Slide 1 Copyright © 2004 Pearson Education, Inc.

Slide 2 Copyright © 2004 Pearson Education, Inc. Chapter 1 Introduction to Statistics 1-1 Overview 1-2 Types of Data 1-3 Critical Thinking 1-4 Design of Experiments

Slide 3 Copyright © 2004 Pearson Education, Inc. Created by Tom Wegleitner, Centreville, Virginia Section 1-1 Overview

Slide 4 Copyright © 2004 Pearson Education, Inc. Overview A common goal of surveys and other data collecting tools is to collect data from a smaller part of a larger group so we can learn something about the larger group. In this section we will look at some of ways to describe data.

Slide 5 Copyright © 2004 Pearson Education, Inc.  Statistics a collection of methods for planning experiments, obtaining data, and then then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data. Definitions

Slide 6 Copyright © 2004 Pearson Education, Inc. Definitions  Population the complete collection of all elements (scores, people, measurements, and so on) to be studied. The collection is complete in the sense that it includes all subjects to be studied.

Slide 7 Copyright © 2004 Pearson Education, Inc.  Census the collection of data from every member of the population.  Sample a sub-collection of elements drawn from a population. Definitions

Slide 8 Copyright © 2004 Pearson Education, Inc. Key Concepts  Sample data must be collected in an appropriate way, such as through a process of random selection.  If sample data are not collected in an appropriate way, the data may be so completely useless that no amount of statistical torturing can salvage them.

Slide 9 Copyright © 2004 Pearson Education, Inc. Created by Tom Wegleitner, Centreville, Virginia Section 1-2 Types of Data

Slide 10 Copyright © 2004 Pearson Education, Inc.  Data Observations (such as measurements, genders, survey responses) that have been collected. Definitions

Slide 11 Copyright © 2004 Pearson Education, Inc. Definitions  Quantitative data numbers representing counts or measurements. Example: weights of supermodels.

Slide 12 Copyright © 2004 Pearson Education, Inc. Definitions  Qualitative (Categorical) data can be separated into different categories that are distinguished by some nonnumeric characteristics. Example: genders (male/female) of professional athletes.

Slide 13 Copyright © 2004 Pearson Education, Inc. Working with Quantitative Data Quantitative data can further be distinguished between discrete and continuous types.

Slide 14 Copyright © 2004 Pearson Education, Inc.  Discrete data result when the number of possible values is either a finite number or a ‘countable’ number of possible values. 0, 1, 2, 3,... Example: The number of eggs that hens lay. Definitions

Slide 15 Copyright © 2004 Pearson Education, Inc.  Continuous (numerical) data result from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumps. Definitions 2 3 Example: The amount of milk that a cow produces; e.g gallons per day.

Slide 16 Copyright © 2004 Pearson Education, Inc.

Slide 17 Copyright © 2004 Pearson Education, Inc.  Parameter a numerical measurement describing some characteristic of a population population parameter Definitions

Slide 18 Copyright © 2004 Pearson Education, Inc. Definitions  Statistic a numerical measurement describing some characteristic of a sample. sample statistic

Slide 19 Copyright © 2004 Pearson Education, Inc.  Descriptive Statistics involves organizing, summarizing, and displaying data; describes the important characteristics of a known set of data  Inferential Statistics use sample data to make inferences (or generalizations) about a population Definitions

Slide 20 Copyright © 2004 Pearson Education, Inc.

Slide 21 Copyright © 2004 Pearson Education, Inc. White House 2008: Republican Nomination Pew Research Center for the People & the Press survey conducted by Princeton Survey Research Associates International. Dec , N=471 registered voters nationwide who are Republicans or lean Republican. MoE ± 5. "I'm going to read you the names of some Republican presidential candidates. Which one of the following Republican candidates would be your first choice for president: [see below]?" If unsure: "Just as of today, would you say you lean toward [see below]?" (Names were rotated). % John McCain 22 Rudy Giuliani 20 Mike Huckabee17 Mitt Romney12 Fred Thompson 9 Ron Paul4 Duncan Hunter1 Other (vol.)1 None (vol.)2 Unsure 12

Slide 22 Copyright © 2004 Pearson Education, Inc. Created by Tom Wegleitner, Centreville, Virginia Section 1-3 Critical Thinking

Slide 23 Copyright © 2004 Pearson Education, Inc. Uses of Statistics  Almost all fields of study benefit from the application of statistical methods

Slide 24 Copyright © 2004 Pearson Education, Inc.  Bad Samples  Small Samples  Misleading Graphs  Pictographs  Distorted Percentages  Loaded Questions  Order of Questions  Refusals  Correlation & Causality  Self Interest Study  Precise Numbers  Deliberate Distortions Misuses of Statistics

Slide 25 Copyright © 2004 Pearson Education, Inc. Misuses of Statistics  Bad Samples Example: Voluntary response sample (or self-selected survey) one in which the respondents themselves decide whether to be included. In this case, valid conclusions can be made only about the specific group of people who agree to participate.

