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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.