Elementary Statistics Lecture Notes - Chapter 1.3: Data Collection & Experimental Design, Summaries of Statistics

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Chapter

Introduction to

Statistics

Chapter Outline

• 1.1 An Overview of Statistics
• 1.2 Data Classification
• 1.3 Data Collection and Experimental Design

Section 1.3 Objectives

• How to design a statistical study and how to distinguish between an observational study and an experiment
• How to collect data by using a survey or a simulation
• How to design an experiment
• How to create a sample using random sampling, simple random sampling, stratified sampling, cluster sampling, and systematic sampling and how to identify a biased sample

Designing a Statistical Study

3. Collect the data.

4. Describe the data using

descriptive statistics techniques.

5. Interpret the data and

make decisions about the population using inferential statistics.

6. Identify any possible

errors.

1. Identify the variable(s)

of interest (the focus) and the population of the study.

2. Develop a detailed plan

for collecting data. If you use a sample, make sure the sample is representative of the population.

Data Collection Experiment

• A treatment is applied to part of a population, called

a treatment group , and responses are observed.

• Another part of the population may be used as a control group, in which no treatment is applied. (The subjects in both groups are called experimental units. ) In many cases, subjects in the control group are given a placebo, which is a harmless, fake treatment that is made to look like the real treatment.

Data Collection Experiment

• An experiment was performed in which overweight subjects were given the artificial sweetener sucralose to drink while a control group drank water. After performing a glucose test, researchers concluded that “sucralose affects the glycemic and insulin responses” in overweight people who do not normally consume artificial sweeteners. (Source: Diabetes Care)

Example: Observational Study or an Experiment Determine whether each study is an observational study or an experiment.

2. Researchers conduct a study to determine how

confident Americans are in the economy. Researchers call 3040 U.S. adults and ask them to rate current U.S. economic conditions and whether the economy

is getting better or worse. (Source: Gallup)

Solution: The study does not attempt to influence the responses of the subjects, the study is an observational study.

Data Collection Simulation

• Uses a mathematical or physical model to reproduce the conditions of a situation or process.
• Often involves the use of computers.
• Allow you to study situations that are impractical or even dangerous to create in real life.
• Often save time and money.
• For instance, automobile manufacturers use simulations with dummies to study the effects of crashes on humans.

Data Collection Survey

• For instance, a survey is conducted on a sample of female physicians to determine whether the primary reason for their career choice is financial stability.
• In designing the survey, it would be acceptable to make a list of reasons and ask each individual in the sample to select her first choice.

Experimental Design

• Three key elements of a well-designed experiment are control , randomization , and replication.

Experimental Design Confounding Variable (continued)

• The placebo effect occurs when a subject reacts favorably to a placebo when in fact the subject has been given a fake treatment.
• To help control or minimize the placebo effect, a technique called blinding can be used.

Experimental Design Blinding

• Blinding is a technique where the subject does not know whether he or she is receiving a treatment or a placebo.
• Double-blind experiment neither the subject nor the experimenter knows if the subject is receiving a treatment or a placebo.

Key Elements of Experimental Design: Randomization Randomized block design An experimenter testing the effects of a new weight loss drink may first divide the subjects into age categories. Then within each age group, randomly assign subjects to either the treatment group or control group.

Experimental Design Matched-Pairs Design

• Subjects are paired up according to a similarity. One subject in the pair is randomly selected to receive one treatment while the other subject receives a different treatment.