4 General Principles of Research Correlational StudiesA positive correlation (+) means that as one variable increases, so does the other.A zero or near zero correlation means that the variables have no relationship
8 General Principles of Research Correlational StudiesThe value of the correlation coefficient can range from –1.00 toThe higher the absolute value, the stronger the relationship is, regardless of the direction.A negative correlation (-) means that as one variable increases, the other decreases.
11 Concept CheckThe greater the score on a depression inventory, the lower the score on a memory testNegative
12 Concept Check Which relationship is stronger? +. 85 or -.90 or 1.2 - .90+. 85 or -.90 or 1.2.25 or or + .63+.63
13 Figure 2.9 A strong correlation between depression and impaired sleep does not tell us whether depression interferes with sleep, poor sleep leads to depression, or whether another problem leads to both depression and sleep problems.
16 Height and Temperament of 20 Men CorrelationHeight and Temperament of 20 Men12345678910111213141516171819208063617974696275776064767166737068904281394872573084SubjectHeight inInchesTemperament
17 Scatterplot of Height and Temperament Correlation959085807570656055504540353025TemperamentscoresHeight in inchesScatterplot of Height and Temperament
18 Pearson correlation coefficient r = the Pearson coefficientr measures the amount that the two variables (X and Y) vary together (i.e., covary) taking into account how much they vary apartPearson’s r is the most common correlation coefficient; there are others.
19 Computing the Pearson correlation coefficient To put it another way:Or
20 Sum of Products of Deviations Measuring X and Y individually (the denominator):compute the sums of squares for each variableMeasuring X and Y together: Sum of ProductsDefinitional formulaComputational formulan is the number of (X, Y) pairs
21 Correlation Coefficent: the equation for Pearson’s r:expanded form:
22 ExampleWhat is the correlation between study time and test score: