Introduction to Statistics LESSON 1 Introduction to Statistics

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What is Statistics? Statistics is the science of collecting, organizing, summarizing, and analyzing information in order to make decisions and answer questions.

The Big Questions What kinds of questions can we answer using statistical thinking? Which arthritis drug is most effective? Do students who participate in tutoring do better on exams? Which political candidate is most likely to win the election? Is living near a high-voltage power line related to higher incidence of cancer?

Some Definitions Data: Population: Sample: Population parameters: are pieces of information eg. measurements of heights, gender, number of donuts eaten, political party … Population: the entire set of people or things being studied Sample: a selected subset of the population Population parameters: are specific numerical summary measures of the population Sample statistics: are specific numerical summary measures of the sample

Some Definitions - examples The Gallup organization wants to determine the average number of cars in American households. They conduct a telephone survey of 1204 Americans by telephone. Describe the population. Describe the sample. What population parameter(s) are they interested in? What sample statistic(s) will they compute?

Types of Data Quantitative Data Qualitative Data numerical measures of individuals. eg. heights, number of pets, blood pressure Qualitative Data also called Categorical Data characteristics or attributes of an individual eg. eye color, gender, favorite sport, ethnicity

Types of Data - Examples Is the data collected quantitative or qualitative? 1. A school records GPA for all students enrolled in Introductory Statistics last year. 2. An employment form asks for “country of origin”. 3. A consumer-rights group measures the true volume of gasoline dispensed from pumps.

The Process of Statistics Start with a question or goal Collect data through sampling Compute Descriptive Statistics organizing and summarizing collected data Inferential Statistics using information from a sample to infer something about a population, and measuring confidence in that inference Make decisions

Data Collection Observational Study Designed Experiment Survey observe characteristics of sample members but do not attempt to influence what happens Designed Experiment apply a specific treatment to members of the sample and measure the results Survey a questionnaire used to measure the characteristics or attitudes of sample members Simulation using technology to simulate what might happen based on a model

Data Collection - examples What type of data collection method is used? Researchers want to determine if living near high-voltage power lines is related to a higher incidence of cancer in children. The researchers compare the rates of cancer for children who live near high-voltage power lines with the rate for children who do not live near high-voltage power lines.

Data Collection - examples What type of data collection method is used? To determine which arthritis drug is most effective, study participants were randomly assigned to 4 treatment groups each receiving a different arthritis drug and one treatment group receiving a placebo drug.

Data Collection - examples What type of data collection method is used? Epidemiologists want to explore how fast a virus would spread in a large city.

Data Collection - examples What type of data collection method is used? Pollsters conduct 347 telephone interviews to determine which political candidate they will vote for in the coming election.

Experiments - Definitions Placebo looks and tastes like the real medication, but lacks the active ingredients that are being tested in a study Single-blind participants do not know which treatment they are receiving Double-blind neither the participants nor the researchers who administer the treatment to participants know which treatment they are receiving

Sampling Methods Census Sample Convenience Sample Systematic Sample Random Sampling Simple Random Sampling Stratified Sample Cluster Sample

Simple Random Sampling 1 2 3 4

Simple Random Sampling 1 2 3 4

Simple Random Sampling 1 2 3 4 1 5 6 7 8 2 9 10 11 12 3 13 14 15 16 4

Simple Random Sampling 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Sampling Methods Census Sample Convenience Sample Systematic Sample Random Sampling Simple Random Sampling Stratified Sample Cluster Sample

Sampling Methods - examples Determine which sampling method is used (Convenience, Systematic, Simple Random, Stratified, or Cluster) To predict which presidential candidate will win, NBC randomly selects 210 voting precincts, then polls every voter leaving that voting location to ask who they voted for. (Note that states are divided into geographical voting precincts.)

Sampling Methods - examples Determine which sampling method is used (Convenience, Systematic, Simple Random, Stratified, or Cluster) To determine whether students who participate in tutoring do better on exams than those who do not, an instructor randomly selects 50 students from each of two categories: students who do not participate in tutoring, and students who do participate in tutoring.

Sampling Methods - examples Determine which sampling method is used (Convenience, Systematic, Simple Random, Stratified, or Cluster) To determine how long students spend on their statistics homework, an investigator asked 34 statistics students at a study session in the library.

What Should We Believe?