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This guide outlines essential steps for planning a statistical study, including identifying individuals of interest, specifying variables, and addressing ethical considerations. Methods of data production such as census, sampling, and experimentation are discussed. Key experimental concepts are explained, including the placebo effect, randomized two-treatment experiments, and double-blind studies to eliminate biases. Additionally, it highlights potential problems such as lurking variables and the importance of control groups. Appropriate statistical methods, such as descriptive and inferential statistics, are essential for drawing conclusions from collected data.
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Section 1.3 Introduction to Experimental Design
Planning a Statistical Study • Identify individuals of interest. • Specify variables, protocols, procedures. • Decide on sampling method, if appropriate. • Address ethics and privacy issues. • Collect data. • Use descriptive and inferential statistics to make decisions. • Note any concerns and recommendations.
Methods of Producing Data • Census • Sampling • Simulation • Experimentation • Observation
Methods of Producing Data Census: Using measurements from the entire population Sampling: Draw a part of the population Simulation: Numerical facsimile of real-world phenomena Observational Study: Observations and measurements of individuals are conducted in a way that doesnot change the response or the variable being measured Experiment: A treatment is deliberately imposed on the study individuals in order to observe a possible change in the response or variable being studied.
Placebo Effect A subject receives no treatment but (incorrectly) believes he or she is receiving treatment and responds favorably
Randomized Two-treatment Experiment • Placebo effect is common in medical experiments. • Subjects divided into two groups. • One group receives actual treatment. • Control group receives placebo treatment disguised as real. • After treatment cycle, conditions of groups are compared.
Double-blind Experiment • Neither individuals in study nor observers know which subjects are receiving actual treatment. • Helps control for subtle biases.
To prevent bias or inaccurate results • Use a control group. • Assign individuals to groups randomly. • Replicate experiment many times to insure differences did not occur by chance.
Lurking or Confounding Variables • Known or unknown variables that might be an underlying cause of a change in response in experimental group. • Reason for need for control group
Potential Problems • Strong opinions may be over-represented if responses are voluntary. • A hidden bias may exist because of the way data is collected. • There may be hidden effects of other variables. • There is no guarantee that results can be generalized.
TI-84Plus / TI-83Plus • To select a random set of integers between two specified values, • press MATH highlight PRB then press 5. • Example • RandInt (1, 100, 5) • (63 89 13 46 47) • RandInt (1, 100, 5) • (29 82 99 50 41)