1.3: Experimental Design
- Page ID
- 45166
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- Define observational studies and experiments as primary methods of data collection.
- Distinguish between non-interference in observational studies and controlled conditions in experiments.
- Understand common experimental designs, including completely randomized, block, and control designs
The section is an introduction to experimental design. There are two types of research: observational studies and experiments. This section describes how to design an experiment or a survey so that they are statistically sound. Experimental design is a very involved process, so this is just a small introduction.
Observational Studies
An observational study is when the investigator collects data merely by watching or asking questions. He doesn’t change anything.
Many observational studies involve surveys. A survey uses questions to collect the data and needs to be written so that there is no bias.
Cross-Sectional Study:
Data observed, measured, or collected at one point in time.
Retrospective (or Case-Control) Study:
Data was collected from the past using records, interviews, and other similar artifacts.
Prospective (or Longitudinal or Cohort) Study:
Researchers closely observe and gather data on groups of individuals with common factors over some time to track outcomes and determine potential relationships between factors.
Experiments
An experiment is when the investigator changes a variable or imposes a treatment to determine its effect.
In an experiment, there are various options, such as a randomized two-treatment experiment, a randomized block design, a rigorously controlled design, and more. For this class, we will only focus on the ones mentioned.
Randomized Two-Treatment Experiment:
In this experiment, there are two treatments, and individuals are randomly placed into the two groups. Either both groups get a treatment, or one group gets a treatment and the other gets either nothing or a placebo. The group getting either no treatment or the placebo is called the control group. The group getting the treatment is called the treatment group. The idea of the placebo is that a person thinks they are receiving a treatment, but in reality, they are receiving a sugar pill or fake treatment. Doing this helps to account for the placebo effect, which is where a person’s mind makes their body respond to a treatment because they think they are taking the treatment when they are not taking the treatment. Note that every experiment does not need a placebo, such as when using animals or plants. Also, you can’t always use a placebo or no treatment. For example, if you are testing a new blood pressure medication, you can’t give a person with high blood pressure a placebo or no treatment for moral reasons.
Randomized Block Design:
A block is a group of subjects that are similar, but the blocks differ from each other. Then randomly assign treatments to subjects inside each block. An example would be separating students into full-time versus part-time, and then randomly picking a certain number of full-time students to receive the treatment and a certain number of part-time students to receive the treatment. This way, each type of student gets the treatment, and some do not.
Rigorously Controlled Design:
Carefully assign subjects to different treatment groups, so those given each treatment are similar in ways that are important to the experiment. An example would be if you want to have a full-time student who is male, takes only night classes, has a full-time job, and has children in one treatment group, then you need to have the same type of student getting the other treatment group. This type of design is hard to implement since you don’t know how many differentiations you would use, and should be avoided.
Replication:
Repetition of an experiment on more than one subject ensures that the sample is large enough to distinguish true effects from random effects. It is also the ability for someone else to duplicate the results of the experiment.
Blind Study:
A blind study is where the individual does not know which treatment they are getting or if they are getting the treatment or a placebo.
Double-Blind Study:
A double-blind study is used when neither the individual nor the researcher knows who is getting the treatment or the placebo. This is important so that there can be no bias created by either the individual or the researcher.
One last consideration is the time period during which you are collecting the data. There are three types of periods that you can consider.
State if the following is an observational study or an experiment.
- Poll students to see if they favor increasing tuition.
- Give some students a tutor to see if their grades improve.
Solution
- This is an observational study. You are only asking a question.
- This is an experiment. The tutor is the treatment.
Guidelines for Planning a Statistical Study or Experiment
- Identify the individuals that you are interested in. Realize that you can only make conclusions for these individuals. For example, if you use a fertilizer on a certain type of plant, you can’t say how the fertilizer will work on any other type of plant. However, if you diversify too much, then you may not be able to tell if there really is an improvement since you have too many factors to consider.
- Specify the variable. You want to make sure this is something you can measure and make sure you control for all other factors, too. As an example, if you are trying to determine if a fertilizer works by measuring the height of the plants on a particular day, you need to make sure you can control how much fertilizer you put on the plants (which would be your treatment), and make sure that all the plants receive the same amount of sunlight, water, and temperature.
- Specify the population. This is important to know what conclusions you can make and who you are making the conclusions.
- Specify the method for taking measurements or making observations.
- Determine if you are taking a census or a sample. If taking a sample, decide on the sampling method.
- Collect the data.
- Use appropriate descriptive statistics methods and make decisions using appropriate inferential statistics methods.
- Note any concerns you might have about your data collection methods and list any recommendations for the future.
Authors
"1.3: Experimental Design" by Toros Berberyan, Tracy Nguyen, and Alfie Swan is licensed under CC BY-SA 4.0
Attributions
"1.3: Experimental Design" by Kathryn Kozak is licensed CC BY-SA 4.0