chapter 4 - scatterplots and correlation dealing with several variables within a group vs. the same...
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![Page 1: Chapter 4 - Scatterplots and Correlation Dealing with several variables within a group vs. the same variable for different groups. Response Variable:](https://reader035.vdocuments.site/reader035/viewer/2022062221/56649f575503460f94c7c2b0/html5/thumbnails/1.jpg)
Chapter 4 - Scatterplots and Correlation
• Dealing with several variables within a group vs. the same variable for different groups.
• Response Variable: measures the outcome of a study.
• Explanatory Variable: attempts to explain the observed outcomes.
• ex: Body Temp vs. Alcohol (Mice)
• ex: Predicting SAT Math if you know SAT Verbal
![Page 2: Chapter 4 - Scatterplots and Correlation Dealing with several variables within a group vs. the same variable for different groups. Response Variable:](https://reader035.vdocuments.site/reader035/viewer/2022062221/56649f575503460f94c7c2b0/html5/thumbnails/2.jpg)
WARNING! WARNING!EXPLANATORY VARIABLES DO NOT
NECESSARILY CAUSE CHANGESIN RESPONSE VARIABLES!!!
![Page 3: Chapter 4 - Scatterplots and Correlation Dealing with several variables within a group vs. the same variable for different groups. Response Variable:](https://reader035.vdocuments.site/reader035/viewer/2022062221/56649f575503460f94c7c2b0/html5/thumbnails/3.jpg)
Scatter Plot: The most effective way to display the relationship between two quantitative variables measured on the same individuals.
(2.1 cont’d)
Horizontal Axis (x) = explanatory variable (if there is one)
Vertical Axis (y) = response variable (if there is one)
If there is no exp/resp distinction, it can be plotted either way…
![Page 4: Chapter 4 - Scatterplots and Correlation Dealing with several variables within a group vs. the same variable for different groups. Response Variable:](https://reader035.vdocuments.site/reader035/viewer/2022062221/56649f575503460f94c7c2b0/html5/thumbnails/4.jpg)
![Page 5: Chapter 4 - Scatterplots and Correlation Dealing with several variables within a group vs. the same variable for different groups. Response Variable:](https://reader035.vdocuments.site/reader035/viewer/2022062221/56649f575503460f94c7c2b0/html5/thumbnails/5.jpg)
Interpreting Scatter Plots
• Look for overall pattern
• Direction / Form / Strength
• Direction = “Positive” or “Negative “ Association:
•Positive Association: Above average values of one variable tend to accompany above average values of the other variable.
•Negative Association: Above average values of one variable tend to accompany below average values of the other variable.
• Form - can be linear / curved / clustered
• Strength Stronger = less scatter - closer to a straight line… Weaker = more scatter, not as linear…
![Page 6: Chapter 4 - Scatterplots and Correlation Dealing with several variables within a group vs. the same variable for different groups. Response Variable:](https://reader035.vdocuments.site/reader035/viewer/2022062221/56649f575503460f94c7c2b0/html5/thumbnails/6.jpg)
Direction = Positive
Form = Linear
Strength = Fairly Strong
Direction = Positive
Form = Scattered
Strength = Weak
![Page 7: Chapter 4 - Scatterplots and Correlation Dealing with several variables within a group vs. the same variable for different groups. Response Variable:](https://reader035.vdocuments.site/reader035/viewer/2022062221/56649f575503460f94c7c2b0/html5/thumbnails/7.jpg)
Direction = Negative Form = Scattered Strength = Weak
![Page 8: Chapter 4 - Scatterplots and Correlation Dealing with several variables within a group vs. the same variable for different groups. Response Variable:](https://reader035.vdocuments.site/reader035/viewer/2022062221/56649f575503460f94c7c2b0/html5/thumbnails/8.jpg)
Direction = Negative Form = Curved / Clustered Strength = Weak
![Page 9: Chapter 4 - Scatterplots and Correlation Dealing with several variables within a group vs. the same variable for different groups. Response Variable:](https://reader035.vdocuments.site/reader035/viewer/2022062221/56649f575503460f94c7c2b0/html5/thumbnails/9.jpg)
Calculator Steps for Scatter plot
