01/28/2020
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The following topics will be covered in this lecture:
We have begun to consider the differences between a sample and population.
The motivation of sampling is to represent the population with a smaller collection of data points, the sample.
However, if the data is not collected in methodological way, it the sample may grossly mis-represent the population.
We will now consider in detail how we can methodically choose samples, to reduce the effects of bias.
We typically have data that can be categorized into on of the two following types of data:
The differences between the two types of data can be easily seen considering a clinical trial.
An observational version of this study might take the following form:
A major difference between the types of observations is that observational studies do not have a way to control for non-measured variables that may have an effect on the study.
Discuss with a neighbor: suppose a poll is given to UNR students about the quality of UNR food services. Is this poll an observational study or an experiment?
Discuss with a neighbor: suppose UNR wants to examine student satisfaction with possible menu changes in its food services. One group of students is given the current menu, while another group is given a new menu, and the satisfaction of each student is recorded for a month. Is this study an observational study or an experiment?
We have seen that voluntary sampling is flawed because it leads to certain groups (with strong feelings about the questions) to be highly represented while other groups (who may not care) to have limited representation.
Put another way, one group has a higher probability of responding than other groups.
This is the motivation for random sampling…
Simple random sample: a simple random sample of \( n \) subjects is selected in such a way that every possible sample of the same size \( n \) has the same chance of being chosen.
Courtesy of Mario Triola, Essentials of Statistics, 5th edition
Courtesy of Mario Triola, Essentials of Statistics, 5th edition
Courtesy of Mario Triola, Essentials of Statistics, 5th edition
Discuss with a neighbor: what sampling method is being used in each of the following examples?
Courtesy of Mario Triola, Essentials of Statistics, 5th edition
Discuss with a neighbor: what kind of observational study is being discussed in the example?
Courtesy of Mario Triola, Essentials of Statistics, 5th edition
The 401,974 children in the Salk vaccine experiment were assigned to the Salk vaccine treatment group or the placebo group via a process of random selection equivalent to flipping a coin.
You can encode wheter someone is in the treatment or control group in a binary way:
Randomly drawing “Treatment” or “Control” with equal probability is equivalent to flipping a fair coin.
The logic behind randomization is to use chance as a way to create two groups that are similar.
With a large enough sample for both treatment and control groups, this can be very effective when it is difficult to balance factors like age, gender, height, weight, etc… across groups.
Chance is being utlized to balance the many population factors across the control and treatment groups.
Randomization can lead to unbalanced samples ;
Replication – the repetition of an experiment on more than one subject.
Good experiments have enough subjects to recognize differences resulting from different treatments.
A large sample is not necessarily a good sample in itself.
Although it is important to have a sample that is sufficiently large, it is even more important to have a sample in which subjects have been chosen in some appropriate way.
We must both:
Blinding – this is when the subject doesn’t know whether they are receiving a treatment or are in the control group.
Blinding enables us to determine whether the treatment effect is significantly different from a placebo effect.
Blinding minimizes the placebo effect or allows investigators to account for it.
The polio experiment was double-blind, which means that blinding occurred at two levels:
Courtesy of Mario Triola, Essentials of Statistics, 5th edition
Courtesy of Mario Triola, Essentials of Statistics, 5th edition
Courtesy of Mario Triola, Essentials of Statistics, 5th edition
Courtesy of Mario Triola, Essentials of Statistics, 5th edition
Imagine now that we are flipping a fair coin.
Suppose we take a sample of 4 flips and get 3 heads and 1 tails.
In our sample it may appear that it was a \( 75\% \) probability of getting heads and \( 25\% \) probability of getting tails.
If we flipped the coin 100 more times, our sample statistics will approach the true population parameter on average.
The random discrepancy between the sample statistic and the population parameter is known as sampling error.
A nonsampling error is the result of human error, including: