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Experimental Design Sections 1.2 & 1.3

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Section 1.2 - Random Samples Samples are used to gain an understanding of “Total Population” Def: Simple Random Sample (SRS) - is a subset of the population that is selected in a way where each member had an equal chance of being chosen. What does it mean to be “random”?

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Using the Random Number Table (Appendix 1) Gives a starting point for you to find “matches” or select individuals. Steps: 1. number all members of population sequentially. 2. determine starting point on random # table (given). 3. looking at correct number of digits, find matches which will produce the sample.

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Example 1 - SRS Pick an SRS of size 4 from the class starting on the 7 th row, 3 rd block Label students 01-25 Looking at 2 digits at a time, start on the 7 th row, 3 rd block to locate matches 7 th row: 82739 57890 20807 47511 81676 55300 94383 14893 8 th row: 60940 72024 17868 24943 61790 90656 87964 18883

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Example 3 - SRS Pick an SRS of size 30 from a population of 500 cars starting on the 11 th row, 1 st block. List only the first 5 matches. Example 2 - SRS Pick 150 students from the Univ. of Florida which has a population of 50,000 students starting on the 1 st row, 7 th block. List the first 5 matches. Answer: 42544, 47150, 01927, 27754, 42648 Answer: 092,041,271,238,276

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Other types of Sampling (Summary on page 17) 1.Stratified - draw a certain number of individuals from a population after it is divided up into smaller groups (strata) Lynchburg College Students Fr.So.Jr.Sr. Sample (10 from each strata)

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2.Systematic – arrange individuals in some order, then select every k th element. Ex. Elementary school – count up by 3’s: 1-2-3, 1-2-3, 1-2-3, … to form 3 groups. Downfall: if a machine produces something and you check every 16 th element, but there is a mistake in every 17 th element, big problem. Other types of Sampling (Summary on page 17)

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3.Cluster – divide up demographic area into sections, select a few sections, and then sample every individual in that section. Ex. Large city school children: select 5 schools (clusters) and then sample all kids from those 5 schools. Sample is compose of 5 schools rather than an SRS of 2500 students. Other types of Sampling (Summary on page 17)

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4.Multistage – start with a large group to sample and then break down group based on certain factors with final stage consisting of clusters. Ex. 60,000 households → then by race → smaller groups (age, income, etc.) → clusters → interviews/surveys Other types of Sampling (Summary on page 17)

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5.Convenience – use results/data that is available, some information is better than no information. Ex. Ask your friends to complete a survey on nuclear reactors, stratification layers in lakes, or equilibrium points of a specific parasite that infect dogs. Other types of Sampling (Summary on page 17)

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Types of errors Sampling errors: difference between measurements from a sample compared to what the population data should actually be. Nonsampling errors: result of poor sample design, sloppy data collection, faulty machines, bias, undercoverage, etc.

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Section 1.3 – Intro. To Experimental Design Guidelines for a Study 1.Identify individuals of interest 2.Specify variables to be studied 3.Sample or population? Size? 4.Create data collection plan and obtain permissions. 5.Collect data 6.Analyze data using statistics 7.Conclusions and concerns

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Good Practices / Terminology Treatment – Specific condition administered to subjects (diet pill, music, etc.) Placebo – “dummy” treatment given to a test group. Has no actual effect on subjects. Placebo Effect – subject receives no actual treatment, but thinks he/she is receiving treatment and responds favorably. Blind study – subjects do not know which treatment they are receiving. Double Blind – neither subjects nor persons performing study know treatment groups.

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Good Practices / Terminology Control Group – treatment group who is given a placebo. Should not show any changes, but if there is change, results could be used to account for any lurking or confounding variables. Lurking Variable – variable that isn’t studied, but may have an influence on other variables in the study. ex. Diet pills and weight loss: Lurking variable could be exercise or nutrition. Confounding Variable – Two variables whose effects can’t be distinguished from each other. ex. Study involving GPA: difficulty of courses, IQ, and available study time are all confounding variables.

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Good Practices / Terminology Matched Pairs Design Test the time it takes for two groups to complete a maze with the treatment being a certain type of music. with musicwithout music Trial 1:Group AGroup B Trial 2:Group BGroup A Compare results and make conclusions using data about each group with both treatments.

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Good Practices / Terminology Replication – Perform an experiment on many individuals to reduce the possibility of error or a result occurring by chance. Census – data from the entire population is used Sample – data from part of the population is used Bias – Results skewed in some way due to personal opinion / favoritism.

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Usefulness of Data Situation 1 A uniformed police officer interviews a group of 20 college freshman. The officer asks each one his or her name and then if he or she has used an illegal drug in the last month. In fear of getting in trouble – students may not answer truthfully or refuse to participate.

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Usefulness of Data Situation 2 Jessica saw some data showing that cities with more low-income hosing have more homeless people. Does building low-income hosing cause homelessness? Lurking / Confounding Variables such as the size of the city.

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Usefulness of Data Situation 3 A survey about food in the café was conducted by placing forms for students to pick up as you got your card scanned. A drop box was then placed in the foyer outside the café. Voluntary response likely produced negative comments Nonresponse by losing document before it was turned in Fill out form before you ate, not accurate account of the quality of the food

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Usefulness of Data Situation 4 Extensive studies on coronary problems were conducted using men over the age of 50. Results may not help out other age groups or the female gender

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Types of Studies Observational Simply observe subjects without any influence on the variable being studied Ex. A researcher stood by a busy intersection to see if the color of the car someone drove related to running red lights. Experiment Researcher actually does something (treatment) to the subject being studied Ex. Subjects were assigned to two groups. The first group was given an herbal supplement and the other a placebo. After 6 months the red blood cell counts were compared.

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Types of Experimental Designs 1.Completely Randomized – random process (ie. random number table) is used to assign each individual to one of the treatment groups. Ex. Laser heart treatment on 300 individuals with heart pain problems. Patients w/heart pain problems Random Assignments Group 1, 150 patients, laser treatment Group 2, 150 patients, no treatment Compare pain relief

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Types of Experimental Designs 2.Randomized Block Experiment – sort individuals into blocks and then use random process to assign individuals in the block to one of the treatments. Def: block – group of individuals that share a common feature that may affect the treatment.

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Patients w/heart pain problems Random Assignments MenWomen Compare pain relief Random Assignments Compare pain relief Group 1, laser treatment Group 2, no treatment Group 1, laser treatment Group 2, no treatment

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Data Collection By means of surveys Sampling, census, observation, or experiments. Not just questionnaires. Methods most commonly used 1.Surveys – quick and effective 2.Observational study – less permission needed and don’t have to bother anyone to obtain data 3.Experiments – time consuming, but yield the most meaningful and valid results.

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Problems with Data Collection Surveys Nonresponse / Small sample size Truthfulness Faulty recall – forgot details of an event Hidden bias – wording leads subjects to respond a certain way Vague wording – words with different meanings to different persons are used (often, seldom, occasionally) Interview influence – tone of voice, body language, attire, etc. influence results Voluntary response – Individuals with strong feelings about a subject are more likely to respond in a positive way, which is not reflective about the entire population.

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Problems with conclusions when using a sample Inference about a population – Results of a sample may not reflect the entire population correctly – Large sample sizes give more accurate results

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Homework Section 1.2 Pg. 18 #’s: 6a, 7 starting at line 7, 8 starting at line 8, 9 starting at line 9, 10 starting at line 10, 13 starting at line 13. Section 1.3 Pg. 28 #’s: 5,7a,9 & Pg. 32 #’s: 3a,6,7

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MATH 2311-06 Section 6.1. Sampling: Terms: Population – each element (or person) from the set of observations that can be made Sample – a subset of the.

MATH 2311-06 Section 6.1. Sampling: Terms: Population – each element (or person) from the set of observations that can be made Sample – a subset of the.

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