Prob and Stats, Aug 26

Unit 1 Review - Fundamental Terms and Definitions

Book Sections: N/A

Essential Questions: What are the building blocks of Statistics, what do I call

them, and what do they mean?

Standards: PS.SPMJ.3, PS.SPMJ.5

StatisticsAs a Branch of Mathematics

Statistics – The science of collecting, organizing, analyzing, and interpreting data in order to make decisions.

Data - Information that pertains to some population

Statistics Relationships

StatisticsA Mathematical Science

Descriptive Statistics

Inferential Statistics

Reporting the Facts Outside of the FactsPredicting

Common Manifestations Descriptive or Inferential?

The most common use of descriptive statistics is a statistical graph or visual representation.

The most common use of inferential statistics is a prediction.

More Key Words for Statistics

Data Sets – populations and samples.

Population – An entire group (all of them, whatever they are)

Sample – A subset of a population

Computed or Observed Quantities

Parameter – A description of a population characteristic.

A statistic – A description of a sample characteristic.

The Types of Data

Qualitative Data –Words

Quantitative Data –Numbers

Quantitative Data (Numbers)

Quantitative Data are further separated into two categories: Discrete and Continuous.

• Discrete – Data that assume values that can be counted. They are always whole numbers.

• Continuous – Data that can assume any value between two specific boundaries. They are obtained by measuring. They can be rational numbers.

Data Classification

Data

QualitativeWords

QuantitativeNumbers

Continuous ValuesRational Numbers

Discreet ValuesWhole Numbers

A Good Sample

A good sample of a population is one whose target statistics are very close in value to the corresponding population parameters. There are four generally accepted methods that have proven to be good sampling techniques over time.

Note that none of them is perfect.

Sampling Techniques

• There are four sampling methods that usually make the process as random as possible The sampling techniques are:

Random SamplingSystematic SamplingStratified SamplingCluster Sampling

These four methods of sampling will usually lead to an unbiased sample.

Random Sampling

Random samples are selected by using some random method to select a sample. It must use some technique designed to give every population member an equal chance of being selected.

• For a smaller sized population, a true random sample is attainable; but as the population grows true randomness becomes impossible.

Systematic Sampling

Systematic sampling results from using a timing or item interval to select the sample from a population.

• Although not perfectly random, a consistent system will usually produce a good cross-section of a target population.

Stratified SamplingStratified sampling is a process of dividing a population

into non-overlapping groups and then a simple random sample is selected from each group and surveyed.

• The groups in this process are called the strata.

• If the stratified groups are too large, all the problems of a random sample are still present. Also, some grouping strategies (such as using geography) can introduce biases into the data.

Cluster Sampling

Cluster sampling is using an intact group that is representative of the population and surveying the entire group.

• A good diverse group that is representative of the population is hard to come by and the common bond of the group could reduce true group diversity.

Biased Sampling

There are two types of sampling often used that are not random and usually lead to biased statistics. They are:

• Convenience Sampling: Sampling only members of a population that are easily accessed.

• Voluntary Response Sample: A sample that only consists of respondents who want to participate in the survey.

The Survey

A survey – is an investigation of one or more characteristics of a population.

• Most often surveys are carried out on people by asking them questions.

• Common types of surveys: InterviewMailTelephoneOn-Line

The Survey II

A survey – is an investigation of one or more characteristics of a population.

• This can apply to any populationPeople – previous slideAnimals – they can’t answer questions – you can

get information from measurements, DNA, etc.Objects – manufacturing – test until failure

Besides a Survey

The Controlled Experiment (usually medically related)– Two groups are tracked by a specified drug or treatment.

• In the experiment the first group is administered the treatment or drug and are observed and tracked over time.

• A second group, called the Control Group, are not administered the treatment and they are observed and compared to the other group over time.Usually a placebo is administered to the control group to

simulate the treatment.

Besides a Survey 2

Observational Study – Researchers observe and measure characteristics of interest of part of a population but do not change existing conditions.

Researchers are usually in the background, those being observed are better off not even knowing about it

Besides a Survey 3

Simulation – Use of a mathematical or physical model to reproduce the conditions of a situation or process. Simulations allow the study situations that are impractical or even dangerous to create in real life and can save time and money.

Classwork: CW 8/26/15, 1-25

Homework – HW Due 8/27/15, 1-12

Classwork Solutions

1a) Stratified 1b) Random 1c) Cluster 1d) Systematic 1e) convenience 2) Qualitative 3) Quantitative, continuous 4) Quantitative, discrete, 5) Qualitative 6) Descriptive 7) Sample 8) population 9) parameter 10) Statistic 11) Survey 12) Observational study 13) Simulation