The document discusses different types of statistical questions: - Difference questions compare two or more groups on an outcome. - Relationship questions examine if a change in one variable is associated with a change in another. - Independence questions determine if two variables with multiple levels are independent. - Goodness of fit questions assess if a claim matches reality. Examples are provided for each type of question to illustrate the concepts.

1. Is your question a question of:
Difference? Relationship?
Goodness of Fit?Independence?

2. Is your question a question of: Difference?

3. Difference
How do two or more groups compare with one another in
terms of some outcome?

4. Difference
How do two or more groups (younger/older drivers) compare
with one another in terms of some outcome (average driving
speed)?

5. Difference
How do two or more groups (younger/older drivers) compare
with one another in terms of some outcome (average driving
speed)?
vs.
average MPHolder driver younger driver
in terms of

6. Difference
How do two or more groups (those with migraines / those
without migraines) compare with one another in terms of
some outcome (average sugar intake)?
vs.
migraine no migraine
average sugar
intake
in terms of

7. Difference
How do two or more groups (sophomores/juniors/seniors)
compare with one another in terms of some outcome
(average amount of homework)?
sophomore
vs.
average amount
of homework
in terms of
junior senior
vs.

8. In summary

9. Difference
How do two or more groups compare with one another in
terms of some outcome?
vs.
vs.
migraine no migraine
average MPHolder driver younger driver
average sugar
intake
in terms of
in terms of
sophomore
vs.
average amount
Of homework
in terms of
junior senior
vs.

10. Is your question a question of: Relationship?

11. Relationship
Is a change in one characteristic accompanied by a change in
another characteristic?

12. Relationship
Is a change in one characteristic (age) accompanied by a
change in another characteristic (flexibility)?

13. Relationship
Is a change in one characteristic (age) accompanied by a
change in another characteristic (flexibility)?
Is an increase in accompanied by a decrease in

14. Relationship
Is a change in one characteristic (height) accompanied by a
change in another characteristic (weight)?
Is an increase in accompanied by a increase in

15. Relationship
Is a change in one characteristic (speed) accompanied by a
change in another characteristic (road rage incidents)?
Is an decrease in accompanied by a decrease in

16. In summary

17. Relationship
Is a change in one characteristic accompanied by a change in
another characteristic?
Is an increase in accompanied by a decrease in
Is an increase in accompanied by a increase in
Is an decrease in accompanied by a decrease in

18. Is your question a question of: Independence?

19. Independence
Is one variable with two or more levels independent of
another variable with two or more levels?

20. Independence
Is one variable (university enrollment) with two or more levels
(enrolled or not enrolled) independent of another variable
(state residence) with two or more levels (resident or not)?

21. Example 1 – Independent
Independence
Is one variable (university enrollment) with two or more levels
(enrolled or not enrolled) independent of another variable
(state residence) with two or more levels (resident or not)?

22. enrolled not enrolled
resident 20 students 20 students
not a resident 20 students 20 students
Example 1 – Independent
Independence
Is one variable (university enrollment) with two or more levels
(enrolled or not enrolled) independent of another variable
(state residence) with two or more levels (resident or not)?

23. enrolled not enrolled
resident 20 students 20 students
not a resident 20 students 20 students
Example 1 – Independent
Enrollment and state residence are
independent, because being a
resident or non resident doesn’t
make it more likely you are enrolled.
Independence
Is one variable (university enrollment) with two or more levels
(enrolled or not enrolled) independent of another variable
(state residence) with two or more levels (resident or not)?

24. enrolled not enrolled
resident 20 students 20 students
not a resident 20 students 20 students
enrolled not enrolled
resident 10 students 30 students
not a resident 30 students 10 students
Example 1 – Independent
Enrollment and state residence are
dependent, because being a non-
resident makes it more likely you are
enrolled.
Enrollment and state residence are
independent, because being a
resident or non resident doesn’t
make it more likely you are enrolled.
Example 2 - Dependent
Independence
Is one variable (university enrollment) with two or more levels
(enrolled or not enrolled) independent of another variable
(state residence) with two or more levels (resident or not)?

25. Independence
Is one variable (year in school) with two or more levels (9th,
10th, 11th, 12th) independent of another variable (foreign
language ability) of two or more levels (fluent or not)?

26. Independence
Is one variable (year in school) with two or more levels (9th,
10th, 11th, 12th) independent of another variable (foreign
language ability) of two or more levels (fluent or not)?
9th 10th 11th 12th
fluent 200 300 200 250
not fluent 200 300 200 250
Example 1 – Independent

27. Independence
Is one variable (year in school) with two or more levels (9th,
10th, 11th, 12th) independent of another variable (foreign
language ability) of two or more levels (fluent or not)?
9th 10th 11th 12th
fluent 200 300 200 250
not fluent 200 300 200 250
Example 1 – Independent
Fluency is independent of year in
school because being in a lower or
upper class doesn’t make it more
likely that you are fluent.

28. Independence
Is one variable (year in school) with two or more levels (9th,
10th, 11th, 12th) independent of another variable (foreign
language ability) of two or more levels (fluent or not)?
9th 10th 11th 12th
fluent 200 300 200 250
not fluent 200 300 200 250
Example 1 – Independent
Fluency is independent of year in
school because being in a lower or
upper class doesn’t make it more
likely that you are fluent.
9th 10th 11th 12th
fluent 100 100 200 400
not fluent 300 400 100 100
Example 2 – Independent

29. Independence
Is one variable (year in school) with two or more levels (9th,
10th, 11th, 12th) independent of another variable (foreign
language ability) of two or more levels (fluent or not)?
9th 10th 11th 12th
fluent 200 300 200 250
not fluent 200 300 200 250
Example 1 – Independent
Fluency is independent of year in
school because being in a lower or
upper class doesn’t make it more
likely that you are fluent.
9th 10th 11th 12th
fluent 100 100 200 400
not fluent 300 400 100 100
Example 2 – Independent
Fluency is dependent on year in
school because being in an upper
class makes it more likely that you
are fluent.

