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# Topics: Correlation PowerPoint PPT Presentation

Topics: Correlation. The road map Examining “bi-variate” relationships through pictures Examining “bi-variate” relationships through numbers . Correlational Research. Exploration of relationships between variables for better understanding

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Topics: Correlation

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### Topics: Correlation

• The road map

• Examining “bi-variate” relationships through pictures

• Examining “bi-variate” relationships through numbers

### Correlational Research

• Exploration of relationships between variables for better understanding

• Exploration of relationships between variables as a means of predicting future behavior.

### Correlation:Bi-Variate Relationships

• A correlation describes a relationship between two variables

• Correlation tries to answer the following questions:

• What is the relationship between variable X and variable Y?

• How are the scores on one measure associated with scores on another measure?

• To what extent do the high scores on one variable go with the high scores on the second variable?

### Types of Correlation Studies

• Measures of same individuals on two or more different variables

• Measures of different individuals on the “same” variable

• Measures of the same individuals on the “same” variable(s) measured at different times

### Representations of Relationships

• Tabular Representation: arrangement of scores in a joint distribution table

• Graphical Representation: a picture of the joint distribution

• Numerical Represenation: a number summarizing the relationship

### Creating a Scatter Plot

• Construct a joint distribution table

• Draw the axis of the graph

• Label the abscissa with name of units of the X variable

• Label the ordinate with the name of the units of the Y variable

• Plot one point for each subject representing their scores on each variable

• Draw a perimeter line (“fence”) around the full set of data points trying to get as tight a fit as possible.

• Examine the shape:

• The “tilt”

• The “thickness”

### Reading the Nature of Relationship

• Tilt: The slope (or slant) of the scatter as represented by an imaginary line.

• Positive relationship: The estimated line goes from lower-left to upper right (high-high, low-low situation)

• Negative relationship: The estimated line goes from upper left to lower right (high-low, low-high situation)

• No relationship: The line is horizontal or vertical because the points have no slant

### Reading the Strength of Relationship

• Shape: the degree to which the points in the scatter plot cluster around the imaginary line that represents the slope.

• Strong relationship: If oval is elongated and thin.

• Weak relationship: If oval is not much longer than it is wide.

• Moderate relationship: Somewhere in between.

### Numerical Representation: The Correlation Coefficient

• Correlation Coefficient = numerical summary of scatter plots. A measure of the strength of association between two variables.

• Correlation indicated by ‘r’ (lowercase)

• Correlation range:-1.00 0.00 +1.00

• Absolute magnitude: is the indicator of the strength of relationship. Closer to value of 1.00 (+ or -) the stronger the relationship; closer to 0 the weaker the relationship.

• Sign (+ or -): is the indication of the nature (direction,)tilt) of the relationship (positive,negative).

### Influences on Correlation Coefficients

• Restriction of range

• Use of extreme groups

• Combining groups

• Outliers (extreme scores)

• Curvilinear relationships

• Sample size

• Reliability of measures

### Coefficient of Determination

• Coefficient of Determination: the squared correlation coefficient

• The proportion of variability in Y that can be explained (accounted for) by knowing X

• Lies between 0 and +1.00

• r2 will always be lower than r

• Often converted to a percentage

### Some Warnings

• Correlation does not address issue of cause and effect: correlation ≠ causation

• Correlation is a way to establish independence of measures

• No rules about what is “strong”, “moderate”, “weak” relationship