1. Inference for Experiments
Section 8.5
Inference for Experiments

2. Comparing Two Proportions
So far, we’ve looked at methods of using confidence intervals and significance tests for comparing two proportions.
Underlying condition was the data came from ?

3. Comparing Two Proportions
So far, we’ve looked at methods of using confidence intervals and significance tests for comparing two proportions.
Underlying condition was the data came from two random samples selected independently from two different populations.

4. Experiments
Oftentimes, random samples can not be taken for an experiment.

5. Experiments
Oftentimes, random samples can not be taken for an experiment.
Who or what are used for experiments?

6. Experiments
Oftentimes, random samples can not be taken for an experiment.
Experiments use the available subjects or volunteers.

7. Experiments
Population is the group of subjects being used in study.

8. For statistical results to be valid, what must be involved in the collection of the data?

9. For statistical results to be valid, what must be involved in the collection of the data?
Random selection

10. For statistical results to be valid, what must be involved in the collection of the data?
Random selection
If we do not use random selection of subjects in an experiment, where does the randomness come in?

11. Experiments Population is the group of subjects being used in study.
If there are two treatments, this group of subjects is split into two groups by random assignment of the treatments.

12. Confidence Interval for Difference of Two Proportions from Experiment

13. Confidence Interval for Difference of Two Proportions from Experiment
Form of confidence interval and all computations remain the same as we did for CI for difference in proportions from survey, as do conditions for sample size (checking normality).

14. Confidence Interval for Difference of Two Proportions from Experiment
Interpretation is different as we’re estimating the difference of proportion of successes as if all units had received Treatment A and proportion of successes as if all units had received Treatment B.

15. Confidence Interval for Difference of Two Proportions from Experiment
Interpretation is different as we’re estimating the difference of proportion of successes as if all units had received Treatment A and proportion of successes as if all units had received Treatment B.
Note: not the same as saying all units received both treatments

16. Confidence Interval for Difference of Two Proportions from Experiment
Confidence interval for difference p1 – p2 in the proportions of successes in a population of experimental units subjected to different treatments is:

17. Confidence Interval for Difference of Two Proportions from Experiment
is observed proportion of successes in
group of size n1 given first treatment, and
group of size n2 given second treatment

18. Computing Confidence Interval
Use 2-PropZInt as we did previously

19. Confidence Interval for Difference of Two Proportions from Experiment
To ensure we can use a confidence interval for estimating the difference in proportions from an experiment, we must first ?

20. Confidence Interval for Difference of Two Proportions from Experiment
To ensure we can use a confidence interval for estimating the difference in proportions from an experiment, we must first check conditions.

21. Confidence Interval for Difference of Two Proportions from Experiment
Conditions that must be met:
(1) the two treatments are randomly assigned to the population of available experimental units

22. Confidence Interval for Difference of Two Proportions from Experiment
Conditions that must be met:
(1) the two treatments are randomly assigned to the population of available experimental unit
(2)

23. Confidence Interval for Difference of Two Proportions from Experiment
Conditions that must be met:
(1) the two treatments are randomly assigned to the population of available experimental unit
(2)
(3) ???

24. Confidence Interval for Difference of Two Proportions from Experiment
Only two conditions to check.
Impossible for population to be 10 times a sample size.
Why?

25. Confidence Interval for Difference of Two Proportions from Experiment
Only two conditions to check.
Impossible for population to be 10 times a sample size.
Why?
If treatments are randomly assigned to
members of the population, then each
treatment would have approximately
one-half the population.

26. Survey versus Experiment
How does the randomization used in a two-population sample survey differ from the randomization used in a two-treatment experiment?

27. Survey versus Experiment
In a two-population sample survey, a sample is randomly and independently selected from each population being studied.

28. Survey versus Experiment
In a two-population sample survey, a sample is randomly and independently selected from each population being studied.
Conclusions can then be made about the populations from which the samples were taken.

29. Survey versus Experiment
In a two-treatment experiment, the treatments are randomly assigned to the population of volunteers or experimental units.
This is not a random sample from a larger population.

