Chapter 1 Statistics: The Art and Science of Learning from Data Section 1.1 Using Data to Answer Statistical Questions

Data and Examples of Collecting Data The information we gather with experiments and surveys is collectively called data Example: Experiment on low carbohydrate diet Data could be measurements on subjects before and after the experiment Example: Survey on effectiveness of a TV ad Data could be percentage of people who went to Starbucks since the ad aired

Define Statistics Statistics is the art and science of: Designing studies: Who to be studied? Analyzing the data produced by these studies: After the survey, what can we say about the data? Translating data into knowledge and understanding of the world around us: What conclusion we can draw from the study and how confident we are about the conclusion?

Is our president doing a good job? Is cell phone safe to use? Designing studies Analyzing the data produced by these studies Translating data into knowledge and understanding of the world around us Is our president doing a good job? Is cell phone safe to use? Does Aspirin help prevent heart attacks? What do the public feel about the gun control? May we predict an election based on its exit poll? learning objective of

Reasons for Using Statistical Methods The three main components of statistics for answering a statistical question: Design: Planning how to obtain data Description: Summarizing the data obtained Inference: Making decisions and predictions Translating data into knowledge and understanding of the world around us

Design Design questions: Examples: How to conduct the experiment, or How to select people for the survey to ensure trustworthy results Examples: Does Aspirin help prevent heart attacks? Is our president doing a good job? Description

Description Description: Summarize the raw data and present it in a useful format (e.g., average, charts or graphs) Examples: Graph the number of heart attacks for each of our patients taking Aspirin. How many percentage of people approve our president and how many does not, and how are the percentages different from the past. Description

Inference Inference: Make decisions or predictions based on the data. Examples: Does Aspirin help prevent heart attacks? Is our president doing a good job? Description

Chapter 1 Statistics: The Art and Science of Learning from Data Section 1.2 Sample Versus Population

We Observe Samples but are Interested in Populations Subjects The entities that we measure in a study. Subjects could be individuals, schools, rats, countries, days, or widgets. Examples: Does Aspirin help prevent heart attacks? Is our president doing a good job?

Population and Sample Population: All subjects of interest Sample: Subset of the population on which information is obtained Census: when sample is the entire population. Population Sample

Population versus sample Population: The entire group of individuals in which we are interested but can’t usually assess directly. Example: All humans, all working-age people in California, all crickets A parameter is a number describing a characteristic of the population. Sample: The part of the population we actually examine and for which we do have data. How well the sample represents the population depends on the sample design. A statistic is a number describing a characteristic of a sample. Population Sample

Example: An Exit Poll The purpose was to predict the outcome of the 2010 gubernatorial election in California. An exit poll sampled 3889 of the 9.5 million people who voted. Define the sample and the population for this exit poll. The population was the 9.5 million people who voted in the election. The sample was the 3889 voters who were interviewed in the exit poll.

Sample Statistics and Population Parameters A parameter is a numerical summary of the population. Ex:1. Proportion of people favor controls over the sales of handguns. 2. Proportion of all teenagers in the US who have smoked in the last month. A statistic is a numerical summary of a sample taken from the population. Ex: 1. In that poll, 54.0% of the sampled subjects said they favored controls over the sales of handguns. 2. Proportion of teenagers who have smoked in the last month out of a sample of 200 randomly selected teenagers in the United States. Note: Parameter values are hard to reach, but statistics are relatively easy to get. Once we have statistics, we will use them to make inference on parameter values.

Descriptive Statistics and Inferential Statistics Descriptive Statistics refers to methods for summarizing the collected data. Summaries consist of graphs and numbers such as averages and percentages. Graphical Summaries and Numerical Summaries. Figure 1.1 Types of U.S. Households, Based on a Sample of 50,000 Households in the 2005 Current Population Survey.

Inferential Statistics Inferential statistics refers to methods of making decisions or predictions about a population based on data obtained from a sample of that population. Example: Suppose we’d like to know what people think about controls over the sales of handguns. We can study results from a recent poll of 834 Florida residents. In that poll, 54.0% of the sampled subjects said they favored controls over the sales of handguns. We are 95% confident that the percentage of all adult Floridians favoring control over sales of handguns falls between 50.6% and 57.4%.

Towards Statistical Inference Use information from sample (known information) to infer about the population (unknown) Statistics – information from a sample. Parameter – information from a population. Sampling variability – information from a sample will differ from one sample to the next.

Randomness and Variability Random sampling allows us to make powerful inferences about populations. Randomness is also crucial to performing experiments well. Ann Landers summarizing responses of readers 70% of (10,000) parents wrote in to say that having kids was not worth it—if they had to do it over again, they wouldn’t. Bias: Most letters to newspapers are written by disgruntled people. A random sample showed that 91% of parents WOULD have kids again.

Bias and variability: Arrow shooting as an example Figure 3.14 Introduction to the Practice of Statistics, Sixth Edition © 2009 W.H. Freeman and Company