Chapter 14: Correlation (unit 12)
what is the range of possible correlation coefficients?
+1.0 to -1.0
Which of the following correlations indicates the most consistent relationship between x and y?
-0.90
Which of the following person correlations show the strongest, most consistent relationship?
-0.90 The larger the correlation (independent of sign), the stronger the relationship
A set of n=12 pairs of x and y values produces a Pearson correlation of r=-.70. How much variability in the y scores can be predicted from the relationship with x?
49%
Pearson Correlation
A measure of strength and direction of the linear relationship between two variables. Know those correlation coefficients are always rounded to the hundredth place.
Relieability
A measurement procedure is considered reliable to the extent that it that it produced stable, consistent measurements.
Why does correlation not equal causation?
It describes the relationship between the two variables, but it does not explain why the two variables are related.
How can an outlier affect a correlation?
It drastically alters the value for the correlation and thereby can affect ones interpretation of the variables x and y.
What does r^2 measure and what is it called?
It is called the coefficient of determination and it measures the proportion of variability in one variable that can be determined from the relationship with another variable.
A Pearson correlation of r=0.38 indicates that the data points are...
very loosely clustered around a line sloping up from left to right.
Suppose that there is a correlation of +0.92 between test scores on math exams and test scores on physics exams, what does that mean?
y
The correlation between reading comp and problem solving skills is found to be r=.70. How much variability in problem solving skills can be accounted for by the relationship with reading comp?
y
Which of the following most completely describes the possible values for the Pearson correlation?
-1.00 ≤ r ≤ 1.00
A set of n=5 pairs of x and y scores has ∑X = 15, ∑Y = 5, and ∑XY = 10. For these data, the value of SP is
-5 SP=10-5(15)/5
A set of n=10 pairs of scores has ∑X = 20, ∑Y = 30, and ∑XY = 54. What is the value of SP for these data?
-6 SP=54-20(30)/10
a set of n=15 pairs of x and y values has a Pearson correlation of r=0.40. If the 2 points were added to each of the x values, then what is the correlation for the resulting data?
0.40
A set of n=5 pairs of x and y scores produces a Pearson's correlation of r=0.10. The x values vary from 40-50 and the y values vary 30-60. If one new individual with x=4 and y=4 is added to the sample, them what is the most likely value for the new correlation?
0.60
List the 4 applications for the correlational coefficients (p. 458-459)
1. Prediction 2. Validity 3. Reliability 4. Theory verification.
List three characteristics of the x and y relationships measured by a correlation
1. The direction of the relationship. 2. The form of the relationship 3. The degree (strength)
What do correlations of 1.0, 0.0, and -1.0 signify?
1.0 positive, 0.0 zero, -1.0 negative
A set of n=10 pairs of scores (x and y values) has SSx=5, SSy=15, and SP=16. The Pearson correlation for these data is
16/√75
A set of n=25 pairs of x and y scores has ∑X = 25, ∑Y = 10, and ∑XY = 30. For these data, the value of SP is
20
A set of n=50 pairs of x and y scores has SSx=180, SSy=80, ∑x=50, ∑y=150, and ∑XY 180. What is the Pearson correlation for these scores?
30/120=0.25
A set of n=15 pairs of scores (x and y values) has SSx=4, SSy=16, and SP=4 The Pearson correlation for these data is
4/√64 =0.50 The correlation is equal to 4 divided by the square root of (4*16)
What is the value of SP for a set of n=5 pairs of x and y values with ∑x=10, ∑y=15, and ∑xy=75
45
Note that a correlational design is a type of nonexperimental design.
ok
Be able to calculate the sum of products (SP) using the computational formula.
ok.
Theory Verification
A process whereby a scientific theory is tested through observation and analysis. If the process falsifies the theory, the theory must be revised to account for the observed events.
a researcher obtains a strong positive correlation between aggressive behavior for 6-year-old children and the amount of violence they watch on TV. Based on this correlation, which of the following conclusion is justified?
Children who watch more TV violence tend to exhibit more aggressive behavior
A researcher student is chosen to observe and record purchases made at the local party store. The student notices that her fellow college students purchase larger quantities of low quality bear and lower quantities of higher quality beer. This is an example of a positive correlation.
False
the Spearmen correlation will always be a positive value between zero and one.
False, the value of the spearmen correlation can range in value from +1.00 to -1.00
The value of sum of products (SP) can never be less then zero
False. The value of SP can be either positive or negative.
Prediction:
If two variables are known to be related in some systematic way, it is possible to use one of the variables to make accurate predictions about the other.
The pattern would appear in a graph of person correlation of r=-0.30?
Points widely scattered around a line that slopes down to the right. r=-0.30 is a weak, negative correlation.
A researcher notices that the farther an organic produce item has to be shipped, the higher the price of said item. What type of correlation does this example suggest?
Positive correlation.
The value of the Pearson Correlation will be negative of
SP is negative
A positive correlation will be negative if
SP is negative. the sign of the SP controls the sign of the correlation. SS is always positive
Validity
The ability of a test to measure what it is intended to measure
Positive correlation
two variables tend to move in the same direction -when x increases, Y also increases -when x increases, y also decreases
What is an outlier?
an individual with x and/or y values that are substantially different (L or S ) from the values obtained from other individuals in the data set. The data point of a single outlier can have a dramatic influence on the value obtained for the correlation.
A Pearson correlation of r = +1.00 and a correlation of r=-1.00 both indicates a perfect linear relationship.
True
A Pearson correlation of r=+1.00 and a correlation of r=-1.00 both indicates a perfect linear relationship
True
A Pearson correlation of r=-0.90 indicates that the data points are tightly clustered around a line sloping down from left to right
True
A person correlation of r=-1.00, indicates that the data points fits perfectly on a straight line.
True
A researcher observing children a school playground notices that a number of aggressive acts tends to increase as the temperature increases. This is an example of a positive correlation
True
A researcher observing children on a school playground noticed that the number of aggressive acts tends to increase as the temperature increases. This is an example if a positive correlation.
True
One or two extreme scores can have a large effect on the value of the Pearson correlation.
True
Given the formula for the Pearson correlation (r), be able to calculate r given a set of data.
ok
How can correlation be distorted by using a restricted range of the scores?
Whenever a correlation is computed from scores that do not represent the full range of possible values, you should be cautious in interpreting the correlation.
In general, the more square footage a person's home has, the greater the value of the car they drive. This demonstrates...
a positive relationship. Square footage and car value change in the same direction.
Which of the following is a justified conclusion if a correlation is negative?
increase in x tend to be accompanied by a decrease in y
Be able to calculate the sum of squares (SS) for both X and Y variables using the computational formula (see unit 4)
ok
Given a value for R, you should be able tp calculate r-squared and explain what this value in terms of variability.
ok
A set of 15 pairs if scores (x and y values) produces a correlation of r=0.85. If 5 points are added to each of the x values and the correlation is computed for the new scores, what value will be obtained for the new correlation?
r=0.85 Adding a constant to each x simply shifts the set of scores to the right. The pattern of the relationship (and the correlation) are not changed.
negative correlation
the two variables tend to go in opposite directions. As the x variable decreases, the y variable decreases. That is, an inverse relationship.
A positive correlation indicates that as one variable decreases, the other value also tends to decrease
true
Note that correlation requires measures on
variables (x and y) for each individual
