Re-expressing Data

Question 1

Re-expression

Answer 1

Do this by taking the logarithm, the square root, the reciprocal, or some other mathematical operation of all values of a variable.

Question 2

Tukey’s Rule for Re-expression Graph

Answer 2

Question 3

Tukey’s Rule if the data have a shape similar to that shown in the first quadrant (high x, high y):

Answer 3

If the data have a shape similar to that shown in the first quadrant (high x, high y), then the data analyst tries re-expressing by going up-ladder for X, Y or both.

Question 4

Tukey’s Rule if the data have a shape similar to that shown in the second quadrant (low x, high y):

Answer 4

If the data have a shape similar to that shown in the second quadrant (low x, high y), then the data analyst tries re-expressing by going the down-ladder for X, and/or up-ladder for Y.

Question 5

Tukey’s Rule if the data have a shape similar to that shown in the third quadrant (low x, low y):

Answer 5

If the data have a shape similar to that shown in the third quadrant (low x, low y), then the data analyst tries re-expressing by going down-ladder for X, Y or both.

Question 6

Tukey’s Rule if the data have a shape similar to that shown in the fourth quadrant (high x, low y):

Answer 6

If the data have a shape similar to that shown in the fourth quadrant (high x, low y), then the data analyst tries re-expressing by going the up-ladder for X, and/or down-ladder for Y.

Question 7

Exponential Re-expression

Answer 7

x, log (y)

This model is the “0” power in the ladder approach, useful for values that grow by percentage increases.

Question 8

Logarithmic Re-expression

Answer 8

log (x) , y

Useful when data has wide range of x-values or scatterplot descending rapidly at the left but leveling off toward the right

Question 9

Power Re-expression

Answer 9

log (x) , log (y)

The Goldilocks Model:

When one of the ladder’s powers is too big and the next is too small, this one may be just right.