30. In summary

31. Independence
Is one variable with two or more levels independent of
another variable with two or more levels?

32. Independence
Is one variable with two or more levels independent of
another variable with two or more levels?
enrolled not enrolled
resident 20 students 20 students
not a resident 20 students 20 students
Is university enrollment
independent of state residency?

33. Independence
Is one variable with two or more levels independent of
another variable with two or more levels?
9th 10th 11th 12th
fluent 200 300 200 250
not fluent 200 300 200 250
enrolled not enrolled
resident 20 students 20 students
not a resident 20 students 20 students
Is university enrollment
independent of state residency?
Is year in school independent
foreign language fluency?

34. Is your question a question of: Goodness of Fit?

35. Goodness of Fit
Does your claim fit reality?
(4 out of 5 dentist recommend flavored floss) (3 out of 5 of
your dentist friends recommend flavored floss)

36. Goodness of Fit
Does your claim (4 out of 5 dentist recommend flavored floss)
fit reality (3 out of 5 of your dentist friends recommend
flavored floss)?

37. Goodness of Fit
Does your claim (4 out of 5 dentist recommend flavored floss)
fit reality (3 out of 5 of your dentist friends recommend
flavored floss)?
Does the CLAIM . . . FIT REALITY?
4 out of 5
recommend
3 out of 5
recommend

38. Goodness of Fit
Does your claim (72% of the county will vote democrat) fit
reality (65% of the county actually voted democrat)?
Does the CLAIM . . . FIT REALITY?
65% 72%
18%35%

39. In summary

40. Goodness of Fit
Does your claim fit reality?
(4 out of 5 dentist recommend flavored floss) (3 out of 5 of
your dentist friends recommend flavored floss)

41. Goodness of Fit
Does your claim fit reality?
(4 out of 5 dentist recommend flavored floss) (3 out of 5 of
your dentist friends recommend flavored floss)
4 out of 5
recommend
3 out of 5
recommend
65% 72%
18%35%
The Claim The Reality
The Claim The Reality

42. Final Summary

43. Final Summary
Difference – (average) between groups. vs.
Relationship – increase or decrease in two variables
Independence – two+ levels by two+ levels.
Does the CLAIM . . . FIT REALITY?
Goodness of Fit – claim versus reality

44. Let’s Practice!

45. Does employee moral increase significantly the
longer employees work at Company X? You
sample a group of 45 and generalize the results.
Difference? Relationship?
Independence? Goodness of Fit?

46. Does employee moral increase significantly the
longer employees work at Company X? You
sample a group of 45 and generalize the results.
Difference? Relationship?
Independence? Goodness of Fit?

47. Does employee moral increase significantly the
longer employees work at Company X? You
sample a group of 45 and generalize the results.
Difference? Relationship?
Independence? Goodness of Fit?

48. Does employee moral increase significantly the
longer employees work at Company X? You
sample a group of 45 and generalize the results.
Is a change in one characteristic (moral) accompanied by a
change in another characteristic (time worked)?
Difference? Relationship?
Independence? Goodness of Fit?

49. Next Example

50. How do management and staff compare in
terms of average work satisfaction? You sample
both groups and generalize the results.
Difference? Relationship?
Independence? Goodness of Fit?

51. How do management and staff compare in
terms of average work satisfaction? You sample
both groups and generalize the results.
Difference? Relationship?
Independence? Goodness of Fit?

52. How do management and staff compare in
terms of average work satisfaction? You sample
both groups and generalize the results.
Difference? Relationship?
Independence? Goodness of Fit?

53. How do management and staff compare in
terms of average work satisfaction? You sample
both groups and generalize the results.
Difference? Relationship?
Independence? Goodness of Fit?
How do two or more groups (management/staff) compare
with one another in terms of some outcome (average work
satisfaction)?

54. Next Example

55. A salesman claims that 95% of employees
increase their work productivity using his
software. You test that claim with a sample of 26
employees and find that 86% increase their
productivity.
Difference? Relationship?
Independence? Goodness of Fit?

56. A salesman claims that 95% of employees
increase their work productivity using his
software. You test that claim with a sample of 26
employees and find that 86% increase their
productivity.
Difference? Relationship?
Independence? Goodness of Fit?

57. A salesman claims that 95% of employees
increase their work productivity using his
software. You test that claim with a sample of
26 employees and find that 86% increase their
productivity.
Difference? Relationship?
Independence? Goodness of Fit?

58. A salesman claims that 95% of employees
increase their work productivity using his
software. You test that claim with a sample of
26 employees and find that 86% increase their
productivity.
Difference? Relationship?
Independence? Goodness of Fit?
Does your claim (95% increase work productivity) fit reality
(86% increase work productivity)?

59. Is religious affiliation independent of age levels
(young, prime, mature, and seasoned)?
Difference? Relationship?
Independence? Goodness of Fit?

60. Is religious affiliation independent of age levels
(young, prime, mature, and seasoned)?
Difference? Relationship?
Independence? Goodness of Fit?

61. Is religious affiliation independent of age levels
(young, prime, mature, and seasoned)?
Difference? Relationship?
Independence? Goodness of Fit?

62. Is religious affiliation independent of age levels
(young, prime, mature, and seasoned)?
Difference? Relationship?
Independence? Goodness of Fit?
Is one variable with two or more levels (religious affiliation)
independent of another variable with two or more levels
(age levels)?

63. Is your question a question of:
Difference? Relationship?
Goodness of Fit?Independence?