30. Survey versus Experiment
In a two-treatment experiment, the treatments are randomly assigned to the population of volunteers or experimental units, which are not a random sample from a larger population.
Here, conclusions can be made about the effects of the treatment on this group of experimental units only.

31. Experiment
Experiments are sometimes described as a “double-blind, randomized, clinical trial.”
What is the meaning of each part of this phrase?

32. Experiment
“Double-blind” means that neither the doctor nor the patient knows which treatment the patient is given.
“Randomized”

33. Experiment
“Double-blind” means that neither the doctor nor the patient knows which treatment the patient is given.
“Randomized” means the two treatments are randomly assigned to patients.
“Clinical trial”

34. Experiment
“Double-blind” means that neither the doctor nor the patient knows which treatment the patient is given.
“Randomized” means the two treatments are randomly assigned to patients.
“Clinical trial” means a comparative experiment to evaluate a medical treatment that is based on actual patients in realistic situations.

35. Experiment
What is a placebo?

36. Experiment
A placebo is a “sugar-pill.”

37. Experiment A placebo is a “sugar-pill.”
A placebo is a nontreatment that mimics the treatment(s) being studied in all essential ways except that it does not involve the crucial component.

38. Page 550, P52
Check conditions

39. Page 550, P52
The problem states this was a randomized, double-blind, placebo-controlled clinical trial so the treatments were randomly assigned to the subjects.

40. Page 550, P52
The problem states this was a randomized, double-blind, placebo-controlled clinical trial so the treatments were randomly assigned to the subjects.
Thus, conditions met.

41. Page 550, P52
Do computations

42. Page 550, P52

43. Page 550, P52 2-PropZInt x1: 169 } took aspirin n1: 11,037
x2: } took placebo
n2: 11,034
C-level: .95
Calculate

44. Page 550, P52 2-PropZInt x1: 169 } took aspirin n1: 11,037
x2: } took placebo
n2: 11,034
C-level: .95
Calculate
(-3E-4, .0059) = ( , )

45. Page 550, P52
Interpret the confidence interval

46. Interpret Confidence Interval
Suppose all of the subjects could have been
given the aspirin treatment and all of the
subjects could have been given the placebo
treatment.
Then,

47. Interpret Confidence Interval
Suppose all of the subjects could have been
given the aspirin treatment and all of the
subjects could have been given the placebo
treatment.
Then, I’m 95% confident that the difference
in the proportions who would get ulcers is in
the interval ( , ).

48. Interpret Confidence Interval
Suppose all of the subjects could have been
given the aspirin treatment and all of the
subjects could have been given the placebo
treatment.
Then, I’m 95% confident that the difference
in the proportion who would get ulcers is in
the interval ( , ).
Because 0 is in this interval, it is plausible that
there is no difference in the proportions who
would get ulcers.

49. What does being “95% confident” mean?

50. What does being “95% confident” mean?
The term “95% confident” means that this
method of constructing confidence intervals
results in p1 - p2 falling in an average of 95
out of every 100 confidence intervals you
construct.

51. Page 551, E77

52. Page 551, E77
(1) Subjects were randomly assigned to treatments.

53. Page 551, E77 (2) Here, n1 and n2 are the numbers of children
in the vaccine group and the placebo group,
respectively, and are the proportions
in these respective groups who were
diagnosed with polio.

54. Page 551, E77 2-PropZInt x1: 82 } received vaccine n1: 200,745
x2: 162 } received placebo
n2: 201,229
C-level: .95
Calculate

55. Page 551, E77 2-PropZInt x1: 82 } received vaccine n1: 200,745
x2: 162 } received placebo
n2: 201,229
C-level: .95
Calculate
(-5E-4, -2E-4) = ( , )

56. Page 551, E77 I’m 95% confident that if all of the children in
this experiment had been given the vaccine
and if all had been given the placebo, the
difference in the proportions who would
have developed polio would have been
between and

57. Page 551, E77 This is a statistically significant difference
because 0 isn’t in the confidence interval.
Thus, we believe that the vaccine reduced
the proportion of children who developed
polio.

58. Questions?