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The Power of Statistics. Statistical Reasoning. Intro to Probability and Statistics Mr. Spering – Room 113. 1.1 What is/are statistics?. - PowerPoint PPT Presentation
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Statistical Reasoning
Intro to Probability and Statistics
Mr. Spering – Room 113
The Power of Statistics
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: http://faculty.uncfsu.edu/dwallace/Lesson%201.pdf (Fayetteville University N.C.)
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
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%.
sample statistic - error parameter sample statistic + error
1.1 What is/are statistics?
MAPPING A STATISTICAL STUDY
start
POPULATION
SAMPLE STATITICS
SAMPLE
POPULATION PARAMETERS
1. Identify goals
2. Draw from population
5. Draw conclusions
4. Make inferences about population
3. Collect raw data and summarize
Figure 1.2 from page 7 of your textbook…
1.1 What is/are statistics?
Descriptive vs. InferentialDescriptive → 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.
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??
1.2 Sampling Census is a collection of data from every
member of a population Example – height of all students at your
schoolOften impracticalPopulation too largeExpensiveTime-consuming
1.2 Sampling
CensusMost statistical studies can be done without
oneCollect data from a SAMPLE, to make an
inference to the whole population REPRESENTIVE SAMPLE – Relevant
characteristics of the sample which generally represents the population
1.2 Sampling
Example #1: Representative Sample 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.
1.2 Sampling
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
1.2 Sampling
Example # 3: Types of SamplingConduct 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
1.2 Sampling
Systematic sampling vs. simple random sampling
A systematic sample can be a relatively random sample. Example # 4: Museum Assessment
1.2 Sampling
Example # 5: When Systematic Sampling FailsCo-ed dormitoryOdd rooms vs. even rooms (DUH!)
Picking every 10th room
Try a convenience sample Sampling Type 3: Convenience sampling
It is convenient
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
1.2 Sampling
Sampling Type 4: Cluster sampling
Example # 7:Gasoline PricesCluster 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
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.
1.2 Sampling
Summary of Sampling MethodsSuccessful when the population is
representedBiased??? Check that your sampling method
DOES representChoose carefully and properly, but you may
still have bad luckPage 17 Figure 1.3 reviews sample methods
1.2 Sampling
Summary of Sampling MethodsSimple RandomSystematicConvenienceClusterStratified
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
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
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 samplingStratified samplingCluster samplingSystematic samplingConvenience sampling