1.4-Design of ExperimentsObjective: To understand the various types of experimental designs and techniques

4 Ways to Collect Data Observational study – observe and

measure specific characteristics, but we don’t attempt to modify the subject being studied

Experiment – a treatment is applied to observe its effect on the subjects

Simulation – mathematical or physical model used to reproduce a situation

Survey – investigation of characteristics of a population

4 Ways to Collect Data Examples

A study of the effect of changing flight patterns on the number of airplane accidents

A study of the effect of eating oatmeal on lowering blood pressure

A study showing how fourth grade students solve a puzzle

A study of US residents’ approval rating of the US president

Basic Steps to Designing Experiments

Identify the objective

Collect sample data

Use a random procedure that avoids bias

Analyze the data and form conclusions

Ways to Control Treatments

Placebo – a faux treatment that looks like the real treatment (i.e. sugar pill)

Placebo Effect – occurs when an untreated subject incorrectly believes that he/she is receiving a treatment and reports an improvement in symptoms.

Ways to Control Treatments (continued)

Blinding – a technique in which the subject doesn’t know whether he/she is receiving a treatment or a placebo.

This is used so we can determine if the treatment effect is significantly greater than the placebo effect Single-Blind – the researcher knew which

subject received which treatment, but the subjects did not know

Double-Blind – neither the researcher nor the subjects know who received a placebo or treatment

Ways to Control Treatments (continued)

Block – a group of subjects (or experimental units) that are similar to test the effectiveness of one or more treatments

The groups need to be similar in the ways that might affect the outcome.

Randomized design – this is a way to assign subjects to blocks through random selection

Randomly assigning treatments or placebos to groups

Controlled design – experimental units are carefully chosen so that the subject in each block are similar in the ways that are important.

Testing the use of a nicotine patch on groups of similar age and gender. A heavy smoker in her 40’s gets the treatment, and a similar heavy smoker in her 40’s gets a placebo.

Ways to Control Treatments (continued)

Confounding – occurs in an experiment when the effects from two or more variables cannot be distinguished from each other

Example – A professor in Vermont experiments with a new attendance policy (your course average drops one letter grade for each class cut), but an exceptionally mild winter moderates the discomforts that have reduce attendance in the past. If attendance improves, we can’t tell whether it was because of the new attendance policy or due to weather conditions.

Ways to Control Treatments (continued)

Sample Size Make sure your sample is large enough,

however, an extremely large sample is not necessarily a good sample.

Make sure the sample is large enough to see the true nature of the effects

Replication Replication helps to confirm results by

repeating the experiment

Ways to Control Treatments (continued)

Randomization Collect data in an appropriate way, otherwise

your data are useless.

Random Sample – members of the population are selected in a way that each has an equal chance of being selected

Five Sampling TechniquesSimple Random Sample (SRS) – n subjects are selected in a way that every possible sample of size n has the same chance of being chosen.

Steps in simple random sampling1. Identify and define the population.2. Determine the sample size.3. List all members of the population.4. Assign each member of the population a consecutive number from

zero to the desired sample size (i.e. 00 to 35 – each member needs to have a number with the same number of digits).

5. Select an arbitrary starting number from the random number table.6. Look for the subject who was assigned that number. If there is a

subject with that assigned number, they are in the sample.7. Look at the next number in the random number table and repeat

steps 6 and 7 until the appropriate number of participants has been selected.

SRS Example:

Randomly assign 5 members to participate in Ms. Halliday’s experiment using Line 21 of Appendix G:

Kesley Jake Sean

John Anne Derek

Joe Dan Alyssa

Sarah Katie Tara

Tandi Hallie Karen

Bella Corey Jim

Five Sampling Techniques Systematic Sampling – randomly select a starting

point through a random # generator, see calculator or software, and take every kth subject of the population

Steps in systematic sampling1. Identify and define the population.2. Determine the sample size.3. List all members of the population.4. Determine K by dividing the number of members in the

population by the desired sample size. 5. Choose a random starting point in the population list.6. Starting at that point in the population, select every Kth

name on the list until the desired sample size is met. 7. If the end of the list is reached before the desired sample

size is drawn, go to the top of the list and continue.

Five Sampling Techniques Stratified Sampling – we subdivide the

population into at least two different subgroups (or strata) that share the same characteristics (such as age or gender), then draw a sample from each stratum

Steps in stratified random sampling1. Identify and define the population.2. Determine the sample size.3. Identify variable and strata for which equal

representation is desired.4. Classify all members of the population as a member

of one strata.5. Choose the desired number of subjects from each

strata using the simple random sampling technique.

Stratified Example:A math club has 30 students and 10 faculty members. The students are:

Abel Ellis Huber Miranda CarsonGhosh Reinman Jimenez Chen Moskowitz

Santos GriswoldDavid Jones Neyman Deming HeinKimFisher Thompson HernandezPearl Utz HollandPotter Verani Shaw O’Brien Klotz Liu

The faculty members are:Krauland Karkaria Graham Semega Walker

KeffalasMagill Magnani HallidayKotula

The club can send 4 students and 2 faculty members to the convention. Use a random # generator.

Five Sampling Techniques Cluster Sampling – first divide the population area into

sections (or clusters), then randomly select some of those clusters, and then choose ALL members from those selected clusters.

Steps in cluster sampling1. Identify and define the population.2. Determine the sample size.3. Identify and define a cluster (neighborhood, classroom, city block)4. List all clusters.5. Estimate the average number of population members per cluster.6. Determine the number of clusters needed.7. Choose the desired number of clusters using the simple random

sampling technique. 8. All population members in the included clusters are part of the

sample.

Five Sampling Techniques

Convenience Sampling – a researcher chooses a sample that is convenient or easy for them to access.

Ms. Halliday is conducting research at Pitt. She needs a sample of students and chooses all of her CHS Statistics students to participate in her study.

Sampling Techniques Examples: You select a class at random and question each

student in the class.

You divide the student population with respect to majors and randomly select and question some students in each major.

You question every 20th student you see in the hall.

You assign each student a number and generate random numbers. You then question each student whose number is randomly selected.

Multistage Sampling Sometimes we use a variety of sampling

methods together.

Sampling schemes that combine several methods are called multistage samples.

EXAMPLE: Most surveys conducted by professional polling organizations use some combination of stratified and cluster sampling as well as simple random sampling.

Sampling Error Sampling Error – the difference

between a sample result and the true population result; such as an error results from chance sample fluctuations

Non-Sampling Error – occurs when the sample data are incorrectly collected, recorded, or analyzed (such as selecting a biased sample, using a defective measurement instrument, or copying the data incorrectly)

1.4 Book Assignment pp. 23 – 25 # 1 – 16, 18, 21