MAT 120 Section 1.3 Experimental Design

Census

Census: a count or measure of the entire population. Example: You want to find out the average age of the students in your course.

Convenience Sample

Convenience sample consists of only available members of the population (usually biased). Example: Surveyors asking questions in the mall.

Experiment

Experiment: a treatment is applied to a part of the population and response to the treatment observed. (This is used a lot for clinical trials.)

Cluster Sample

For cluster samples, the population is divided into naturally groups (called clusters), then ALL the members of the selected cluster are included in the sample (but not all clusters are chosen). Example: Suppose that the Department of Agriculture wishes to investigate the use of pesticides by farmers in New Jersey. A cluster sample could be taken by first identifying the different counties as clusters. A sample of counties would then be chosen at random and all farmers in the selected counties would be included. Example: There are 600 bars in a large city. Sixty of the bars are selected and every employee in each of the sixty bats is interviewed regarding the type of clients they serve.

Systematic Sample

Systematic sample is when the members of the population are ordered then chosen at regular intervals from a random starting number. Alt Def: A systematic sample is a sample in which each member of the population is assigned a number. The members of the population are ordered in some​ way, a starting number is randomly​ selected, and then sample members are selected at regular intervals from the starting number. EXAMPLE: Choose every 4th member of the population. EXAMPLE: An electric company decides to test every third house along a street to make sure its meters are working properly.

Identify the sampling techniques​ used, and discuss potential sources of bias​ (if any). Explain. Assume the population of interest is the student body at a university. Questioning students as they leave a university parking lot, a researcher asks 365 students about their drinking habits. (a) What type of sampling is​ used? A. Convenience sampling is​ used, because students are chosen due to convenience of location. B. Cluster sampling is​ used, because students are divided into​ groups, groups are chosen at​ random, and every student in one of those groups is sampled. C. Systematic sampling is​ used, because students are selected from a​ list, with a fixed interval between students on the list. D. Stratified sampling is​ used, because students are divided into​ groups, and students are chosen at random from these groups. E. Simple random sampling is​ used, because students are chosen at random. (b) What potential sources of bias are​ present, if​ any? Select all that apply. A. Because of the personal nature of the​ question, students may not answer honestly. B. University students may not be representative of all people in their age group. C. The sample only consists of members of the population that are easy to get. These members may not be representative of the population. D. There are no potential sources of bias.

ANSWER: (a) A. Convenience sampling is​ used, because students are chosen due to convenience of location. ANSWER: (b) A. Because of the personal nature of the​ question, students may not answer honestly. C. The sample only consists of members of the population that are easy to get. These members may not be representative of the population.

Identify the sampling techniques​ used, and discuss potential sources of bias​ (if any). Explain. In​ 1965, researchers used random digit dialing to call 1300 people and ask what obstacles kept them from eating healthier. (a) What type of sampling was​ used? A. Cluster sampling was​ used, since the phone numbers were divided into​ groups, several groups were​ selected, and each number in those groups was called. B. Systematic sampling was​ used, since phone numbers were selected from a list using a fixed interval between phone numbers. C. Convenience sampling was​ used, since the 1300 phone numbers that were easiest to reach were selected. D. Simple random sampling was​ used, since each number had an equal chance of being​ dialed, so all samples of 1300 phone numbers had an equal chance of being selected. (b) What potential sources of bias were​ present, if​ any? Select all that apply. A. No one talks honestly about their eating habits with people they do not know because it is too personal a subject. This may have led to untrue responses to the survey question. B. Telephone sampling only includes people who had telephones. People who owned telephones may have been older or wealthier on​ average, and may not have been representative of the entire population. C. Individuals may have refused to participate in the sample. This may have made the sample less representative of the population. D. Individuals may have not been available when the researchers were calling. Those individuals that were available may have not been representative of the population. E. There were no potential sources of bias.

ANSWER: (a) D. Simple random sampling was​ used, since each number had an equal chance of being​ dialed, so all samples of 1300 phone numbers had an equal chance of being selected. ANSWER: (b) B. Telephone sampling only includes people who had telephones. People who owned telephones may have been older or wealthier on​ average, and may not have been representative of the entire population. C. Individuals may have refused to participate in the sample. This may have made the sample less representative of the population. D. Individuals may have not been available when the researchers were calling. Those individuals that were available may have not been representative of the population.

