The Correlational Research Strategy

Chapter 12

Correlational Research

The goal of correlational research is to describe the relationship between variables and to measure the strength of the relationship.

3 characteristics

• A correlation describes three characteristics of a relationship.

• The direction (positive / negative)of the relationship.

• The form (linear/ nonlinear) of the relationship.

• The consistency or strength (magnitude) of the relationship.

Direction

• In a positive relationship, there is a tendency for two variables to change in the same direction.

• In a negative relationship, there is a tendency for two variables to change in opposite directions.

Scatter Plot

Examples of positive and negative relationships

2 forms of correlation• Linear correlationData points in the scatter plot tend to cluster

around a straight line. The size of increase in Y is consistently predictable (not accurately).

(height and age)- Pearson

• Monotonic (nonlinear) correlationThe relationship is consistent and predictable, but

not linear. (practice & Performance) Spearman

2 forms of correlation

2 forms of correlation

Evaluating Relationships for Non- numerical Scores

• If one of the scores is numerical, like IQ, and the other is non- numerical, and If the non- numerical variable consists of exactly two categories, the resulting correlation is called a point-biserial correlation.

phi- coefficient.

• If the two non- numerical variables both consist of exactly two categories, each can be numerically coded as 0 and 1. For example, male 0 and female 1; failure 0 and success 1.

Phi

chi- square

• If both variables are non- numerical, the relationship is typically evaluated by organizing the data in a matrix.

• the matrix shows the frequency or number of individuals in that cell and the data are evaluated using a chi- square hypothesis test

Chi- Square

Drama Action Comedy

Latino 4 12 10

Asian 8 10 12

White 19 18 14

APPLICATIONS OF THE CORRELATIONAL STRATEGY

1. Prediction (SAT & GPA)2. Reliability and Validity (Test & Retest)3. Evaluating Theories (IQ and Math)

coefficient of determination

• The squared value of a correlation is called the coefficient of determination and measures the percentage of variability in one variable that is determined, or predicted, by its relationship with the other variable.

Sample size

• With a sample of two individuals, you will always obtain a perfect correlation of 1.00

• As the sample size increases, it becomes increasingly more likely that the sample correlation accurately represents the real relationship that exists in the population.

• You should be warned, however, that a statistically significant correlation does not necessarily mean that the correlation is large or strong.

Advantages

• can identify variables and describe relationships between variables that might suggest further investigation using the experimental strategy to determine cause- and- effect relationships.

• allow researchers an opportunity to investigate variables that would be impossible or unethical to manipulate.

• Correlational studies tend to have high external validity.

Weaknesses - Internal Validity

• Correlational studies tend to have low internal validity.

• A correlational study does not determine which variable is the cause and which is the effect.

• The third- variable problem.

RELATIONSHIPS WITH MORE THAN TWO VARIABLES

• For studying multivariate relationships we use a statistical procedure known as multiple regression.