13.1 - 213.1 - 2– Population: The collection of objects or Population: The collection of objects or

individuals.individuals.• N-value: The number of individuals in the population.N-value: The number of individuals in the population.

• Sampling frame: The group from which the sample is Sampling frame: The group from which the sample is chosen (would like to be the same as the population)chosen (would like to be the same as the population)

• Survey: data is selected from a subgroup, then used Survey: data is selected from a subgroup, then used to draw conclusions about the entire population.to draw conclusions about the entire population.

• Sample: Subgroup chosen from the sampling frame.Sample: Subgroup chosen from the sampling frame.– Issue 1: find a sample that represents a population.Issue 1: find a sample that represents a population.– Issue 2: determining how big the sample should be.Issue 2: determining how big the sample should be.

Discrete MathDiscrete Math

To be continued…

13.1 - 2 (Continued...)13.1 - 2 (Continued...)– Public Opinion Polls: survey in which the Public Opinion Polls: survey in which the

members of the sample provide information members of the sample provide information by answering questions from the by answering questions from the interviewer.interviewer.

– Selection Bias: sample has excluded a Selection Bias: sample has excluded a particular group or characteristic from the particular group or characteristic from the populationpopulation

– Response Rate: people who responded / Response Rate: people who responded / total number of people in sample.total number of people in sample.

– Response Bias: when the response rate is Response Bias: when the response rate is low.low.

Discrete MathDiscrete Math

To be continued…

13.1 - 2 (Continued...)13.1 - 2 (Continued...)– Quota Sampling: forcing a sample to fit a Quota Sampling: forcing a sample to fit a

certain national profile by using quotas. certain national profile by using quotas. Ex.- same number of women, men, blacks, Ex.- same number of women, men, blacks, whites, urban, rural...whites, urban, rural...

• Convenience Sampling: Not random but Convenience Sampling: Not random but is an easy way to produce a sample.is an easy way to produce a sample.

• Self-Selection: when a sample was Self-Selection: when a sample was produced by volunteers.produced by volunteers.

Discrete MathDiscrete Math

13.313.3– Random SamplingRandom Sampling

• Simple Random Sampling: Any set of objects of Simple Random Sampling: Any set of objects of a given size has an equal chance of being a given size has an equal chance of being chosen as any other set of objects that size.chosen as any other set of objects that size.

• Stratified Random Sampling: sampling frame is Stratified Random Sampling: sampling frame is broken into categories and then randomly broken into categories and then randomly chosen from these groups or strata. (cost chosen from these groups or strata. (cost efficient)efficient)

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13.413.4– SamplingSampling

• Statistic: numerical information drawn from a Statistic: numerical information drawn from a sample. (Estimate of parameter)sample. (Estimate of parameter)

• Parameter: an unknown measure of the population.Parameter: an unknown measure of the population.

• Sampling Error: The difference between the Sampling Error: The difference between the parameter and a statistic used to estimate that parameter and a statistic used to estimate that parameter. parameter.

– (True % - Estimate %)(True % - Estimate %)

• Chance Error: result of sampling variability (two Chance Error: result of sampling variability (two samples are likely to give two different statistics), samples are likely to give two different statistics), it’s the fact that a statistic cannot give exact it’s the fact that a statistic cannot give exact information about the population.information about the population.

Discrete MathDiscrete Math

To be continued…

13.4 (Continued...)13.4 (Continued...)– Sampling (Continued...)Sampling (Continued...)

• Sample Bias: result of having a poorly chosen sample.Sample Bias: result of having a poorly chosen sample.

• Sampling Rate: n/N: sample size/ Size of Population.Sampling Rate: n/N: sample size/ Size of Population.

• Capture - Recapture: method for estimating Capture - Recapture: method for estimating population size.population size.

