# Statistics part 2

1. Explanatory variable

Variable that affects (or explains) the value of the responce.

2. Response variable

Variable of interest in a research study.

3. Observational study

Researcher observes behavior of individuals in the study w/o trying to influence the outcome of the study.

4. Experiment

Researches imposes treatments and controls. Then observes characteristics and takes measurements.

Ex) Determine whether the study depicts an observational study or an experiment.

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13. A survey is conducted asking 400 people, “Do you prefer Coke or Pepsi?”

Observational

14. While shopping, 200 people are asked to perform a taste test in which they drink from two randomly placed, unmarked cups. They are then asked which drink they preferred

Experiment

5. Confounding

Effects of two or more explanatory variables are not separated.

6. Lurking variable

Explain tray variable NOT considered in a study but affects the value of the response variable in the study.

7. Census

List of all individuals in a population along with certain characteristics of each individual.

1. Random sampling –

Process of using chance to select individuals from a population to be included in the sample.

2. Simple random sampling –

A sample of size n is obtained from a population of size N if every possible sample of size n has an equally likely chance of occurring.

3. Sampling without replacement –

Once an individual is chosen, he or she can’t be selected again. * usually used

4. Sampling with replacement –

Selected individual is placed back in population and can be chosen again.

5. Frame –

List of all individuals w/I a population.

Ex) Two students are being chosen from six students (1, 2, 3, 4, 5, 6). List all possible pairs.

1/2 1/3 1/4 1/5 1/6

2/3 2/4 2/5 2/6

3/4 3/5 3/6

4/5 4/6

5/6

2/3 2/4 2/5 2/6

3/4 3/5 3/6

4/5 4/6

5/6

15 pairs

What are the chances of selecting students 2 and 5? __________students 1 and 3? __________

2&5 is 1/15

1&3 is 1/15

1&3 is 1/15

1.4 Other Effective Sampling Methods

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1. Stratified –

Where you separate the population into non- overlapping groups (called strata) and subjects w/I the groups are randomly selected. (see ex. in notes)

2. Systematic –

Select the first subject and then select every Kth individual. (see ex. in notes)

3. Cluster –

Select all individuals w/i a randomly selected group. An intact group that’s representative of the population. (see ex. in notes)

4. Convenience –

Sample in which individuals are easily obtained and not based on randomness.

Ex.) Ask people a question as they walk out of a shopping mall.

Ex.) Ask people a question as they walk out of a shopping mall.

Ex) Identify the type of sampling used.

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11. To estimate the percentage of defects in a recent manufacturing batch, a quality control manager at Intel selects every 8th chip that comes off the assembly line starting with the 3rd until she obtains a sample of 140 chips.

Systematic

13. To determine consumer opinion of its boarding policy, Southwest Airlines randomly selects 60 flights during a certain week and surveys all passengers on the flights.

Cluster

14. A member of Congress wishes to determine her constituency’s opinion regarding estate taxes. She divides her constituency into three income classes: low, middle, and upper income. She then takes a simple random sample of households from each income class.

Stratified

16. A radio station asks its listeners to call in their opinion regarding the use of U. S. forces in peacekeeping missions.

Convenience

22. 24 Hour Fitness wants to administer a satisfaction survey to its current members. Using its membership roster, the club randomly selects 40 club members and asks them about their level of satisfaction with the club.

Simple random

1. Bias –

If the results of the sample are not representative of the population.

A.Sampling bias –

When the technique used to obtain individuals in the sample favors 1 part of the population over another.

B.Nonresponse bias –

When individuals selected to be in the sample who do not respond to the survey have different opinions than those who do.

C.Response bias –

When answers of the survey do NOT reflect the true feelings of the respondent.

2. Nonsampling error –

Error which results because of under coverage, non-response bias, or data entry.

3. Sampling error –

Error which results from using a sample to estimate information about a population.

Ex) Putting It Together:

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43. In the state of California, speed limits are established through traffic engineering surveys. One aspect of the survey is for city officials to measure the speed of vehicles on a particular road.

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a. What is the population of interest for this portion of the engineering survey?

All vehicles that travel on that particular road.

b. What is the variable of interest for this portion of the engineering survey?

Speed of vehicles

c. Is the variable qualitative or quantitative?

Quantitative

d. What is the level of measurement for the variable?

Ratio b/c there is a true zero.

e. Is a census feasible in this situation? Explain why or why not.

No. Impossible to get a list of all of the vehicles.

f. Is a sample feasible in this situation? If so, what type of sampling plan can be used? If not, explain why not.

Yes. Systematic random sample.

g. In July 2007, the Temecula City Council refused a request to increase the speed limit on Pechanga Parkway from 40 to 45 mph despite survey results indicating that the prevailing speed on the parkway favored the increase. Opponents were concerned that it was visitors to a nearby casino who were driving at the increased speeds and that city residents actually favored the lower speed limit. Explain how this might be playing a role in the council’s decision.

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1. Experiment –

A controlled study conducted to determine the effects varying one or more explanatory variables has on a response variable.

-Treatment is any combination of the factors.

Explanatory variables aka factors

-Treatment is any combination of the factors.

Explanatory variables aka factors

2. Experimental unit (Subject) –

Person or object upon which the treatment is applied.

3. Control group –

Recieves base line treatment which can be used to compare to other treatments.

4. Placebo –

An innocuous medicine (sugar tablet) which looks tastes and smells like the experimental medication.

5. Blinding –

Non- disclosure of treatment which the subject is recieving.

A. Single-blind –

The subject does not know the treatment.

B. Double-blind –

Neither subject nor researcher in contact with the subject knows the treatment.

6. Completely randomized design –

Each subject is randomly assigned to a treatment.

7. Matched-pairs design –

Subjects are paired up.

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