Correlational and Causal Comparative Research

Definition and Purpose Correlational research involves the collection of data to determine the extent to which two (or more) variables are related. If a relationship exists, we say that the two variables covary in some non-random way. The strength of the relationship is expressed as a correlation coefficient, r.

Correlational Research Concerned with examining the strength of associations (or relations) among two or more variables. Strength is expressed as a correlation coefficient between -1.0 and +1.0. The relationship can be positive or negative. Correlations with absolute values close to 1.0 imply strong relationships; close to 0.0 imply weak (or no) relationships.

Purpose of Correlation Research Descriptive: Show (or describe) the associations among variables. Hypothesis testing: Test whether variables expected to be related are, in fact, related. Theory driven. Correlations often occur spuriously. Should not examine correlations, first, and then construct a theory to explain them.

Correlational Research Design Collect data on two or more variables for each participant in the research study. Minimally accepted sample size is 30. If the measures have low reliability, larger sample sizes are needed. If participants are to be subdivided (say, into males and females) larges sample sizes are needed.

More on Sample Sizes Depends on the reliability of the measures. With reasonable reliability a minimum of 30 cases with bivariate measures is usually acceptable. The statistical test is a t test of the null hypothesis: H0: xy = 0.0

Analysis Correlation coefficients (rxy) describe both the size and direction of the relationship between two variables, x and y. Positive correlations close to +1.0 indicate that two variables are strongly positively related (scores on one variable can be used to predict scores on the other). Negative correlations close to -1.0 indicate that the two variables are strongly negatively correlated. Again scores on one can be used to predict scores on the other.

Analysis Assuming all or most of the coordinates (points) fall within the ellipse (of a scatter graph), the figure below represents a weak (near zero) correlation.

Analysis This figure represents a weak positive correlation:

Analysis Here we have a strong positive correlation:

Analysis This would be a representation of a weak negative correlation.

Analysis Finally, a graphic representation of a strong negative correlation.

A Table of Correlations Correlations among several variables are usually given in a correlation table. Correlations Among Four Variables Var 1 Var 2 Var 3 Var 4 1.00 .32 .78 .66 .89 .21 .11

A Table of Correlations Only one half of a correlation table need be displayed. The upper triangular half or…… Correlations Among Four Variables Var 1 Var 2 Var 3 Var 4 1.00 .32 .78 .66 .89 .21 .11

A Table of Correlations The lower triangular half. Correlations Among Four Variables Var 1 Var 2 Var 3 Var 4 1.00 .32 .78 .89 .66 .21 .11

A Table of Correlations Often the diagonal is replaced by dashes. Correlations Among Four Variables Var 1 Var 2 Var 3 Var 4 - - - .32 .78 .89 .66 .21 .11

How large should a correlation be? Correlations where Abs(rxy ) > .50 are typically useful for prediction purposes The square of the correlation coefficient (rxy2) gives the percent of variation x and y have in common. The size of the correlation required in order to be useful depends on the purpose.

Statistical significance and Practical significance Correlation coefficients should not be interpreted unless it is first shown that the coefficient is statistically significant (i.e., until we can state that there is sufficient statistical evidence that the correlation is NOT zero). With large enough samples, even small correlations can be statistically significant. Statistically significant correlations may not be practically significant. A low correlation is still a low correlation.

Linear correlations vs Curvilinear correlations The chart below indicates a correlation between two variables that has a near- zero linear correlation but a strong curvilinear correlation.

Causal-Comparative Research Also called ex post facto research. An attempt is made to find the cause or explanation for existing differences between (or among) groups. Two or more existing groups are compared retrospectively. Note that in correlational research we had one group and two or more variables. Here we have two or more groups and one variable.

Causal-Comparative research vs Experimental research In experimental research (or quasi-experimental research) the researcher controls the administration of the independent variable. In causal-comparative research the groups being formed have already been differentiated according to the independent variable (e.g., either they have been exposed to pre-school or not).

Causal Comparative Research Groups… are classified according to common preexisting characteristic, and compared on some other measure There is NO intervention, manipulation, or random assignment Groups classified according to common preexisting characteristic (habits, lifestyle, condition, etc.) and compared on some other measure (typically from past) Describe current condition & look to the past to identify possible causes Use existing data to look for relationships Example: What causes lung cancer? Get data on people with lung cancer and see if they have common traits or experiences that might explain why they have cancer compared to those who don’t Groups classified according to existing habits, lifestyle, condition, etc. Not randomly assigned

Major difficulty: Establishing the cause. Three conditions for establishing cause-effect relationships: The presumed cause must precede the effect. The relationship between the cause and effect must be statistically significant. Other probable causes must be eliminated (most difficult condition to meet).

Spurious Causation Here are two examples of spurious causation. In the top example, the correlation between A and C requires the mediator, B. In the bottom example the correlation between B and C exists because both variables are caused by A. A B C B C A

Reaching Conclusions At best, causal-comparative research produces evidence that supports a theoretical conjecture. The strength of evidence relies heavily on two things: The extent to which rival causes can be ruled out. The extent to which the results can be predicted (according to theory) beforehand.

Conducting a Causal-Comparative Study Identify two or more populations (or groups) that differ on some independent variable (IV) of interest (e.g., novice teachers and veteran teachers). Formulate some theory about how the groups should perform differently on some dependent variable (DV) of interest (e.g., classroom management). Select representative samples from the populations and compare them on the dependent variable.