– Capture and tag (n) animalsCapture and tag (n) animals– Release back into general populationRelease back into general population– Recapture a new sample of size (s).Recapture a new sample of size (s).– Let (t) represent the number of tagged animals in the Let (t) represent the number of tagged animals in the

sample (s).sample (s).– Estimate Population (p) using the proportion: n / p = t / sEstimate Population (p) using the proportion: n / p = t / s

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13.513.5– Clinical Studies:Clinical Studies:

• A different type of data collection that attempts to A different type of data collection that attempts to answer a question for which there is no clear and answer a question for which there is no clear and immediate answer. Generally involves a single immediate answer. Generally involves a single variable or treatment and determines if can cause a variable or treatment and determines if can cause a certain effect.certain effect.

– Involves a cause and effect.Involves a cause and effect.– Requires observation over a period of time.Requires observation over a period of time.

• Confounding variables: any variable that could have Confounding variables: any variable that could have caused the same effect as the treatment.caused the same effect as the treatment.

• Control Study: subjects are divided into two groups, Control Study: subjects are divided into two groups, called the treatment and control groups. The called the treatment and control groups. The control group receives no Treatment.control group receives no Treatment.

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To be continued…

13.5 (Continued...)13.5 (Continued...)– Clinical Studies: (Continued...)Clinical Studies: (Continued...)

• Randomized Control Group: subjects are placed into Randomized Control Group: subjects are placed into the groups randomly.the groups randomly.

• Placebo effect: The idea that one is getting a Placebo effect: The idea that one is getting a treatment can produce positive results.treatment can produce positive results.

• Placebo: Make believe treatment.Placebo: Make believe treatment.

• Controlled Placebo study: Control group is given a Controlled Placebo study: Control group is given a placebo.placebo.

• Blind Study: The subjects do not know which group Blind Study: The subjects do not know which group they are in (control or treatment)they are in (control or treatment)

• Double Blind study: Neither the subjects nor Double Blind study: Neither the subjects nor observers know which group they are in.observers know which group they are in.

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Famous Clinical TrialsFamous Clinical Trials

• Polio Vaccine: 1953 Jonas Salk developed Polio Vaccine: 1953 Jonas Salk developed killed virus vaccine.killed virus vaccine.

• 1954 Large scale, double blind controlled 1954 Large scale, double blind controlled placebo study was chosenplacebo study was chosen

• Over 400,000 children were randomly Over 400,000 children were randomly selected. selected.

• 200,000 were randomly selected for 200,000 were randomly selected for treatment and the other 200,000 were treatment and the other 200,000 were selected as the control group.selected as the control group.

• So successful, that by 1962 vaccinations So successful, that by 1962 vaccinations were offered to the public. were offered to the public.

Clinical Trials Gone Bad !!Clinical Trials Gone Bad !!

• Tuskeegee ExperimentsTuskeegee Experiments• African American males with syphilis were African American males with syphilis were

not given proven treatment. Study went not given proven treatment. Study went on from 1932 until 1972. on from 1932 until 1972.

• Willowbrook Hepatitis ExperimentsWillowbrook Hepatitis Experiments• Mentally handicapped children were Mentally handicapped children were

purposely infected with hepatitis. purposely infected with hepatitis. • Alar Scare One obscure study in 1973 was Alar Scare One obscure study in 1973 was

over emphasized and impacted the apple over emphasized and impacted the apple industry.industry.

Regulations for Clinical Regulations for Clinical TrialsTrials• Nuremberg Code of Ethics 1946Nuremberg Code of Ethics 1946• Belmont Commission 1979Belmont Commission 1979

• Respect for persons: protecting the autonomy of all people and Respect for persons: protecting the autonomy of all people and treating them with courtesy and respect and allowing for informed treating them with courtesy and respect and allowing for informed consent. Researchers must be truthful and conduct no deception; consent. Researchers must be truthful and conduct no deception;

• Beneficence: The philosophy of "Do no harm" while maximizing Beneficence: The philosophy of "Do no harm" while maximizing benefits for the research project and minimizing risks to the benefits for the research project and minimizing risks to the research subjects; and research subjects; and

• Justice: ensuring reasonable, non-exploitative, and well-Justice: ensuring reasonable, non-exploitative, and well-considered procedures are administered fairly — the fair considered procedures are administered fairly — the fair distribution of costs and benefits to distribution of costs and benefits to potentialpotential research participants research participants — and equally— and equally. .

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