personality measures.

Ordinal data: used in Spearman rho rank difference correlation is used when ordinal data (i.e. ranks) are correlated.

Predictor variables

Criterion Variables

Predictor variables: the variable used to predict

Criterion variables: the variable that is predicted