·
A Problem: Often students are confused about the various
statistical concepts, especially in inference. One source of this confusion is
a result of fuzziness in the use of the terms variable
and population.
·
A Solution: By employing
a variable-centered approach—where the terms variable
and population are used
consistently and properly—those statistical concepts can be unified and
clarified.
·
Details: The following table provides details about employing a
variable-centered approach with some commonly used inferential procedures. By
specifying the variable(s) and population(s) for any given problem, students
can more easily understand the nature of the problem and inference and, as
well, better comprehend similarities and differences among the various types of
inferences.
|
Type of inference |
Number of
populations |
Number of
variables |
Type of
variables |
Example of
population(s) |
Example of
variable(s) |
|
One
mean |
1 |
1 |
Quantitative |
Females |
Height |
|
Two
means |
2 |
1 |
Quantitative |
Females/Males |
Height |
|
ANOVA |
k |
1 |
Quantitative |
Four
U.S. regions |
Energy
consumption |
|
Simple
regression |
1 |
2 |
Quantitative |
Corvettes |
Age/Price |
|
Independence
test |
1 |
2 |
Categorical |
U.S.
adults |
Edu
level/Income class |
|
Homogeneity
test |
k |
1 |
Categorical |
Four
U.S. regions |
Political
party |
·
Example: The American Association of University Professors (AAUP) conducts
salary studies of college professors and publishes its findings in AAUP Annual Report on the Economic Status of the
Profession. Suppose that we want to decide whether the mean annual
salaries of college faculty in public and private institutions are different.
Populations: Here there are two populations—college faculty in
public institutions and college faculty in private institutions.
Variable: Here there is one variable—annual salary.