1. AP Statistics
Chapter 5

2. Class Survey 1. Are you male or female?
2. How many brothers or sisters do you have?
3. How tall are you in inches to the nearest inch?
4. Estimate the number of pairs of shoes you have.
5. How much money in COINS are you carrying right now?
6. On a typical school night, how much time do you spend doing HW?
7. On a typical school night, how much time do you spend watching TV?

3. Can we know it all? We have a “POPULATION”? Want information about it!
We cannot “get at it” all! Why not?
So …
We gotta “Sample”!
To represent the entire Population

4. Careful how you choose! Choosing a sample is not that simple.
Randomness is A MUST!
You want accurate representation
You want to make decisions … often very important … based on the information
Life & Death
Business – millions of $$$ - jobs
Scientific Research

5. Chow do I collect data?
OBSERVATIONAL STUDY
EXPERIMENT

6. Example of an Observational Study
Sample Survey
Reaches only a subset of a larger population of interest
Relatively easy to do
Quick
Does not disturb the population much at all in gathering the information – YOU, the observer, are not imposing a “treatment” on the subjects
Can gain information in several variables … or just one quick yes/no question

7. TREATMENT! Experimental Design
Control the variation of confounding variables
USE OF RANDOMNESS
DO SOMETHING TO ONE GROUP and not the other
That thing you “DO”: “TREATMENT”

8. Observational Study vs. Experiment
An observational study : observes individuals and measures variables of interest but does not attempt to influence the responses.
An experiment : (on the other hand) deliberately imposes some treatment on individuals in order to observe their responses.

9. The best way to determine this is a: WELL DESIGNED EXPERIMENT
CAUSE & EFFECT
The best way to determine this is a: WELL DESIGNED EXPERIMENT

10. WELFARE Why can we not conclude a cause and effect here?
Observational studies show job-training & job-search programs correlate to leaving the welfare system
CONFOUNDING: Education, Values, Motivation
To establish that the programs WORK (CAUSE) - need and EXPERIMENT!

11. SIMULATION In many situations …
it may be impossible to observe individuals directly
it may be impossible to perform an experiment
it may be logistically difficult / inconvenient to sample
it may be unethical/costly to impose a treatment
Simulations provide an alterative method for producing data in such circumstances.

12. STATISTICAL INFERENCE
Statistical techniques for producing data open the door to formal branch of statistics
Statistical Inference
Making judgments about a unknown population
Conclusions are only true “with a known degree of confidence”

13. Population and Sample
POPULATION The entire group of individuals that we want information about
SAMPLE Part of the population that we actually examine in order to gather information

14. Sampling vs. Census
Sampling involves studying a part in order to gain information about the whole
Census an attempt to contact every individual in the entire population.

15. Sampling vs. Census Accuracy
How could a sample be actually MORE ACCURATE?
The census will take too long, and things change IN THAT TIME
The census is impractical to really rely on
People get bore, tired and produce inaccurate results
It is too hard ot organize and maintain the volume of data

16. Sample Designs SAMPLE DESIGN
How a sample is chosen - the method used to choose the sample from the population.
If conclusions based on a sample are to be valid - a sound design for selecting the sample is required

17. Voluntary Response Sample
BAD DESIGN
consists of people who choose themselves by responding to a general appeal
these samples are nearly always very biased because people with strong opinions, especially negative opinions, are most likely to respond.

18. Convenience Sampling BAD DESIGN
another sampling design - which chooses individuals that are the easiest to reach
Both sample designs choose a sample that is almost guaranteed not to represent the entire population
These sampling methods display bias

19. BIAS
systematic error - in favoring some parts of the population over others
The design of a study is biased if it systematically favors certain outcomes

20. SRS - Simple Random Sample
A statistician’s remedy to BIAS
Allow impersonal chance to choose the sample
A sample chosen by chance allows neither favoritism by the sampler nor self-selection by respondents
Choosing a sample by chance attacks bias by giving all individuals an equal chance to be chosen …

21. Simple Random Samples Cont’d
A simple random sample (SRS) of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be the sample actually selected
A SRS not only gives each individual an equal chance to be chosen but also gives every possible sample an equal chance to be chosen.

22. Random Digits
A table of random digits is a long string of digits chosen from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} with these two properties:
Each entry in the table is equally likely to be any of the 10 digits 0 through 9.
The entries are independent of each other
Table of Random Digits

23. Choosing an SRS Choose an SRS in two steps:
Label. Assign a numerical label to every individual in the population.
Table. Use table B to select labels at random.

24. Choosing a Client
Listed in Book: 30 clients numbered from 01 through 30
Example: 01 = A-1 Plumbing; 16 = JL Records; 30 = Von’s Video Store
We want to select 5 clients RANDOMLY from the list
Line 130:
Chunk in sets of 2:
Ignore those above 30 and repeats: …
Bailey Trucking … JL Records; Johnson Commodities, etc.

25. Other Sampling Designs
A probability sample – not really one we will use
Some probability sampling designs (such as SRS) give each member of the population an equal chance to be selected. This may not be true in more elaborate sampling designs. In every case, however, the use of chance to select a sample is the essential principle of statistical sampling.

26. Other Sampling Designs – Stratified Random Sample
First - divide the population into groups of similar individuals, called strata.
Choose a separate SRS in each stratum and combine these SRSs to form the full sample.
The strata is based on facts known before the sample is taken.
Can produce more exact information than an SRS of the same size by taking advantage of the fact that individuals in the same stratum are similar to one another.
If all individuals in each stratum are identical, just one individual from each stratum is enough to completely describe the population.

27. Other Sampling Designs Cont.
Another common means of restricting random selection is to choose the sample in stages.
Multistage samples select successively smaller groups with the population in stages, resulting in a sample consisting of clusters of individuals.
Ex: White … Males … Age 30 – 45 … Income between 50 & 100 K … who do not smoke.

28. Cautions About Sample Surveys
Undercoverage occurs when some groups in the population are left out of the process of choosing the sample
Non-response occurs when an individual chosen for the sample can’t be contacted or does not cooperate

29. More Cautions About Sample Surveys
Response Bias: The behavior of the respondent or of the interviewer can cause response bias in sample results. The respondent might lie in a face to face situation (shame). The interviewer my prod or imply a response
The wording of questions is the most important influence on the answers given to a sample survey. Confusing or leading questions can introduce strong bias, or even minor changes in wording can change a survey’s outcome

30. Inference About the Population
If we select two samples at random from the same population, we will draw different individuals. So the sample results will almost certain differ somewhat
Properly designed samples avoid systematic bias but their results are rarely exactly “correct” and they vary from sample to sample
The results from random sampling don’t change haphazardly from sample to sample
The results obey the laws of probability that govern chance behavior. We can say how large an error we are likely to make in drawing conclusions about the population from a sample

31. Inference About the Population Cont’d
One point we should consider: larger random samples give more PRECISE results that smaller samples – as it leads to smoothing out the variability of the extremes
Using a probability sampling design and taking care to deal with practical difficulties reduce bias in a sample. The size of the sample then determines how close to the population truth the sample result is likely to fall.