Slide 26 Copyright © 2004 Pearson Education, Inc. Misuses of Statistics  Bad Samples  Small Samples  Misleading Graphs

Slide 27 Copyright © 2004 Pearson Education, Inc.

Slide 28 Copyright © 2004 Pearson Education, Inc. Misuses of Statistics  Bad Samples  Small Samples  Misleading Graphs  Pictographs

Slide 29 Copyright © 2004 Pearson Education, Inc. Double the length, width, and height of a cube, and the volume increases by a factor of eight To correctly interpret a graph, analyze the numerical information given in the graph and don’t be mislead by its general shape.

Slide 30 Copyright © 2004 Pearson Education, Inc.

Slide 31 Copyright © 2004 Pearson Education, Inc. Misuses of Statistics  Bad Samples  Small Samples  Misleading Graphs  Pictographs  Loaded Questions “Should the President have the line item veto to eliminate waste?” ( 97% yes: ) “Should the President have the line item veto?” ( 57% yes: )

Slide 32 Copyright © 2004 Pearson Education, Inc.  Bad Samples  Small Samples  Misleading Graphs  Pictographs  Distorted Percentages  Loaded Questions  Correlation and Causality Misuses of Statistics

Slide 33 Copyright © 2004 Pearson Education, Inc. Correlation does not imply Cause and Effect

Slide 34 Copyright © 2004 Pearson Education, Inc.  Bad Samples  Small Samples  Misleading Graphs  Pictographs  Distorted Percentages  Loaded Questions  Correlation & Causality  Self Interest Study  Precise Numbers  Deliberate Distortions Misuses of Statistics

Slide 35 Copyright © 2004 Pearson Education, Inc.

Slide 36 Copyright © 2004 Pearson Education, Inc. Created by Tom Wegleitner, Centreville, Virginia Section 1-4 Design of Experiments

Slide 37 Copyright © 2004 Pearson Education, Inc.  1. What is the objective?  2. Who/what is the population?  3. Collect Data**  4. Descriptive Statistics  5. Inferential Statistics Design of Experiments

Slide 38 Copyright © 2004 Pearson Education, Inc. Major Points of Samples  The sample must be unbiased and fairly represent the entire population.  If sample data are not collected in an appropriate way, the data may be so completely useless that no amount of statistical tutoring can salvage them. “Garbage in, garbage out”  Want the maximum information at the minimum cost. Sample size?

Slide 39 Copyright © 2004 Pearson Education, Inc.  Observational Study observing and measuring specific characteristics without attempting to modify the subjects being studied Methods of Collecting Data  Experiment apply some treatment and then observe its effects on the subjects

Slide 40 Copyright © 2004 Pearson Education, Inc. Sampling Techniques  Convenience Samples Use results that are readily available and easy to get. Often leads to biased samples. ex. Self selected surveys (online, magazine)

Slide 41 Copyright © 2004 Pearson Education, Inc.  Random Sample members of the population are selected in such a way that each individual member has an equal chance of being selected.  Simple Random Sample  Systematic Sample Sampling Techniques

Slide 42 Copyright © 2004 Pearson Education, Inc. Simple Random Sample A random sample where every member of the population and every group of the same has an equal chance of being selected. Method: Number each member of the population from 1 to “N” (where N is the population size). Use a random number generator to randomly select a sample of size “n”. TI-83: randint(1,N,n)

Slide 43 Copyright © 2004 Pearson Education, Inc. Systematic Sampling A random sample where after a random start, you select every Kth element in the population. ex. Select every 3 rd patient who enters the E.R.

Slide 44 Copyright © 2004 Pearson Education, Inc. Other Sampling Techniques  Stratified Sampling subdivide the population into at least two different subgroups (strata) that share the same characteristics (age, gender,ethnicity,income, etc.). Then draw a sample from each strata. Advantages: More information

Slide 45 Copyright © 2004 Pearson Education, Inc. Other Sampling Techniques  Cluster Sampling divide the population into many like subgroups (or clusters); randomly select some of those clusters; choose all members from selected clusters. Advantage: members of population are geographically separated

Slide 46 Copyright © 2004 Pearson Education, Inc.  Sampling Error the expected difference between a sample result and the true population result. (e.g. “Margin of error”).  Nonsampling Error sample data is incorrectly gathered, collected, or recorded. Selection Bias - biased sample Response Bias- bad data: incorrect responses, inaccurate measurements, etc.) Error in Sampling