Chapter 4 - More About Relationships Between Two Variables

Front 1

Transforming/Re-expressing

Back 1

To apply a function to a quantitative variable

Hint 1

Taking the natural log of a variable

Front 2

Linear Growth

Back 2

A fixed increment increases by a fixed amount in each equal time period

Hint 2

Front 3

Exponential Growth

Back 3

A variable increases by a fixed percent of the previous total in each equal time period

Hint 3

Front 4

Properties of Logarithms

Back 4

Hint 4

Front 5

Exponential Model

Back 5

Hint 5

Front 6

Power Model

Back 6

Hint 6

Front 7

Achieving Linearity

Back 7

If the relationship is exponential, ln(y-values) achieves linearity.

If the relationship is a power model, ln (x-values) and ln(y-values) achieves linearity.

Hint 7

Front 8

Two-Way Table

Back 8

Organizes data about two categorical variables

Hint 8

Front 9

Marginal Distribution

Back 9

Distributions of the column variable and row variable alone

Hint 9

Distributions of sex alone and age alone

Front 10

Conditional Distribution

Back 10

Compares the percents of a column variable between two row variables

Hint 10

Comparing the percent of women in two age groups

Front 11

Simpson's Paradox

Back 11

An association that holds for all of several groups can reverse direction when the data are combined to form a single group.

Hint 11

Observed associations can be misleading when there are lurking variables.

Front 12

Causation

Back 12

Changes in x cause changes in y.

Hint 12

x = amount of artificial sweetener saccharin in rat's diet, while y = count of tumors in the rat's bladder. The best evidence for causation comes from experiments that actually change x while holding all other factors fixed. If y changed, we would have good reason to think that x caused the change in y. Experiments show conclusively that large amounts of saccharin in the diet cause bladder tumors in rats.

Front 13

Common Response

Back 13

Changes in both x and y are caused by changes in a lurking variable, z.

Hint 13

x = a high school senior's SAT score, while y = the student's first year college GPA. Students who are smart and who have learned a lot tend to have both high SAT scores and high college grades. The positive correlation is explained by this common response to students' ability and knowledge.

Front 14

Confounding

Back 14

The effect of x on y is confounded with the effect of a lurking variable, z.

Hint 14

x = whether a person regularly attends religious services, while
y = how long the person lives.

Many studies have found that people who are active in their religion live longer than nonreligious people. But people who attend religious institutions also take better care of themselves than nonattenders. They are less likely to smoke, more likely to exercise, and less likely to be overweight, among other things. THUS the effects of these good habits are confounded with the direct effects of attending religious services.