1. Experiments vs. Observational Studies vs. Surveys and Simulations

2. Recognizing Different Forms of Statistical Research
Statistical research takes various forms depending on whether the purpose of the research is to:
Measure a variable in a population,
To see if there is evidence of an association between two variables, or
To determine whether one variable actually influences another variable.

3. Ex:
Suppose a graduate school researcher is considering three studies related to math and music. One study involves asking a random sample of high school students in a large school district whether they listen to music while doing math homework. A second study involves asking a random sample of students at a large university whether they are majoring in math and whether they also play a musical instrument or sing. A third study involves a group of adult participants where half will be randomly assigned either to listen to classical music for 15 minutes before taking a logical reasoning test or to listen to white noise for 15 minutes before taking the same test.

4. Ex:
Suppose a graduate school researcher is considering three studies related to math and music. One study involves asking a random sample of high school students in a large school district whether they listen to music while doing math homework. A second study involves asking a random sample of students at a large university whether they are majoring in math and whether they also play a musical instrument or sing. A third study involves a group of adult participants where half will be randomly assigned either to listen to classical music for 15 minutes before taking a logical reasoning test or to listen to white noise for 15 minutes before taking the same test.

5. Ex:
Suppose a graduate school researcher is considering three studies related to math and music. One study involves asking a random sample of high school students in a large school district whether they listen to music while doing math homework. A second study involves asking a random sample of students at a large university whether they are majoring in math and whether they also play a musical instrument or sing. A third study involves a group of adult participants where half will be randomly assigned either to listen to classical music for 15 minutes before taking a logical reasoning test or to listen to white noise for 15 minutes before taking the same test.

7. Recognizing Different Forms of Statistical Research
Statistical research takes various forms depending on whether the purpose of the research is to:
Measure a variable in a population: survey
To see if there is evidence of an association between two variables: observational studies
To determine whether one variable actually influences another variable: experiment

8. Surveys
A survey measures characteristics of interest about a population using a sample selected from the population. A sample needs to be representative of the population in order for the measurements obtained from the sample to be accurate. Random sampling is generally the best way to ensure representation.
But, even when random sampling is used, a survey’s results can have errors. Some of the sources of errors are:
Biased questions: The wording of questions in a survey can influence the way people respond to questions. Survey questions need to be worded in a neutral, unbiased way.
Interviewer effect: If an interviewer asks the questions in a survey, the person being interviewed may give inaccurate responses to avoid being embarrassed.
Nonresponse: Some people may be difficult to contact, or they may simply refuse to participate once contacted. If nonresponse rates are higher for certain subgroups of a population, then those subgroups will be underrepresented in the survey results.

12. Whole Class Activity: Music or Art?
Ask a few students in the class whether they are more interested in music or in art. Use their responses to make a prediction about the whole class.
Then ask half the students in the class the same question, and make a second prediction.
Finally, direct the question to the entire class and tally the results. Discuss how accurate each prediction is, and whether it is surprising or not that one prediction is more accurate than another.

13. Distinguishing Between Observational Studies and Experiments
In an observational study, researchers determine whether an existing condition, called a factor, in a population is related to a characteristic of interest.
Ex: An observational study might be used to find the incidence of heart disease among those who smoke. In the study, being a smoker is the factor, and having heart disease is the characteristic of interest.
In an experiment, researchers create a condition by imposing a treatment on some of the subjects of the experiment.
Ex: An experiment might be conducted by having some people with eczema take a vitamin E pill daily, and then observing whether their symptoms improve. In the experiment, taking the vitamin E pill is the treatment, and improvement of symptoms is the characteristic of interest.

14. Distinguishing Between Observational Studies and Experiments
Generally, an experiment is preferred over an observational study because an experiment allows researchers to manipulate one variable to see its effect on another.
However, there may be practical or unethical reasons against performing an experiment.
Ex: It would be unethical to ask people to smoke in order to study the effects of smoking on their health. Instead, an observational study should be performed using people who already smoke.

19. Simulations
Simulations are a way to model random events, such that simulated outcomes closely match real-world outcomes.
By observing simulated outcomes, researchers gain insight on the real world.
Why use simulations? Some situations do not lend themselves to precise mathematical treatment. Others may be difficult, time- consuming, or expensive to analyze. In these situations, simulation may approximate real-world results; yet, require less time, effort, and/or money than other approaches.

20. Simulation Example:
Suppose you flip a coin 5 times in a row. Use a simulation to determine the probability distribution for the number of times the coin lands heads up.
When you flip a coin, the possible outcomes are heads and tails.
Let’s use a graphing calculator to generate the integers 0 and 1 randomly, associating each 0 with tails and each 1 with heads.
MATH, PRB, randInt(0,1,5)
Hand out several graphing calculators and have the students generate their own 4 trials.

21. Simulation Ex: Let’s combine the class data:
Enter the outcomes (0 through 5) into the calculator
as list L1. Enter the relative frequencies as list L2.
Make a histogram by turning on a statistics plot,
selecting the histogram option, and using L1 for Xlist
and L2 for Freq. Set the Window as shown. Press
Graph.

22. Simulation Ex:
Describe the shape of the probability distribution. What does the y-axis represent? If you flipped a coin 5 times and got 5 heads, would this cause you to question whether the coin is fair? Why or why not?

23. Simulation Ex:
The probability we got for 5 heads out of 5 flips of a coin was ______.
This amount is called the experimental probability because it is the probability of 5 heads out of 5 flips from our experiment
This probability could DEFINITELY change from experiment to experiment. It’s all chance.

24. Simulation Ex:
But what should the probability of getting 5 heads, out of 5 flips of a coin, have been? Was our probability close? How could our result have gotten closer to the last result?
The result we just obtained is called the theoretical probability. The theoretical probability of an event is the number of ways that the event can occur, divided by the total number of outcomes. It is finding the probability of events that come from a sample space of known equally likely outcomes.
This is the probability if we repeated the experiment infinitely many times

25. Spinner Activity
..\..\Probability and Statistics\2nd Day- Theoretical vs. Experimental & Tree\Spinner Activity.pdf