Inference for Experiments Section 8.5 Inference for Experiments

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 . . . . . ?

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.

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

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

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

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

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

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

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?

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.

Confidence Interval for Difference of Two Proportions from Experiment

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).

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.

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

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:

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

Computing Confidence Interval Use 2-PropZInt as we did previously

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 . . . . . ?

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.

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

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)

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) ???

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?

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.

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

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

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.

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.

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.

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

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

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”

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.

Experiment What is a placebo?

Experiment A placebo is a “sugar-pill.”

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.

Page 550, P52 Check conditions

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.

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.

Page 550, P52 Do computations

Page 550, P52

Page 550, P52 2-PropZInt x1: 169 } took aspirin n1: 11,037 x2: 138 } took placebo n2: 11,034 C-level: .95 Calculate

Page 550, P52 2-PropZInt x1: 169 } took aspirin n1: 11,037 x2: 138 } took placebo n2: 11,034 C-level: .95 Calculate (-3E-4, .0059) = (-0.0003, 0.0059)

Page 550, P52 Interpret the confidence interval

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,

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 (-0.0003, 0.0059).

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 (-0.0003, 0.0059). Because 0 is in this interval, it is plausible that there is no difference in the proportions who would get ulcers.

What does being “95% confident” mean?

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.

Page 551, E77

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

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.

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

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) = (-0.0005, -0.0002)

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 -0.0005 and -0.0002.

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.

Questions?