A pharmaceutical company wants to test the effectiveness of a new allergy drug. The company identifies 250 females​ 30-35 years old who suffer from severe allergies. The subjects are randomly assigned into two groups. One group is given the new allergy drug and the other is given a placebo that looks exactly like the new allergy drug. After six​ months, the​ subjects' symptoms are studied and compared. Answer parts​ (a) through​ (c) below. (a) Identify the experimental units and treatments used in this experiment. Choose the correct answer below. A. The experimental units are the​ 30- to​ 35-year-old females being given the treatment. The treatment is six months. B. The experimental unit is the new allergy drug. The treatments are the severe allergies the patients suffer from. C. The experimental units are the symptoms from the drug. The treatment is the new allergy drug. D. The experimental units are the​ 30- to​ 35-year-old females being given the treatment. The treatment is the new allergy drug. (b) Identify a potential problem with the experiment design being used and suggest a way to improve it. Choose the correct answer below. A. There may be a bias on part of the experiment since only females are being tested. B. There may be a bias on the part of the researcher if the researcher knows which patients were given the real drug. C. There are no biases present. D. There may be a bias on the part of the patients since they do not know if they were given the placebo or the real drug. (c) How could this experiment be designed to be a​ double-blind? Choose the correct answer below. A. The study would be a​ double-blind study if both the researcher and the patient did not know which patient received the real drug or the placebo. B. The study would be a​ double-blind study if both the researcher and the patient knew if they received the real drug or the placebo. C. The study would be a​ double-blind study if all patients received the placebo and no patient received the real drug. D. The study would be a​ double-blind study if the patient knew if they received the real drug or the placebo but the researcher did not.

ANSWER: (a) D. The experimental units are the​ 30- to​ 35-year-old females being given the treatment. The treatment is the new allergy drug. The experimental units are the subjects being​ tested, or the​ 30- to​ 35-year-old women. The treatment is applied to part of the population and the responses are observed. ANSWER: (b) B. There may be a bias on the part of the researcher if the researcher knows which patients were given the real drug. A bias will create results that are not representative of the entire population. ANSWER: (c) A. The study would be a​ double-blind study if both the researcher and the patient did not know which patient received the real drug or the placebo. Blinding is a technique where the subjects do not know whether they are receiving a treatment or a placebo. In a​ double-blind experiment, neither the experimenter nor the subjects know if the subjects are receiving a treatment or a placebo. Since the subjects do not know which treatment they receive​ already, blinding the researcher would create a​ double-blind experiment.

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. The method for selecting a stratified sample is to order a population in some way and then select members of the population at regular intervals. A. False. The method for selecting a cluster sample is to order a population in some way and then select members of the population at regular intervals. B. True. C. False. The method for selecting a systematic sample is to order a population in some way and then select members of the population at regular intervals.

ANSWER: C. False. The method for selecting a systematic sample is to order a population in some way and then select members of the population at regular intervals.

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. The method for selecting a stratified sample is to order a population in some way and then select members of the population at regular intervals. Choose the correct answer below. A. True. B. False. The method for selecting a cluster sample is to order a population in some way and then select members of the population at regular intervals. C. False. The method for selecting a systematic sample is to order a population in some way and then select members of the population at regular intervals.

ANSWER: C. False. The method for selecting a systematic sample is to order a population in some way and then select members of the population at regular intervals. A systematic sample is a sample in which each member of the population is assigned a number. The members of the population are ordered in some​ way, a starting number is randomly​ selected, and then sample members are selected at regular intervals from the starting number.

Determine whether the following statement is true or false. If it is​ false, rewrite it as a true statement. A placebo is an actual treatment. A. The statement is false. A placebo is giving the subjects no treatment at all. B. The statement is false. A placebo is a process of randomly assigning subjects to treatment groups. C. The statement is true. D. The statement is false. A placebo is a fake treatment.

ANSWER: D. The statement is false. A placebo is a fake treatment. A placebo is a fake treatment used in experiments. To minimize the possibility of the subjects reacting favorably to a​ placebo, the subjects will typically be blinded as to whether they are receiving a real treatment or the placebo.

Determine whether you would take a census or use a sampling to collect data for the study described below. If you would use a​ sampling, determine which sampling technique you would use. Explain. The most popular chain restaurant among the 25 employees of a company. Choose the correct answer below. A. The study would use a sampling. The study would use cluster sampling because the employees of a company fall into naturally occurring subgroups. B. The study would use a sampling. The study would use simple random sampling because it would be easy to randomly select 25 employees of a company. C. The study would use a sampling. The study would use stratified sampling because it would be important to have members from each segment of the population. D. The study is a census​, because the population is small enough for it to be practical to record all of the responses.

ANSWER: D. The study is a census​, because the population is small enough for it to be practical to record all of the responses.

Determine whether the study is an observational study or an experiment. Explain. In a survey of 1391 adults in a​ country, ​58% said the​ country's leader should release all medical information that might affect their ability to serve. The study is __blank__ because it __blank__ a treatment to the adults.

ANSWER: Observational, does not apply. The study is __observational__ because it __does not apply__ a treatment to the adults.

Identify the sampling techniques​ used, and discuss potential sources of bias​ (if any). Explain. Potatoes are planted on a 45​-acre field. The field is divided into​ one-acre subplots. A sample is taken from each subplot to estimate the harvest. Part (a) What type of sampling is​ used? A. Simple random sampling is​ used, since each sample of potato plants of the same amount has the same chance of being selected. B. Cluster sampling is​ used, since the field is divided into​ subplots, a number of subplots are​ selected, and every potato plant in the selected subplots is sampled. C. Stratified sampling is​ used, since the field is divided into subplots and a random sample is taken from each subplot. D. Convenience sampling is​ used, since the potato plants closest to the barn are sampled. Part (b) What potential sources of bias are​ present, if​ any? Select all that apply. A. It is possible​ that, due to sampling​ error, the sample will not be representative. B. Certain subplots may have more or fewer potato plants than others. Samples from these subplots may bias the overall sample. C. The sample only consists of the potato plants that are easiest to reach. This may not be representative of the entire population. D. There are no potential sources of bias.

