Correlational Research

Correlation

Statistical analysis that quantifies the strength and relationship between two variables. It indicates the degree to which two scores covary.

Example Interpreting Correlation

if r= .5, r^2 will equal .25. So, 25% of the variability in happiness can be accounted for by self-esteem OR 25% of the variability of self-esteem can be accounted for by happiness.

Path Analysis

tests the strength of evidence for a specific causal model using correlational data. Boxes represent variables, arrows and dotted lines represent correlation. "There is a significant relation between IQ and GPA; as IQ increases GPA increases." "After controlling for SES and IQ, there is a positive relation between motivation and GPA. As motivation increases GPA increases." "After controlling for IQ and motivation, there is no significant relation between SES and GPA."

Correlation Coefficient Types

1) Pearson Product-Moment Correlation: Score data. 2) Spearman rank-order Correlation: Either or both variables are ordinal. 3) Chi Square- Phi Correlation: Both of the variables are nominal

Analysis of Differential Research (2)

1) T test: used if the dependent measure is score data and there are two groups. 2) ANOVA: used if there are more than two groups and score data. Compare the p-value with a predetermined alpha level to decide whether we should reject the null hypothesis.

Basis for Correlation

A causes B; B causes A; A causes B and B causes A (self-reinforcing system); A and B are consequences of a common cause, but do not cause each other. Confounding variables: increased ice cream sales and murder rates-> one does not cause the other, increased temperature increases both of these. There is no relationship between A and B; the correlation is coincidental-> Spurious relation

Bivariate & Partial Correlation

Bivariate correlation: correlation between two variables. Partial correlation: correlate one variable with another after statistically removing the effects of a third variable. Ex. Using people who all have the same SES

Differential Research

Compares two or more groups that differ on preexisting variables. Independent Variable: classification variable (non manipulated); Ex. Categorical (gender). Dependent Variable: behaviors measured. Control Group: any group selected as a basis of comparison with the primary or experimental group. An ideal control group is identical to the experimental group on all variables except the independent variable that defines the groups. It is rare to find an ideal control group; researchers try to find a group that controls the most important and powerful confounding variables. You can create a control group by random assignment.

Correlation vs Causation

Correlation does not establish causality. Covariation is a necessary but insufficient condition for causality. If you have a causal relation between two variables, you will see a correlation between those two variables. But simply seeing a correlation between those two variables doesn't mean that there are causal factors at play. There could be a third variable coming into play causing the correlation. The data show that one relationship out of thousands of possible predicted relationships exists. To prove a theory, we would have to test every possible prediction. Scientists are reluctant to use the word "prove". Correlational research cannot prove a theory, but it can negate one. If you don't see a correlation between two variables, then there is no relation.

Interpreting Findings from Correlations

P-value: probability of achieving a correlation this large (or larger) if the correlation in the population were actually zero. If the probability is low (that the correlation is zero), we say the correlation is statistically significant. r: correlation coefficient: It indicates the strength and direction of the relationship. r^2: coefficient of determination; squared correlation. It indicates the proportion of variance accounted for.

Mediation vs Moderation

Moderation asks the question: does the nature of the relationship between two variables differ as a function of the moderating variable? Mediation asks the question: is the relationship between X and Y accounted for (or mediated) by a third variable? (confounding variables)

Moderation

Moderator Variable: a variable that seems to modify (or moderate) the relationship between other variables. (Gender, Culture, Ethnicity). Example: compliments increase self-esteem of females more than males.

Confounds

Two variables are confounded if they vary at the same time. Artifact: any apparent effect of the independent variable that is actually the result of the independent variable that is actually the result of some other variable that was not properly controlled. Artifacts are the result of confounding. A variable can have a confounding effect in a differential study only if it affects the scores on the dependent variable and there is a difference between the experimental and control groups on the potential confounding variable.

Differential Research cont.

Typically used when manipulation of an independent variable is impractical, impossible, inappropriate, or unethical. Avoid drawing casual conclusions from differential research because no variable has been manipulated. Demographic Variables: characteristics of individuals, such as age, education, and social class. Example: are there differences in income between males and females? You would use an independent t test.

Correlational Research

When conducting correlational research, researchers are often interested in causal questions. Frequently ethical or practical constraints prevent experimental manipulation. Correlational research quantifies the strength and direction of the relationship between two variables. At least two variables are measured. Can be used to predict future events when tested using regression. Provide data that are consistent or inconsistent with scientific theories.