What is Statistics? Chapter 0

What is Statistics? Statistics is the science (and art) of learning from data. Statistics is the study of variability. Statistics is the study of how to collect, organize, analyze, and interpret numerical information from data.

4 Areas of Statistics 1.Data Production (quality data – surveys, observations, experiments) 2.Exploratory Data Analysis (organizing, describing, and analyzing data) 3.Probability (the study of chance) 4.Inference (making stat. sound decisions with confidence)

Data Production

Data VS. Personal Experience Read example P.1 on page 7 and be prepared to discuss. Just because one plane crashes does not mean flying is dangerous. “Well, my grandma…” or “My Uncle John…”

Data Production Data VS. Personal Experience Suppose a group of students wanted to find out if their classmates prefer cheeseburgers from McDonald’s or Burger King. They decide to ask 50 people under the age of 20 which fast-food restaurant they prefer. In order to save time and energy, they conduct their survey at the McDonald’s closest to campus.

Available Data Available data are data that were produced in the past fro some other purpose but that ay help answer a present question. (Federal Statistics) (National Center for Health Statistics) (National Center for Education Statistics)

Having Kids or not? Read example P.3 on page 9, and be prepared to discuss

Where the data come from is important! A representative sample is a sample that takes on all the characteristics of the population. “In 1976, Shere Hite published The Hite Report on Female Sexuality, Seven Stories Press, New York, NY, The conclusions reported in her book were based on 3,000 returned surveys from some 100,000 surveys distributed by various women’s groups. The results were that women were highly critical of men. In what way might the author’s findings have been biased.”

Surveys Surveys are popular ways to gauge public opinion. 1.Select a sample of people to represent a larger population. 2.Ask the individuals in the sample some questions and record their responses. 3.Use sample results to draw some conclusions about the population. * Getting valid survey results is not easy!

Observational Study VS Experiment In an observational study, we observe individuals and measure variables of interest but d not attempt to influence the responses. In an experiment, we deliberately do something to individuals in order to observe their responses.

Different Studies, Different Reasons Surveys are usually intended to tell us something about the population the survey was drawn from. Experiments/Observational studies are usually intended to compare one or more groups (ie, does this new pill reduce stress?). In short, our goal with surveys is to generalize. Our goal with experiments/ obs. studies is to compare.

Estrogen and Heart Attacks Read Example P.4 on page 10 and be prepared to discuss.

Effect of Change An observational study, even one based on statistical sample, is a poor way to gauge the effect of a change. To see the response to a change, we must actually impose the change. When our goal is to understand cause and effect, experiments are the best source of convincing data.

Examples Question: Does drinking at least five carbonated sodas a week improve a student’s GPA? Observation: Compare GPA’s of a sample of students who drink more than five sodas a week with those who drink less. Experiment: From a random group of students, require some to drink more than five sodas per week and require the rest to drink less. After a couple of years, compare their GPAs.

Data Analysis Making Sense of Data

Data Analysis Statistical tools and ideas can help you examine data in order to describe their main features. This examination is called exploratory data analysis. 1.Begin by examining each variable by itself. Then move on to study relationships among the variables. 2.Begin with graphs. Then add numerical summaries of specific aspects of the data.

Data Analysis Data analysis is the act of transforming data with the aim of extracting useful information and facilitating conclusions.

W 5 HW Who What Why When Where How By Whom* Studies are often produced by people with an agenda that creeps into their interpretation of the data they generate.

Population and Sample In statistics, we use the term population to refer to the entire group of people or objects about which information is desired. A study that examines data on the entire population is called a census. However, conducting a census is rarely feasible. A sample is a (typically small) part of the population. If the sample is selected carefully, so that it is representative of the population, we still gain very useful information about the population. The number of observational units studied in a sample is the sample size. The essential idea of a sample is to learn about the whole by studying a part.

Individuals and Variables Individuals (observational unit) are the objects described by a set of data Individuals may be people, but they may also be animals or things. A variable is any characteristic of an individual. A variable can take different values for different individuals. (A characteristic that changes from individual to individual.)

Categorical and Quantitative A categorical variable (qualitative) places an individual into one of several groups or categories. A quantitative variable takes a numerical values fro which arithmetic operations such as adding and averaging make sense.

Distribution The distribution of a variable tells us what values the variable takes and how often it takes these values. The pattern of variation of a variable is its distribution.

Describing Variables Categorical (Qualitative) Bar Graphs Side-by-Side Bar Graphs Pie Charts Quantitative (Numerical) Dotplots Stemplots Histograms Ogives

Dotplots Example P.7 on page 16

Exploring Relationships Between Variables Variables rarely exist in isolation and that one of the many uses of data analysis is to uncover how a change in one or more variables influences change in another variable. Ultimately, we want to uncover cause-and-effect relationships, but that comes after we gain an understanding of how quality data is collected and used in inference. Many relationships between two variables are influenced by other variables lurking in the background.

Exploring Relationships Between Variables Example P.8 – On-time Flights Read and prepare to discuss.

Probability What are the chances?

Probability The study of random variables, which includes the study of probability, provides the mathematical basis through which we can use results from data to make inferences about populations. Coin Toss Chance behavior is unpredictable in the short run but has a regular and predictable pattern in the long run.

Statistical Inference Drawing Conclusions from Data

Inference Read Statistical Inference: Drawing Conclusions from Data on page 23. Read example P.11 on page 24. Be prepared to discuss both articles.

Homework Can magnets help reduce pain?