1 / 37

r xy

r xy. r xy. When two variables are correlated, we can predict a score on one variable from a score on the other The stronger the correlation, the more accurate our prediction will be. r xy. We need a measure of the “strength” of a correlation. r xy.

marc
Download Presentation

r xy

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. rxy

  2. rxy • When two variables are correlated, we can predict a score on one variable from a score on the other • The stronger the correlation, the more accurate our prediction will be

  3. rxy • We need a measure of the “strength” of a correlation

  4. rxy • We need a number that gets bigger when big numbers are paired with big numbers and small numbers are paired with small numbers • We need a number that gets smaller when big numbers are paired with small numbers and small numbers are paired with big numbers

  5. 5’ 5’2 5’4 5’6 5’8 5’10 rxy • Remember the height/weight example: • Big number indicates this (strong positive correlation) f c d a b, e 100 110 120 130 140 150 b c d a e f

  6. 5’ 5’2 5’4 5’6 5’8 5’10 rxy • Remember the height/weight example: • Small number indicates this (strong negative correlation) f c d a b, e 100 110 120 130 140 150 d f e b a c

  7. rxy • Two sets of scores, xi and yi • What could we do?

  8. rxy • What could we do?

  9. rxy • What could we do? • When pairs are multiplied and the products are summed up: • Greatest when big numbers paired with big numbers and small numbers with small numbers • Least when small numbers are paired with big numbers and big numbers are paired with small numbers

  10. rxy • analogy: This gets you most money Pennies Quarters Loonies

  11. rxy • analogy:this gets you the least… Pennies Quarters Loonies

  12. rxy • analogy: Because: 3 x $1 plus 2 x $0.25 plus 1 x $0.01 is more than 1 x $1 plus 2 x $0.25 plus 3 x $0.01

  13. rxy • But there’s a problem Not a good measure because the value ultimately depends on n AND the size of the numbers

  14. rxy • Try this

  15. rxy • Try this Still not so good - doesn’t depend on n anymore, but does depend on size of x’s and y’s

  16. rxy • How about multiply deviation scores • comparing each variable relative to its respective mean

  17. rxy • Multiply deviation scores Now value depends on the spread of the data

  18. rxy • So standardize the scores

  19. rxy • This measures strength of correlation: = rxy =

  20. rxy • rxy ranges from -1.0 indicating a perfect negative correlation to +1.0 indicating a perfect positive correlation • an rxy of zero indicates no correlation whatsoever. Scores are random with respect to each other.

  21. rxy • rxy also has a geometric meaning

  22. rxy • rxy also has a geometric meaning • Recall that the mean of the zx and zy distributions is zero and each z-score is a deviation from the mean

  23. rxy • Each point lands in one of four quadrants point zx,zy zy zx

  24. rxy • notice that: rxy = both zx and zy are positive

  25. rxy • notice that: rxy = zx is negative and zy is positive

  26. rxy • notice that: rxy = zx is negative and zy is negative

  27. rxy • notice that: rxy = zx is positive and zy is negative

  28. rxy • So Thus if most points tend to fall around a line with a positive (45 degree) slope (I and III), the cross-products will tend to be positive I II IV III

  29. rxy • So Thus if most points tend to fall around a line with a positive (45 degree) slope (I and III), the cross-products will tend to be positive I II If most points tend to fall around a line with a negative slope (II and IV), the cross products will tend to be negative IV III

  30. rxy • So If the points were randomly scattered about, the negative and positive cross-products cancel

  31. Covariance • a related measure of the relationship between scores on two different variables is the covariance

  32. Covariance • notice that the variance (S2x) is the covariance between a variable and itself !

  33. Regression • If two variables are perfectly correlated (r = + or - 1.0) then one can exactly predict a score on one variable given a score on another

  34. Regression • For example: a university charges $250 registration fee plus $100 / credit

  35. Regression • tuition = $100(X) + $250 • where X is the number of credits • Notice this is a linear relationship (an equation of the form y = ax + b • a = $100/credit • b = $250 • x = number of credits

  36. Regression • Tuition as a function of credit hours is a straight line • There is a perfect correlation between credit hours and tuition • You could predict perfectly the tuition required given the number of credit hours

  37. Next Time • Regression - read chapter 8

More Related