A Day In The Life Of A Lightbulb

Virtual Tool for Exploring

Experimental Design Concepts

And Data Analysis

Copyright: LUMENWORKS, 2004

Content

• Introduction
• Preliminaries
• Data Production
• Planning to Produce Data?
• The Scenario
• References
• Resources: Pre test, Post test, Excel worksheet, Intermediate Report.

Introduction

This module allows users to perform exploratory data analysis by:

• Conducting an experiment to study the effects of explanatory variables on a response variable.
• Choosing random samples that represent some wider population.
• Performing comparative analysis of experiments with two independent samples.
• Predicting outcomes under a set of experimental conditions.
• Exploring the consequences of using different sampling methods and sample sizes on the outcomes for the response variable.

PRELIMINARIES

Carrying out an experiment is doing something or observing something happen under certain conditions, resulting in a final state of affairs or outcome. (1)

About the experiment.

• The experiment may be physical, social, educational, industrial, etc.
• The experiment may be conducted in a real setting, a laboratory, a classroom, or as in this case, in a virtual world.
• The design of an experiment is biased if the experiment systematically favors certain outcomes.

About the outcome.

• Outcomes at any trial can be completely determined by the experimental conditions, and described by deterministic models.
• Outcomes can be determined by chance. This occurs when outcomes vary from trial to trial because the conditions cannot be measured, taken into account, or are not known. Probability models are needed to predict the outcome at a given trial. (1)

About Probability Models.

Ingredients:

• Sample Space ( S ): The set of all possible outcomes of an experiment.
• Events ( e1, e2, …eN ): Subsets of the sample space.
• Probabilities of Events ( p1, p2, p3, …, pN ): Likelihood of the occurrence of an Event. (1)

  Applications:

  Predicting outcomes, under a given set of experimental conditions.

DATA PRODUCTION

One of the most significant contributions statisticians have made to our modern world is methods for producing trustworthy data through experimental trials and for judging data produced by others. (2)

The ability to generate random samples of outcomes and to conduct randomized comparative experiments has impacted all areas of human endeavor: health, industry, education, science, social science, etc. (2)

It is now common place to hear about experimental studies where two different laundry powders are compared on their whitening power, two or more diets are contrasted on their potential to reduce cholesterol, or different instructional methods are contrasted on their potential for increasing achievement scores.

Statistics has become a tool to help make sense of measurements or observations by the art of data analysis. Through data analysis users can uncover the properties of data sets, examine patterns and deviations from them, move from graphs to numerical descriptions to mathematical models, and examine distributions of individual variables as well as relationships among several variables. (2)

Two types of data analysis are most frequently conducted.

• Exploratory Data Analysis (EDA): Some data seem interesting and deserve careful analysis. There is no knowledge of what the data may reveal and there might not be questions formulated before the experiment is conducted. Similar to exploring in unknown territory.
• Formal Statistical Inference (FSI): A procedure to answer specific questions and to provide measures of the reliability of the conclusions. (2)

Note: Wise statisticians always explore the data before formal methods are applied.

 PLANNING TO PRODUCE DATA?

Answer the following questions…

• Is the study observational or experimental?
• What variables shall I measure?
• How? i.e., what instruments or methods will be used to give values to the variables?
• Which are the explanatory variables? Which is the response variable? What are the treatments?
• What design would be best for producing the data?
• What is the sample size?
• What sampling method should be used?
• How to further minimize confounding effects?
  • Controlling the effect of lurking variables on the response by comparing several treatments of the explanatory variable?
  • Using Random Techniques to assign subjects to treatments?
  • Replicating the experiment in many trials to reduce chance variation in the outcomes?
  • Conduct double-blind experiments?

The Scenario: "A Day In The Life Of A Light Bulb" 

Recently during a visit to the neighborhood supermarket I decided to buy four fluorescent light bulbs at a cost of $3 each. They seemed expensive when compared to the incandescent light bulbs just sitting next to them, at a cost of $2 for a box of four.

What on Earth (3) could justify this choice?" "Well, I assumed environmental reasons (5), of course!

On my way home I thought about the type of experiment that would be necessary to test some of the allegations in favor of the more expensive fluorescent (7) bulbs. I investigated how light bulbs are tested (4), and realized that it would take considerable amount of time and money to conduct a real experiment to test the properties of the two types of bulbs. (6).

The solution was to create a virtual experiment to answer my research question: Does the assumed increased efficiency of the fluorescent light bulb justify the higher initial cost?

In other words, I would have to design a study to:

• Identify and measure our research variables on random samples of the two types of light bulbs,
• Create data by comparing the performance of two random samples of types of light bulbs,
• Perform a comparative data analysis of the behavior of these samples, and
• Arrive to conclusions regarding the efficiency of each type of light bulb and decide if the higher initial cost is justifiable.

With this project in mind, I designed the following research tool.

http://falcon.tamucc.edu/~hutching/bulbtest.html

References

(1) Lindgren, Bernard W; "Statistical Theory", Chapman & Hall

(2) Moore, David & McCabe George; "Introduction to the Practice of Statistics", Freeman.

(3) Byrne, Jeanne; "Energy Efficient Lighting for the Home"

http://hem.dis.anl.gov/eehem/94/941116.html

(4) "Light bulb Testing"; http://www.stat.sfu.ca/~cschwarz/LongAnswer/light.html

(5) Steve Frolking & Lynn Rosentrater; "Learning to Think Globally", http://pumas.jpl.nasa.gov

(6) "Bulb Specifications"; http://www.run-n-lites.com/bulbspec.htm

(7) "Compact Fluorescent Light Bulbs"; http://www.energystar.gov/index.cfm?c=cfls.pr_cfls