Correlation and Experimentation Study Guide

Foundations of Correlational Research

Psychologists employ various methods to describe, predict, and explain human feelings and actions. Correlational research is a non-experimental method used to describe the relationship between two or more variables. This method is distinct from experimentation, which attempts to establish direct cause-and-effect connections.

• Correlation: A measure of the extent to which two factors vary together, and thus of how well either factor predicts the other.
• Correlation Coefficient ($r$): A statistical index that represents the relationship between two variables, ranging from $-1.00$ to $+1.00$.
• Variable: Any factor that can vary and is feasible and ethical to measure.
• Scatterplot: A graphed cluster of dots, each representing the values of two variables.
  • Direction: The slope of the points suggests the direction of the relationship.
  • Strength: The amount of scatter suggests the strength of the correlation; minimal scatter indicates high correlation.

Understanding Positive and Negative Correlations

Describing behavior naturally leads to predicting it. When observations or surveys show that one trait or behavior coincides with another, those traits are said to correlate. The correlation coefficient ($r$) quantifies how closely two things vary together.

• Positive Correlation: Occurs when two sets of scores tend to rise or fall together. An example is height and weight.
  • Perfect Positive Correlation: represented by an $r = +1.00$, where scores for one variable increase in direct proportion to scores for another.
• Negative Correlation: Occurs when two sets of scores relate inversely; as one set goes up, the other goes down. A negative correlation does not imply a "bad" relationship or a lack of strength.
  • Perfect Negative Correlation: Represented by an $r = -1.00$.
  • Example: The correlation between an individual's height and the distance from their head to the ceiling is perfectly negative.
• Zero Correlation: Represented by an $r = 0.00$, indicating no relationship exists between the variables.

Statistical Illumination and Case Studies

Casual observation often misses patterns that statistics can reveal. Statistics calculate patterns by counting every case equally, whereas human attention is often caught by single events or individuals that may confirm or deny biases.

• The Fear and Disgust Study (Polák et al., 2020): 2291 Czech and Slovakian volunteers rated their fear and disgust regarding 24 animals on a scale from $1$ to $7$. While the relationship might be hard to see in raw data, the correlation between fear and disgust was found to be positive with an $r = +0.72$.

Data Table: Fear and Disgust Responses to Various Animals

The Correlation-Causation Fallacy

A critical point in research is that correlation does not imply causation. Even a strong correlation cannot determine which variable is the cause and which is the effect.

• Directionality Problem: The impossibility of knowing which variable causes the other based only on correlation (e.g., does social media use cause depression, or does depression lead to higher social media use?).
• Third Variable Problem: An outside factor may be responsible for the relationship between two variables. For example, length of marriage positively correlates with hair loss in men, but both factors are actually driven by the third variable of aging.

Illusory Correlations and Regression Toward the Mean

• Illusory Correlation: Perceiving a relationship where none exists, or perceiving a stronger-than-actual relationship. This is often caused by noticing and recalling instances that confirm our beliefs (e.g., believing dreams forecast actual events and remembering only the times they did).
• Illusion of Control: The belief that chance events can be personally influenced. Gamblers often fall victim to this, believing the hardness of a dice throw affects the outcome.
• Regression Toward the Mean: The tendency for extreme or unusual scores/events to fall back (regress) toward the average.
  • Example: A student who receives an outlier grade (unusually high or low) will usually see their next grade move back toward their typical average.
• Superstitious Thinking: Failure to recognize regression can lead to false conclusions. If a coach yells at a team after an unusually poor performance and they improve in the next game, the coach may falsely attribute the improvement to the scolding rather than natural regression to the mean.

Experimental Methodology and Isolation of Variables

To establish cause and effect, researchers use experimentation. This involves manipulating factors of interest and controlling others.

• Experiment: A research method where an investigator manipulates one or more factors (independent variables) to observe the effect on behavior or mental processes (the dependent variable).
• Experimental Group: The group exposed to the treatment (one version of the independent variable).
• Control Group: The group not exposed to the treatment, serving as a comparison for evaluating the treatment's effect.
• Random Assignment: Assigning participants to experimental and control groups by chance. This equalizes the two groups across variables like age, attitudes, and character traits, minimizing preexisting differences.
  • VS Random Sampling: Random sampling creates a representative sample for a survey; random assignment equalizes groups for an experiment.

Procedural Controls and the Placebo Effect

• The Placebo Effect: Experimental results caused by expectations alone. This occurs when a recipient assumes an inert substance (the placebo) is an active agent.
  • Evidence: Decaf-coffee drinkers reporting increased vigor when they think they have caffeine, or expensive placebos ($2.50$) working better than cheap ones ($0.10$).
• Single-blind Procedure: Participants are unaware ("blind") of whether they have received the actual treatment or a placebo.
• Double-blind Procedure: Both the participants and the research staff are ignorant about who has received the treatment or the placebo. This is common in drug-evaluation studies to eliminate researcher and participant bias.
• Bias Mitigation:
  • Social Desirability Bias: Participants affecting results by trying to please researchers.
  • Experimenter Bias: Researchers unintentionally influencing results to confirm their own beliefs.

Defining Variables

• Independent Variable (IV): The factor being manipulated; the variable whose effect is being studied.
• Dependent Variable (DV): The outcome that is measured; the variable that may change when the independent variable is manipulated.
• Confounding Variable: A factor other than the independent variable that might influence the results. Random assignment helps control for these.
• Operational Definitions: Precise specifications of the procedures used to manipulate the independent variable and measure the dependent variable. These allow for replication by other researchers.

Example Study (Victor Benassi):

• Design: College students were given in-class quizzes where some items were restudy (reviewing answers) and others were self-testing (producing answers).
• Results: Testing beat restudy. On the final exam, students scored $75\%$ on self-tested material vs. $51\%$ on restudied material.
• Independent Variable: The study procedure (reading answers vs. self-testing).
• Dependent Variable: Final exam performance.

Questions & Discussion

Q: Which of the following news reports are examples of a positive correlation, and which are examples of a negative correlation?

1. The more college students sleep, the better their academic performance.
2. The more time teen girls spend absorbed with online social media, the more at risk they are for depression and suicidal thoughts.
3. The longer children were breast-fed, the greater their later academic achievement.
4. The more leafy vegetables older adults eat, the less their mental decline over the ensuing 5 years.

A:

1. Positive
2. Positive
3. Positive
4. Negative

Q: How would you interpret a correlation coefficient of -0.87?A: This is a strong negative correlation, meaning that as one variable increases, the other decreases in a very consistent manner.

Q: Describe a scatterplot.A: It is a graphed cluster of dots representing two variables. The slope indicates the direction of the relationship and the amount of scatter indicates the strength of the correlation.

Q: You hear the school basketball coach telling her friend that she rescued her team's winning streak by yelling at the players after an unusually bad first half. What is another explanation of why the team's performance improved?A: Regression toward the mean; an unusually poor performance is statistically likely to be followed by a performance that is closer to the team's average ability level.