statistical reasoning

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


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


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…


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.


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


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


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

statistical reasoning

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