–Population: The collection of objects or 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 chosen (would like to be the same as the population) Sampling frame: The group from which the sample is chosen (would like to be the same as the population) Survey: data is selected from a subgroup, then used to draw conclusions about the entire population. Survey: data is selected from a subgroup, then used 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 2: determining how big the sample should be. Discrete Math To be continued…

(Continued...) –Public Opinion Polls: survey in which the members of the sample provide information by answering questions from the interviewer. –Selection Bias: sample has excluded a particular group or characteristic from the population –Response Rate: people who responded / total number of people in sample. –Response Bias: when the response rate is low. Discrete Math To be continued…

(Continued...) –Quota Sampling: forcing a sample to fit a certain national profile by using quotas. Ex.- same number of women, men, blacks, whites, urban, rural... Convenience Sampling: Not random but is an easy way to produce a sample.Convenience Sampling: Not random but is an easy way to produce a sample. Self-Selection: when a sample was produced by volunteers.Self-Selection: when a sample was produced by volunteers. Discrete Math

13.3 –Random Sampling Simple Random Sampling: Any set of objects of a given size has an equal chance of being chosen as any other set of objects that size. Simple Random Sampling: Any set of objects of a given size has an equal chance of being chosen as any other set of objects that size. Stratified Random Sampling: sampling frame is broken into categories and then randomly chosen from these groups or strata. (cost efficient) Stratified Random Sampling: sampling frame is broken into categories and then randomly chosen from these groups or strata. (cost efficient) Discrete Math

13.4 –Sampling Statistic: numerical information drawn from a sample. (Estimate of parameter) Statistic: numerical information drawn from a sample. (Estimate of parameter) Parameter: an unknown measure of the population. Parameter: an unknown measure of the population. Sampling Error: The difference between the parameter and a statistic used to estimate that parameter. Sampling Error: The difference between the parameter and a statistic used to estimate that parameter. –(True % - Estimate %) Chance Error: result of sampling variability (two samples are likely to give two different statistics), it’s the fact that a statistic cannot give exact information about the population. Chance Error: result of sampling variability (two samples are likely to give two different statistics), it’s the fact that a statistic cannot give exact information about the population. Discrete Math To be continued…

13.4 (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 population size. Capture - Recapture: method for estimating population size. –Capture and tag (n) animals –Release back into general population –Recapture a new sample of size (s). –Let (t) represent the number of tagged animals in the sample (s). –Estimate Population (p) using the proportion: n / p = t / s Discrete Math

13.5 –Clinical Studies: A different type of data collection that attempts to answer a question for which there is no clear and immediate answer. Generally involves a single variable or treatment and determines if can cause a certain effect. A different type of data collection that attempts to answer a question for which there is no clear and immediate answer. Generally involves a single variable or treatment and determines if can cause a certain effect. –Involves a cause and effect. –Requires observation over a period of time. Confounding variables: any variable that could have caused the same effect as the treatment. Confounding variables: any variable that could have caused the same effect as the treatment. Control Study: subjects are divided into two groups, called the treatment and control groups. The control group receives no Treatment. Control Study: subjects are divided into two groups, called the treatment and control groups. The control group receives no Treatment. Discrete Math To be continued…

13.5 (Continued...) –Clinical Studies: (Continued...) Randomized Control Group: subjects are placed into the groups randomly. Randomized Control Group: subjects are placed into the groups randomly. Placebo effect: The idea that one is getting a treatment can produce positive results. Placebo effect: The idea that one is getting a treatment can produce positive results. Placebo: Make believe treatment. Placebo: Make believe treatment. Controlled Placebo study: Control group is given a placebo. Controlled Placebo study: Control group is given a placebo. Blind Study: The subjects do not know which group they are in (control or treatment) Blind Study: The subjects do not know which group they are in (control or treatment) Double Blind study: Neither the subjects nor observers know which group they are in. Double Blind study: Neither the subjects nor observers know which group they are in. Discrete Math

Famous Clinical Trials Polio Vaccine: 1953 Jonas Salk developed killed virus vaccine. Polio Vaccine: 1953 Jonas Salk developed killed virus vaccine Large scale, double blind controlled placebo study was chosen 1954 Large scale, double blind controlled placebo study was chosen Over 400,000 children were randomly selected. Over 400,000 children were randomly selected. 200,000 were randomly selected for treatment and the other 200,000 were selected as the control group. 200,000 were randomly selected for treatment and the other 200,000 were selected as the control group. So successful, that by 1962 vaccinations were offered to the public. So successful, that by 1962 vaccinations were offered to the public.

Clinical Trials Gone Bad !! Tuskeegee Experiments Tuskeegee Experiments African American males with syphilis were not given proven treatment. Study went on from 1932 until African American males with syphilis were not given proven treatment. Study went on from 1932 until Willowbrook Hepatitis Experiments Willowbrook Hepatitis Experiments Mentally handicapped children were purposely infected with hepatitis. Mentally handicapped children were purposely infected with hepatitis. Alar Scare One obscure study in 1973 was over emphasized and impacted the apple industry. Alar Scare One obscure study in 1973 was over emphasized and impacted the apple industry.

Regulations for Clinical Trials Nuremberg Code of Ethics 1946 Nuremberg Code of Ethics 1946 Belmont Commission 1979 Belmont Commission 1979 Respect for persons: protecting the autonomy of all people and treating them with courtesy and respect and allowing for informed consent. Researchers must be truthful and conduct no deception; Respect for persons: protecting the autonomy of all people and treating them with courtesy and respect and allowing for informed consent. Researchers must be truthful and conduct no deception; Beneficence: The philosophy of "Do no harm" while maximizing benefits for the research project and minimizing risks to the research subjects; and Beneficence: The philosophy of "Do no harm" while maximizing benefits for the research project and minimizing risks to the research subjects; and Justice: ensuring reasonable, non-exploitative, and well-considered procedures are administered fairly — the fair distribution of costs and benefits to potential research participants — and equally. Justice: ensuring reasonable, non-exploitative, and well-considered procedures are administered fairly — the fair distribution of costs and benefits to potential research participants — and equally.

Discrete Math