you can calculate: central tendency variability you could graph the data
DESCRIPTION
You can calculate: Central tendency Variability You could graph the data. You can calculate: Central tendency Variability You could graph the data. Bivariate Distribution. Positive Correlation. Positive Correlation. Regression Line. Correlation. r = 1.00. Regression Line. r = .64. - PowerPoint PPT PresentationTRANSCRIPT
Smile
Jerry 10
Elan 6
George 8
Newman 9
Kramer 7
Smile
Jerry 10
Elan 6
George 8
Newman 9
Kramer 7
You can calculate:
Central tendency
Variability
You could graph the data
Talk
Jerry 5
Elan 1
George 3
Newman 4
Kramer 2
You can calculate:
Central tendency
Variability
You could graph the data
Bivariate Distribution
Smile Talk
Jerry 10 5
Elan 6 1
George 8 3
Newman 9 4
Kramer 7 2
Positive Correlation
Smile Talk
Jerry 10 5
Elan 6 1
George 8 3
Newman 9 4
Kramer 7 2
Positive Correlation
0
2
4
6
8
10
12
1 2 3 4 5
Talk
Smil
e
Regression Line
0
2
4
6
8
10
12
1 2 3 4 5
Talk
Smil
e
Correlation
0
2
4
6
8
10
12
1 2 3 4 5
Talk
Smil
e
r = 1.00
Regression Line
0
2
4
6
8
10
12
1 2 3 4 5
Talk
Smil
e
. . .. .
r = .64
Regression Line
0
2
4
6
8
10
12
1 2 3 4 5
Talk
Smil
e
. .. .
r = .64
.
Frown Talk
Jerry 10 2
Elan 6 6
George 8 4
Newman 9 3
Kramer 7 5
Frown Talk
Jerry 10 2
Elan 6 6
George 8 4
Newman 9 3
Kramer 7 5
Negative Correlation
Negative Correlation
0
2
4
6
8
10
12
2 3 4 5 6
Talk
Fro
wn
r = - 1.00
Negative Correlation
0
2
4
6
8
10
12
1 2 3 4 5
Talk
Fro
wn
.
.
. .. r = - .85
Gas in car Talk
Jerry 10 8
Elan 6 9
George 8 3
Newman 9 4
Kramer 7 3
Gas in car Talk
Jerry 10 8
Elan 6 9
George 8 3
Newman 9 4
Kramer 7 3
Zero Correlation
Zero Correlation
0
2
4
6
8
10
12
3 4 5 6 7 8 9
Talk
Gas
in c
ar
.
... .r = .00
Correlation Coefficient
• The sign of a correlation (+ or -) only tells you the direction of the relationship
• The value of the correlation only tells you about the size of the relationship (i.e., how close the scores are to the regression line)
• Which is a bigger effect?
r = .40 or r = -.40
How are they different?
Interpreting an r value
• What is a “big r”
• Rule of thumb:
Small r = .10
Medium r = .30
Large r = .50
Practice• Do you think the following variables are positively,
negatively or uncorrelated to each other?
• Alcohol consumption & Driving skills• Miles of running a day & speed in a foot race• Height & GPA• Forearm length & foot length• Test #1 score and Test#2 score
Practice
• Page 102– #5.8
• Page 96– #5.5 1) Draw a scatter plot
2) Estimate the correlation
5.8
• A) -.60
• B) -.95
• C) .50
• D) .25
Smile Y
Talk X
Jerry 9 5
Elan 2 1
George 5 3
Newman 4 4
Kramer 3 2
0
2
4
6
8
10
12
1 2 3 4 5
Talk
Smil
e
.
.. ..
Statistics Needed
• Need to find the best place to draw the regression line on a scatter plot
• Need to quantify the cluster of scores around this regression line (i.e., the correlation coefficient)
Correlation Coefficient• A correlation coefficient provides a quantitative
way to express the degree of relationship between two variables
• There are 3 different formulas presented in the book
• Z-score formula is a good way to see “what's going on” -- page 93
Blanched Formula
XY = product of each X value multiplied by its paired Y value
X = mean of variable X
Y = mean of variable Y
Sx = standard deviation of variable X
Sy = standard deviation of variable Y
N = number of pairs of observations
r =
Smile Y
Talk X
Jerry 9 5
Elan 2 1
George 5 3
Newman 4 4
Kramer 3 2
SmileY
TalkX XY
Jerry 9 5
Elan 2 1
George 5 3
Newman 4 4
Kramer 3 2
Mean Y = 4.6; SY = 2.41Mean X = 3.0; SX = 1.41
SmileY
TalkX XY
Jerry 9 5 45
Elan 2 1 2
George 5 3 15
Newman 4 4 16
Kramer 3 2 6XY = 84
Mean Y = 4.6; SY = 2.41Mean X = 3.0; SX = 1.41
Blanched Formula
XY = 84
X = 3.0
Y = 4.6
Sx = 1.41
Sy = 2.41
N = 5
r =
Blanched Formula
r =
84
XY = 84
X = 3.0
Y = 4.6
Sx = 1.41
Sy = 2.41
N = 5
Blanched Formula
r =
84 4.63.0
XY = 84
X = 3.0
Y = 4.6
Sx = 1.41
Sy = 2.41
N = 5
Blanched Formula
r =
84
1.41 2.41
5
XY = 84
X = 3.0
Y = 4.6
Sx = 1.41
Sy = 2.41
N = 5
4.63.0
Blanched Formula
r =
844.6 3.0
1.41 2.41
516.8 13.8
XY = 84
X = 3.0
Y = 4.6
Sx = 1.41
Sy = 2.41
N = 5
Blanched Formula
r =
844.6 3.0
2.41 1.41
516.8 13.8
3.40
3.00.88
XY = 84
X = 3.0
Y = 4.6
Sx = 1.41
Sy = 2.41
N = 5
0
2
4
6
8
10
12
1 2 3 4 5
Talk
Smil
e
.
.. .. r = .88