1) Enter data into list 1 & 2
ex 2.5 pg 99:
2) 2nd Y=
3) Enter
4)
Select Type
Set Xlist / Frequency
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Calculator Steps for Scatter plot (cont’d)
5) Turn On
6) Set Window to match Data Window
7) Graph
![Page 11: Chapter 4 - Scatterplots and Correlation Dealing with several variables within a group vs. the same variable for different groups. Response Variable:](https://reader035.vdocuments.site/reader035/viewer/2022062221/56649f575503460f94c7c2b0/html5/thumbnails/11.jpg)
Adding categorical variables to scatter plots
• Use different colors or symbols to indicate a categorical variable or duplicate values…
![Page 12: Chapter 4 - Scatterplots and Correlation Dealing with several variables within a group vs. the same variable for different groups. Response Variable:](https://reader035.vdocuments.site/reader035/viewer/2022062221/56649f575503460f94c7c2b0/html5/thumbnails/12.jpg)
1.0
2.0
3.0
4.0
25 50 75 100 125 150 175 200 225 250
Cell Minutes per Week vs. GPA
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Seniors
Juniors
Soph ++ Duplicate
![Page 13: Chapter 4 - Scatterplots and Correlation Dealing with several variables within a group vs. the same variable for different groups. Response Variable:](https://reader035.vdocuments.site/reader035/viewer/2022062221/56649f575503460f94c7c2b0/html5/thumbnails/13.jpg)
Correlation
• Correlation = a numerical measure of how strong a linear relationship is.
• Visually, correlation is hard to judge. Our eyes can be fooled by white space around a scatterplot and the plotting scales.
**Same Data – Different Scales**
ex:
![Page 14: Chapter 4 - Scatterplots and Correlation Dealing with several variables within a group vs. the same variable for different groups. Response Variable:](https://reader035.vdocuments.site/reader035/viewer/2022062221/56649f575503460f94c7c2b0/html5/thumbnails/14.jpg)
Formula:
Correlation variable
… of the sum
… of the products
ex: Correlation between height and weight – height is x / weight is y….
… of the standardized
heights
… and the standardized
weights
…for each measurement
n - 1
… is an average
![Page 15: Chapter 4 - Scatterplots and Correlation Dealing with several variables within a group vs. the same variable for different groups. Response Variable:](https://reader035.vdocuments.site/reader035/viewer/2022062221/56649f575503460f94c7c2b0/html5/thumbnails/15.jpg)
Calculator Procedure
ex: Fossil Data
Femur Humerus38 4156 6359 70
64 7274 84
Step 1) Insert Data into lists
** Set DiagnosticOn**(one time step)
Step 2) Run Stat Calc LinReg
![Page 16: Chapter 4 - Scatterplots and Correlation Dealing with several variables within a group vs. the same variable for different groups. Response Variable:](https://reader035.vdocuments.site/reader035/viewer/2022062221/56649f575503460f94c7c2b0/html5/thumbnails/16.jpg)
Correlation Facts
• Correlation (r) always falls between -1 and 1.
• The closer to 0 r is, the weaker the relationship.
• Positive r = positive association / negative r = negative association.
• Because r uses standardized values, r has no units.
• Correlation measures the strength of only LINEAR relationships. It cannot be used to describe curved relationships no matter how strong they are.
![Page 17: Chapter 4 - Scatterplots and Correlation Dealing with several variables within a group vs. the same variable for different groups. Response Variable:](https://reader035.vdocuments.site/reader035/viewer/2022062221/56649f575503460f94c7c2b0/html5/thumbnails/17.jpg)
WARNING! WARNING!CORRELATION IS STRONGLY
AFFECTED BY OUTLIERS!!
WARNING! WARNING!CORRELATION IS NOT A
COMPLETE DESCRIPTION OF2-VARIABLE DATA!!
![Page 18: Chapter 4 - Scatterplots and Correlation Dealing with several variables within a group vs. the same variable for different groups. Response Variable:](https://reader035.vdocuments.site/reader035/viewer/2022062221/56649f575503460f94c7c2b0/html5/thumbnails/18.jpg)
The image above shows scatterplots of Anscombe's quartet, a set of four different pairs of variables created by Francis Anscombe. The four y variables have the same mean (7.5), standard deviation (4.12) and correlation (0.81)