STATS 250 Lecture 4: STATS 280 NOTES 9:20
STATS 280 NOTES 9/20/2016
To convert from SU to percentile, you must either
o Assume the histogram follows a normal curve, and then
Use a normal table
Or use the R command pnorm + qnorm
o If you cannot assume a normal curve, do everything manually. As an intermediate
step, you’ll need to convert to the original score
Will need to know the SD and mean
Summarizing the two data sets
o Overlay two histograms
o Create two box plots
For comparing quantitative set vs qualitative set
o Scatterplot
For comparing two quantitative sets
Correlation
o Suppose you have two lists of numbers of the same length: X1, X2, …, Xn and Y1,
Y2, …, Yn
o Correlation is defined as
o The average of all the values of X
in standard units multiplied by Y in
standard units
X and Y are lists
Average((X in SU) * (Y in SU))
Covariance
o You can factor out the SD in the previous equation because it is constant for every
value:
o The numerator is known as covariance of X and Y, written Cov(X, Y)
o You can think of correlation as a “normalized” version of covariance
o Covariance is equal to average(X*Y) – average(X)*average(Y)
o The variance of X is the covariance of X with itself
Var(X) = Cov(X, X)
Why Correlation?
o Correlation is a measure of the strength of linear association between X and Y
o Correlation is unaffected by changes of scale
If you add a constant to every X number, the correlation won’t change. If
you multiply every X number by a constant, the correlation won’t change
o Correlation is always between -1 and 1
A correlation of 1 means perfect positive (linear) associations
A correlation of -1 means perfect negative (linear) association
A correlation of 0 means no (linear) association
o The value of the correlation doesn’t have an easy interpretation
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STATS 250 Full Course Notes
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Document Summary
To convert from su to percentile, you must either: assume the histogram follows a normal curve, and then. Or use the r command pnorm + qnorm: if you cannot assume a normal curve, do everything manually. As an intermediate step, you"ll need to convert to the original score. Will need to know the sd and mean. Summarizing the two data sets: overlay two histograms, create two box plots. For comparing quantitative set vs qualitative set: scatterplot. Average((x in su) * (y in su)) Why correlation: correlation is a measure of the strength of linear association between x and y, correlation is unaffected by changes of scale. If you add a constant to every x number, the correlation won"t change. If you multiply every x number by a constant, the correlation won"t change: correlation is always between -1 and 1. A correlation of 1 means perfect positive (linear) associations. A correlation of -1 means perfect negative (linear) association.
