View
220
Download
1
Embed Size (px)
Citation preview
Let’s Experiment...
Take a Random Sample of 10 pairs of data from our heights and shoe sizes.
Draw a “Scatter plot”Let x-axis = heightLet y-axis = shoe size
Scatter plots “visualize” correlationsWhen dots fall near the line, the
correlation is strongWhen dots are widely scattered,
the correlation is weakGraphs are quick, but math is
more precise (of course!)
And there’s more… If the graph slopes up to the right, the
correlation is PositiveAs X gets bigger, Y gets bigger“Direct relationship”
If the graph slopes down to the right, the correlation is NegativeAs X gets bigger, Y gets smaller“Indirect or Inverse relationship”
QUESTION:
Think of 5 “pairs” of data you could gather to compare (heights and shoe sizes) to observe a correlation.
Teaching Applications
Free Throw % vs. Arm StrengthSwimming Stroke # vs. TimesExpert Judge vs. Skill
AchievementTeaching Method vs. Student
Outcomes
Wellness ApplicationsSmoking vs. CAD RiskSkinfold thickness vs. Body
DensityHeart Rate vs. VO2
Flexibility vs. Lower Back Pain
Uses of correlational researchExploration: “I wonder if
these variables are related?”Prediction: “I wonder if I can
predict one from the other?”
Pearson Product Moment rxy = N(S)xy - ([S]x)([S]y) [N(S)x2
- ([S]x)2] [N(S)y2 - ([S]y2] Thank goodness for Excel! r = -1.0 ->1.0: When r = |1.0| is perfect correlation,
and 0 is no correlation
Interpreting Correlation Coefficients (r)Strength: How close the dots are
to the line r = 0 -1.0Direction: Positive or Negative r =
+ or – 0-1.0Probability: What’s the chance
this happened by chance? P< 0.05 or better
Methods of data collection:One sample populationTwo variables are “paired”
from each individualI.E: Swimming speed and
number of stroke cycles
Correlation is not Causation
Just because two variables are found to “co-vary” with each other doesn’t mean they “Cause” the other.
Suppose: The correlation between Crime Rate and Churches in town is r = +0.89Does that mean having lots of churches causes more crime?
Summary
Correlations look for relationships in variance between two variables
Scatter plots are used to visualize (graph) correlations
Summary, cont...Pearson Product Moment is
an example of statistical quantification of co-variance: r = -1.0 -> +1.0
When r = |1.0|, the relationship is perfectly strong
Summary, cont.
r = 0: There is no correlationNegative: inversely related -
when one gets higher, the other gets lower
Positive: Both get higher or lower together
Lab 3: CorrelationsRead the Lab thoroughly Import Data from my Web siteDetermine your hypothesis
regarding the measurement that has the best correlation with body fatness:
Complete the lab