1.4 -Design of Experiments

1. 1.4-Design of Experiments Objective: To understand the various types of experimental designs and techniques

2. 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

3. 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 of how fourth grade students solve a puzzle • A study of US residents’ approval rating of the US president

4. Basic Steps to Designing Experiments • Identify the objective • Collect sample data • Use a random procedure that avoids bias • Analyze the data and form conclusions

5. 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.

6. 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

7. 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.

8. 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 point 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.

9. 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

10. 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

11. Five Sampling Techniques Simple 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 sampling • Identify and define the population. • Determine the sample size. • List all members of the population. • 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). • Select an arbitrary starting number from the random number table. • Look for the subject who was assigned that number. If there is a subject with that assigned number, they are in the sample. • 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.

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

13. 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 sampling • Identify and define the population. • Determine the sample size. • List all members of the population. • Determine K by dividing the number of members in the population by the desired sample size. • Choose a random starting point in the population list. • Starting at that point in the population, select every Kthname on the list until the desired sample size is met. • If the end of the list is reached before the desired sample size is drawn, go to the top of the list and continue.

14. 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 sampling • Identify and define the population. • Determine the sample size. • Identify variable and strata for which equal representation is desired. • Classify all members of the population as a member of one strata. • Choose the desired number of subjects from each strata using the simple random sampling technique.

15. Stratified Example: A math club has 30 students and 10 faculty members. The students are: Abel Ellis Huber Miranda Carson GhoshReinman Jimenez Chen Moskowitz Santos Griswold David Jones Neyman Deming Hein Kim Fisher Thompson Hernandez Pearl Utz Holland Potter Verani Shaw O’Brien Klotz Liu The faculty members are: Krauland Karkaria Graham Semega Walker Keffalas MagillMagnani Halliday Kotula The club can send 4 students and 2 faculty members to the convention. Use a random # generator.

16. 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 sampling • Identify and define the population. • Determine the sample size. • Identify and define a cluster (neighborhood, classroom, city block) • List all clusters. • Estimate the average number of population members per cluster. • Determine the number of clusters needed. • Choose the desired number of clusters using the simple random sampling technique. • All population members in the included clusters are part of the sample.

17. 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.

18. 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.

19. 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.

20. 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)

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