1. Statistical Reasoning
The Power of Statistics
Statistical Reasoning
Intro to Probability and Statistics
Mr. Spering – Room 113

2. 1.1 What is/are statistics?
Population- Any set of people or objects with something in common. Anything could be a population. We could have a population of college students. We might be interested in the population of the elderly. Other examples include: single parent families, people with depression, or burn victims. For anything we might be interested in studying we could define a population. Population is a complete set of people or objects being studied
Very often we would like to test something about a population. For example, we might want to test whether a new drug might be effective for a specific group. It is impossible most of the time to give everyone a new treatment to determine if it worked or not. Instead we commonly give it to a group of people from the population to see if it is effective. This subset of the population is called a sample.
When we measure something in a population it is called a parameter. Hence, a population parameter are specific characteristics of the population. When we measure something in a sample it is called a statistic. For example, if I got the average age of parents in single-family homes, the measure would be called a parameter. If I measured the age of a sample of these same individuals it would be called a statistic. Thus, a population is to a parameter as a sample is to a statistic.
Works Cited: (Fayetteville University N.C.)

3. 1.1 What is/are statistics?
Raw data: actual measurements or observations collected from the sample.
Sample statistics: characteristics of the sample found by consolidating or summarizing the raw data

4. 1.1 What is/are statistics?
Margin of Error:
Range of values likely to contain the population parameter. Usually cited to a specific confidence interval, such as, 80%, 90%, 95%, or 99%.

5. 1.1 What is/are statistics?
MAPPING A STATISTICAL STUDY
start
1. Identify goals
2. Draw from population
POPULATION
SAMPLE
5. Draw conclusions
3. Collect raw data and summarize
4. Make inferences about population
POPULATION PARAMETERS
SAMPLE STATITICS
Figure 1.2 from page 7 of your textbook…

6. 1.1 What is/are statistics?
Descriptive vs. Inferential
Descriptive → objective simply state the findings…These are numbers that are used to consolidate a large amount of information. Any average, for example, is a descriptive statistic. So, batting averages, average daily rainfall, or average daily temperature are good examples of descriptive statistics.

7. 1.1 What is/are statistics?
Descriptive vs. Inferential
Inferential → make predictions based on findings, most useful…Inferential statistics are used when we want to draw conclusions. For example when we want to determine if some treatment is better than another, or if there are differences in how two groups perform. A good book definition is using samples to draw inferences about populations.
It’s April what should I carry in my car??

8. 1.2 Sampling
Census is a collection of data from every member of a population
Example – height of all students at your school
Often impractical
Population too large
Expensive
Time-consuming

9. 1.2 Sampling Census Most statistical studies can be done without one
Collect data from a SAMPLE, to make an inference to the whole population
REPRESENTIVE SAMPLE – Relevant characteristics of the sample which generally represents the population

10. 1.2 Sampling Example #1: Representative Sample Bias
A Representative Sample for Heights
Which is better…Basketball Team vs. Statistics Class?
Statistics Class
Bias
Favoring certain results
If members of sample differ in specific way
Researcher bias if he or she has a personal stake
Data set itself biased if collected intentionally or unintentionally in a way that makes data a poor representation
A graph is biased if it only tells part of the story in a misleading way.

11. 1.2 Sampling Sampling Methods Why Use Nielsen??
Example #2: Unbiased Samples
Why Use Nielsen??
Independent Source—Reduce Bias
Sampling Methods
Sampling Type 1: Simple Random Samples – Random population
Use a drawing
Using a hat
Random number generator

12. 1.2 Sampling Example # 3: Types of Sampling
Conduct an opinion poll with residents in town…
Telephone Book Sampling: GOOD OR NOT GOOD
NOT A GOOD SAMPLE??
Sampling Type 2: Systematic Sampling
Every 50th member

13. 1.2 Sampling Systematic sampling vs. simple random sampling
A systematic sample can be a relatively random sample. Example # 4: Museum Assessment

14. 1.2 Sampling Example # 5: When Systematic Sampling Fails
Co-ed dormitory
Odd rooms vs. even rooms (DUH!)
Picking every 10th room
Try a convenience sample
Sampling Type 3: Convenience sampling
It is convenient

15. 1.2 Sampling Example # 6: Salsa Taste Test New brand of salsa
Convenience sample??? GOOD OR NOT GOOD…
NOT GOOD! Why?
Self-selected sample
Most likely those who like salsa
Bias?? Try Cluster Samples – divide population into groups, groups selected at random, but obtain sample of all members from cluster

16. 1.2 Sampling Example # 7:Gasoline Prices Cluster Sampling leads to…
Sampling Type 4: Cluster sampling
Example # 7:Gasoline Prices
Cluster Sampling leads to…
Sampling Type 5: Stratified Samples
Concerned with differences among the subgroups or STRATA, within the population
Identify strata, draw a random sample from each stratum which will provide a sample from the individual strata

17. 1.2 Sampling Example # 8: Unemployment Data…
2,000 geographic areas (subgroups)…households randomly selected within areas
Stratified Sampling (Strata are randomly sampled)
Subgroups or strata – in order to correctly represent and make inferences on all subjects within a population.

18. 1.2 Sampling Summary of Sampling Methods
Successful when the population is represented
Biased??? Check that your sampling method DOES represent
Choose carefully and properly, but you may still have bad luck
Page 17 Figure 1.3 reviews sample methods

19. 1.2 Sampling Summary of Sampling Methods Simple Random Systematic
Convenience
Cluster
Stratified

20. 1.1 What is/are statistics?
PURPOSE of STATISTICS….(is not lying)
Statistics has infinite uses and influences, but perhaps the most important purpose is to help us make “good”, well informed predications and decisions regarding issues of uncertainty

21. 1.1 What is/are statistics?
PURPOSE of STATISTICS….
Statistics has infinite uses and influences, but perhaps the most important purpose is to help us make “good”, well informed predications and decisions regarding issues of uncertainty

22. 1.2 Sampling HOMEWORK # 2: pg 9 # 3-27 by 3’s Pg 18 # 9-29 odd
Don’t cheat…
check your work!
Simple random sampling
Stratified sampling
Cluster sampling
Systematic sampling
Convenience sampling