Presentation on theme: "Topics: Correlation The road map"— Presentation transcript:
1 Topics: Correlation The road map Examining “bi-variate” relationships through picturesExamining “bi-variate” relationships through numbers
2 Correlational Research Exploration of relationships between variables for better understandingExploration of relationships between variables as a means of predicting future behavior.
3 Correlation: Bi-Variate Relationships A correlation describes a relationship between two variablesCorrelation 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?
4 Types of Correlation Studies Measures of same individuals on two or more different variablesMeasures of different individuals on the “same” variableMeasures of the same individuals on the “same” variable(s) measured at different times
5 Representations of Relationships Tabular Representation: arrangement of scores in a joint distribution tableGraphical Representation: a picture of the joint distributionNumerical Represenation: a number summarizing the relationship
7 Creating a Scatter Plot Construct a joint distribution tableDraw the axis of the graphLabel the abscissa with name of units of the X variableLabel the ordinate with the name of the units of the Y variablePlot one point for each subject representing their scores on each variableDraw 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”
8 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
9 Examples of Various Scatter Plots Demontrating Tilt
10 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.
11 Examples of Various scatter plots Demontrating Shape (Strength)
12 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: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).
20 Coefficient of Determination Coefficient of Determination: the squared correlation coefficientThe proportion of variability in Y that can be explained (accounted for) by knowing XLies between 0 and +1.00r2 will always be lower than rOften converted to a percentage
21 Coefficient of Determination: Graphical Display
22 Some WarningsCorrelation does not address issue of cause and effect: correlation ≠ causationCorrelation is a way to establish independence of measuresNo rules about what is “strong”, “moderate”, “weak” relationship