Two Variations of Causal Comparative Studies There are two ways to approach causal-comparative research: Prospective: start with a presumed cause an investigate effects (not very common in social science/education research). Retrospective: start with a presumed effect and investigate possible causes (these are more prevalent in social science/education research).

Examples of the Two Variations Investigate the relationship between gender and career aspirations or career choice. Retrospective: Groups identified on the basis of career choice and then compared by gender. Prospective: Groups formed on the basis of gender, and compared on strength of career aspirations.

Examples of the Two Variations Investigate the relationship of time watching TV (the IV) on academic achievement (the DV) Prospective: Form groups on the basis of how much TV they watch and compare them on academic achievement (say, GPA). Retrospective: Form groups on the basis of academic achievement (say, class rank) and compare this to hours of TV watched.

Examples of the Two Variations Investigate the effect of time parents spend reading to children and children’s reading readiness when entering 1st grade. Retrospective: Groups formed on the basis of a reading-readiness test score, and compare in terms of time parents spend reading to their children. Prospective: Form groups of children in terms of time their parents spent reading to them and compare the children on reading readiness scores.

Examples of the Two Variations Investigate the effect of mentoring and tendency to drop out of high school. Prospective: Groups formed on the basis of whether they enjoyed a mentoring relationship while in high school and compared in terms of whether they dropped out of high school Retrospective: Groups formed on the basis of whether they dropped out of high school, and compared on whether they enjoyed a mentoring relationship prior to dropping out.

Example Causal-Comparative Study: What causes lung cancer? Finding: People with lung cancer smoke more than people without lung cancer. There are no other differences in lifestyle characteristics between the groups. Conclusion: Smoking is a possible cause of lung cancer. Caution: Is there a third factor that might explain lung cancer AND smoking? Smoking and cancer might have a common cause that was not examined in the study. Ex: Stress causes cancer and causes people to smoke. Thus, banning smoking will not prevent lung cancer. If stress was not examined, then we have no way of knowing. If stress was examined and found to be different between groups, then we would not know which caused which. Control subjects may not have been properly matched. Lung cancer subjects live in urban areas; control groups lives in rural area. Maybe more smog in urban area causes cancer. Random selection and random assignment of experimental design would take care of these problems.

More Examples of Causal Comparative Research A researcher measured the mathematical reasoning ability of young children who had enrolled in Montessori schools and compared the scores with a group of similar children who had not been to Montessori schools. A researcher measured the frequency of students’ misbehavior at schools which use corporal punishment and compared the frequency to schools which did not use corporal punishment.

More Examples of Causal Comparative Research A researcher compared the high school dropout rate among students who had been retained (held back) in elementary school with similar students who had not been retained A researcher formed 3 groups of preschoolers – those who never watched Sesame Street, those who watched it sometimes, and those who watched it frequently – and then compared the 3 groups on a reading readiness test.

Weaknesses and Controls Lack of randomization, inability to manipulate the independent variables, lack of controls of extraneous variables are all weaknesses in causal-comparative research. Three approaches that help ameliorate some of the problems are: Matching, Comparing homogeneous groups, and Analysis of covariance (to be discussed later).

Strengthening Causal Comparative Designs Strong inference (theory plays a major role). Time sequence (presumed cause precedes presumed effect). Incorporate other, possible, causes in the design (measure common antecedents) . Use designs that control for possibl extraneous causes: matched group design Extreme groups design Statistical control (Analysis of Covariance) Strong inference - test a plausible alternative hypothesis against the research hypothesis Collect data on rival hypothesis so you can rule it out. EX: Groups formed on the basis of how much TV they watch, and compared on academic achievement (GPA). Does TV watching cause lower achievement? Maybe lower achievement causes more TV watching. Or maybe lack of exercise depletes the brain of chemical transmitters, making school learning more difficult, encouraging lethargic behavior, and thus more TV watching The only way to rule this out is to collect data on exercise as part of the design. Time sequence – try to determine which behavior occurred first Which came first – low GPA or increased TV watching? Common prior antecedents – look for prior differences that distinguish the groups Focus on presumed effect (skill at teaching); once groups of highly skilled and less skilled teachers have been identified, one begins a systematic search for prior differences that distinguish the groups (GPA, highest degree, educational philosophy, enrollment in CE courses) Still may be that something else causes teachers to enroll in CE courses, which makes them better teachers Matched group design – groups are dissimilar on hypothesized cause but the same on matching variable believed to be rival hypothesis (age, socioeconomic status) Extreme groups design – selection of groups represents maximum differences on presumed cause or effect Matched extreme groups design - extreme groups designs strengthens finding even more, especially if matched

Establishing Causal Relationships From John Stuart Mills Establish a temporal sequence (the presumed cause must precede the presumed effect). Establish a statistical relation ship between the presumed cause and effect (correlations among variables or differences among groups). Rule-out possible rival causes (control for, or eliminate extraneous sources of influence). This is often the most difficult condition. Strong theory plays an important role here.

Wide Variety of Statistical Procedures t tests, ANOVA, ANCOVA when two or more groups are being compared. Regression analysis when there are multiple independent variables. MANOVA, and multivariate regression, when there are multiple dependent variables. Path analysis and structural equation modeling when the theoretical causal paths are being investigated.

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