ANSWER: Part (a) C. Stratified sampling is​ used, since the field is divided into subplots and a random sample is taken from each subplot. ANSWER: Part (b) B. Certain subplots may have more or fewer potato plants than others. Samples from these subplots may bias the overall sample.

A company has been rating television programs for more than 60 years. It uses several sampling​ procedures, but its main one is to track the viewing patterns of​ 20,000 households. These contain more than​ 45,000 people and are chosen to form a cross section of the overall population. The households represent various​ locations, ethnic​ groups, and income brackets. The data gathered from the sample of​ 20,000 households are used to draw inferences about the population of all households in the United States. Complete parts​ (a) and​ (b) below. Part (a) What strata are used in the​ sample? Choose the correct answer below. A. The various sampling procedures and viewing patterns B. The television ratings C. The various​ locations, ethnic​ groups, and income brackets that are represented D. The number of households and people that are chosen Part (b) Why is it important to have a stratified sample for these​ ratings? Choose the correct answer below. A. Stratified sampling ensures that only households in the U.S. are sampled. B. Stratified sampling ensures that all of the members of one or more groups are used. C. Stratified sampling ensures that each segment of the population is represented. D. Stratified sampling ensures that the television ratings are accurate.

ANSWER: Part (a) C. The various​ locations, ethnic​ groups, and income brackets that are represented. Members of the population are divided into two or more​ subsets, called​ strata, that share a similar characteristic. The households sampled represent various​ locations, ethnic​ groups, and income brackets. Each of these variables is considered a stratum. ANSWER: Part (b) C. Stratified sampling ensures that each segment of the population is represented. Stratified sampling divides the population into subsets that share a similar characteristic. A sample is then randomly selected from each of the strata. Stratified sampling ensures that each segment of the population is represented.

Identify the sampling techniques​ used, and discuss potential sources of bias​ (if any). Explain. Chosen at​ random, 510 customers at a grocery store are contacted and asked their opinions of the service they received. Part (a) What type of sampling is​ used? A. Convenience sampling is​ used, since the business is selecting from its customers that are easiest to reach. B. Stratified sampling is​ used, since the population of customers is divided into groups and a random sample is selected from each group. C. Systematic sampling is​ used, since customers are selected at fixed intervals. D. Simple random sampling is​ used, since the business is selecting from its customers at​ random, and all samples of 510 customers have an equal chance of being selected. E. Cluster sampling is​ used, since the population of customers is divided into groups and several groups are selected and all of their members sampled. Part (b) What potential sources of bias are​ present, if​ any? Select all that apply. A. The sample consists only of customers that are easy to reach. This sample may not be representative of the population. B. The wording of the question asked to the customers may influence them towards a particular response. The results would not be usable in this case. C. If there is a regular pattern to the​ customers, it is possible for the sample to not be representative. D. There are no potential sources of bias.

ANSWER: Part (a) D. Simple random sampling is​ used, since the business is selecting from its customers at​ random, and all samples of 510 customers have an equal chance of being selected. ANSWER: Part (b) B. The wording of the question asked to the customers may influence them towards a particular response. The results would not be usable in this case.

Random Sample

For random samples, every member of the population has an equal chance of being chosen. Example: Putting names in a hat and drawing out a specific number. Example: Suppose you have a school of 500 students, a computer randomly selects 50 students to conduct a short survey of the cafeteria food.

Stratified Sample

For stratified​ samples, members of the population are divided into two or more​ subsets, called strata. A sample is then randomly selected from each of the strata. This ensures that members of each group within the population will be sampled. Example: Suppose a farmer wishes to work out the average milk yield of each cow type in his herd, which consists of Ayrshire, Friesian, and Jersey cows. He could divide his herd into the three sub-groups and take equal or proportionate samples from these groups. Example: For a study on health, 50 men were randomly selected and 50 women were randomly selected to be surveyed on the quality of their health.

Observational Study

Observational study: the experimenter observes and measures characteristics of interest in a subset of the population. An observational study does not change the existing conditions. (This is done a lot in childcare because the IRB will never authorize experiments on children.) Example: A study of the effect on taste of a popular soda made with a sugar substitute. Example: A study of how often students use their calculator when taking a test.

Sampling

Sampling - a count or measure of a portion of the population. Example: You want to find out the average age of students who attend a 2-year institution in South Carolina.

Simulation

Simulation: uses a mathematical model (often with a computer); when models are used to reproduce certain conditions (usually used when an experiment might be considered harmful or dangerous). Example: A study of how fast radiation would spread if a dirty-bomb is detonated in a major city.

Survey

Survey: people are usually asked questions via mail, email, or phone. Questions must be worded carefully to avoid biased results. (This is done a lot in politics for forecasting results.) Example: A study of the effect on taste of a popular soda made with a sugar substitute. Example: A study of how often students use their calculator when taking a test.