Section 5.1 Study Guide

Designing Samples
  Vocabulary
 

An Observational Study observes individuals and measures variables of interest but does not attempt to influence responses. An Experiment imposes a change or treatment to observe the reaction in individuals. The Population is the entire group of individuals that we want information about. The Sample is the part of the population that we actually exam to gather information. A Census attempts to contact every individual in the entire population.

 Bias in Experiments
 The design of a study is biased if it favors certain outcomes.
· Voluntary Response Sampling is only made up of individuals who volunteer to respond.  This often attracts only those with strong opinions, especially those with strong negative opinions.
· Convenience Sampling only consists of individuals who are easy to reach.  This can easily lead to undercoverage of a population.

Table of Random Digits
The table of random digits is a long string of the digits 0,1,2,3,4,5,6,7,8, and 9.  Each entry into the table is equally likely to be any of these numbers.  Each entry is also independent, so knowledge of one section of the table tells us nothing about other parts of the table.  To use the table, assign each individual in the sample a number, then choose a line in the table to follow.

Stratified Random Sample
To create a Stratified Random Sample, divide groups of similar individuals into groups, then perform a simple random sample for each group and combine the SRS’s to form the full sample.

Risks
· Undercoverage—When some groups in the population are not adequately represented
· Nonresponse—When an individual chosen either cannot be contacted or will not cooperate.
 
 

Section 5.2 Study Guide

Designing Experiments

Vocabulary
 

Study—When a stimulus is introduced to a group of people, animals, or objects to observe the response. Experimental Units—Individuals on which the experiment is performed. Subject—A human experimental unit. Treatment—The actual change imposed on the experimental units.

Many experimental designs are very simple.  Simple designs can be outlined as:
 UNITS-->TREATMENT-->OBSERVE RESPONSE

The Placebo Effect
When using human test subjects in a study, this outline can become slightly more complex.  Often times, humans respond favorably to any treatment simply because they believe it will work.  This response is called the placebo effect, and a good experimental design will accommodate it.
 For example, if doctors want to test a new pain relieving medication, their control group will be given a placebo—that is—a dummy treatment.  The results from this placebo group will be compared with the results from a group of subjects who received the actual pain-relieving medication.  By doing this, the doctors can be sure that they are measuring the effectiveness of their medicine, and not just the faith of their patients.

 Randomized Comparative Experiments
 When using large numbers of experimental units, we rely on randomization to sort out any lurking variables.  While there may be outside influences, they should be equally present in both groups.

Basic Setup for Comparative Random Experiments

                                     --> Group 1 (50 subjects)   -  -> Treatment 1
Random Assignment                                                                             ---> Compare
                                      -->Group 2 (50 subjects)    --> Treatment 2
 
 

When designing experiments it is important to remember to….
· Control—Manage the effects of lurking variables
· Randomize—Use chance to avoid any bias
· Replicate—Repeat treatment and use large numbers to reduce variation

The goal of these experimental designs is to find statistically significant evidence—an observed effect that is not likely to occur simply by chance.

Double Blind
Double blind experiments take an extra precaution to avoid bias.  Neither the subject nor the experimenter knows of the treatment imposed on each subject.  This ensures that the person doing the experiment treats all of the subjects exactly the same

Special Designs
· Matched Pairs designs put experimental units into pairs with very similar characteristics.  One subject would receive one treatment, while the other receives a different treatment.  The differences are compared within each pair.
· Block Designs are used when a group of experimental units is known to share certain characteristics that are expected to affect the experiment.  After the units are separated into these blocks, randomization is used to determine the treatment for each subject.
 

Section 5.3 Study Guide

Simulating Experiments

 Vocabulary 
 

Simulation—The imitation of chance behavior, based on a model that accurately reflects the experiment under consideration. Independence—The outcome of one trial does not affect any other outcomes.

Choosing an SRS:

 Step 1:     Label.  Assign a numerical label to every individual in the population.

 Step 2:     Table.  Use table B to select labels at random.
 

 Steps of a Simulation:

1. State the problem or describe the experiment.
2. State the assumptions
3. Assign digits to represent outcomes
4. Simulate many repetitions
5. State your conclusion

Calculator Steps:

 Once both the sample and experiment are designed, the experiment is ready to begin.  However, actually carrying out the experiment may require resources that are not actually available.  Conducting studies can be very expensive and time consuming.  For this reason, experiments are often simulated.  Using simple probability tools, we can estimate outcomes of our experiments.

 Example
 A young couple wants to find the probability of having 3 girls.  This experiment can be simulated using a coin, since the probability of having a girl is about .5.  We can estimate probability by dividing the number of times the desired outcome occurs by the number of total outcomes.  So, by flipping a coin in groups of 3 tosses, we can simulate the experiment.  Each time the coin lands “tails” it represents a girl.  In our simulation there might be ten trials, each trial with three tosses.  Therefore, the estimated probability of getting 3 girls is the number of trials that 3 tails are observed over 10.  If we chose coin-flipping as a tool, we would be assuming that the coin is fair and that a head or tail is equally likely to occur on each toss.
 This same situation could be simulated in a different way.  We could use the table of random digits to simulate the gender of their children.  By assigning odds to the male gender and evens to the female gender, we can follow a line in table B to simulate the experiment.  The table would be read in groups of 3 digits for each trial.  By looking at 10 groups of 3 in the table, we can simulate 10 trials.  Similar to the previous experiment, the estimated probability is equal to the number of times three even numbers occur consecutively divided by 10, the total number of outcomes.
 The same situation could be simulated with the calculator.  The calculator can be a quick and easy way of generating a large number of trials.  By using the randInt feature, we can simulate the probability of having three girls.  Go to MATH, then PRB, then choosing number 5, randInt to bring up the prompt.  Entering randInt (0, 9, 30) will direct the calculator to produce 30 random integers between 0 and 9.  With odds assigned to the male gender and evens assigned to females, we can examine the integers and simulate the experiment.
 
 

STEP ONE: (State the problem and describe the experiment)

  Roll a pair of dice 5 times.  What is the likelihood of rolling a pair?

STEP TWO: (State Assumptions)

  -The dice are fair
  -The trials are independent

STEP THREE:   (Assign digits to represent outcomes)

In the calculator we will use the randInt command to simulate rolling a pair of dice.

  -One toss is two digits
  -Five tosses is 10 digits, which is equal to one trial

STEP FOUR: (Simulate many repetitions)

We will look for pairs of numbers within each set of ten. (Make sure that you match the numbers up in pairs of two. Just because two of the same number appear next to one another, does not mean they were rolled together)

STEP FIVE: (State Conclusion)

It appears that 60% of the trials were a success (we rolled a pair given five tries).  However, it is obvious that ten trials are not enough to be conclusive.

Practice Multiple Choice Questions

Which of these techniques would most likely result in an unbiased sample?
A)  Convenience Samping
B)  Telephone Polls
C)  SRS using table B

The Placebo Effect occurs when....
A)  An experiment is completely unbiased 
B)  Humans respond favorably to any treatment simply because they believe it will work
C)  Too few subjects participate in the sample

The table of random numbers can be found in...
A)  Table 3
B)  Table A
C)  Table B

Other Stats Sites
http://www.shodor.org/interactivate/activities/chances/index.html