Slide 1 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 2 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 3 Copyright © 2004 Pearson Education, Inc.  Data observations (such as measurements, genders, survey responses) that have been collected. Definitions

Slide 4 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 5 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 6 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 7 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 8 Copyright © 2004 Pearson Education, Inc. Created by Tom Wegleitner, Centreville, Virginia Section 1-2 Types of Data

Slide 9 Copyright © 2004 Pearson Education, Inc.  Parameter a numerical measurement describing some characteristic of a population Definitions

Slide 10 Copyright © 2004 Pearson Education, Inc. Definitions  Statistic a numerical measurement describing some characteristic of a sample. Sample Population Statistics Parameters

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 (or categorical or attribute) 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. Levels of Measurement Another way to classify data is to use levels of measurement. Four of these levels are discussed in the following slides.

Slide 17 Copyright © 2004 Pearson Education, Inc.  nominal level of measurement characterized by data that consist of names, labels, or categories only. The data cannot be arranged in a meaningful ordering scheme (such as low to high) Example: survey responses yes, no, undecided Definitions

Slide 18 Copyright © 2004 Pearson Education, Inc.  ordinal level of measurement involves data that may be arranged in some order, but differences between data values either cannot be determined or are meaningless Example: Course grades A, A-, B+, B, B-, etc. Definitions

Slide 19 Copyright © 2004 Pearson Education, Inc.  interval level of measurement like the ordinal level, with the additional property that the difference between any two data values is meaningful. However, there is no natural zero starting point (where none of the quantity is present) Example: Years 1000, 2000, 1776, and 1492 Definitions

Slide 20 Copyright © 2004 Pearson Education, Inc.  ratio level of measurement the interval level modified to include the natural zero starting point (where zero indicates that none of the quantity is present). For values at this level, differences and ratios are meaningful. Example: Prices of college textbooks ($0 represents no cost) Definitions

Slide 21 Copyright © 2004 Pearson Education, Inc. Summary - Levels of Measurement  Nominal - categories only  Ordinal - categories with some order  Interval - differences but no natural starting point  Ratio - differences and a natural starting point

Slide 22 Copyright © 2004 Pearson Education, Inc. Recap Basic definitions and terms describing data  Parameters versus statistics  Types of data (quantitative and qualitative)  Levels of measurement In Sections 1-1 and 1-2 we have looked at:

Slide 23 Copyright © 2004 Pearson Education, Inc. Created by Tom Wegleitner, Centreville, Virginia Section 1-3 Critical Thinking

Slide 24 Copyright © 2004 Pearson Education, Inc. Success in Statistics  Success in the introductory statistics course typically requires more common sense than mathematical expertise.  This section is designed to illustrate how common sense is used when we think critically about data and statistics.

Slide 25 Copyright © 2004 Pearson Education, Inc. Misuses of Statistics  Bad Samples

Slide 26 Copyright © 2004 Pearson Education, Inc. Definitions  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 27 Copyright © 2004 Pearson Education, Inc. Misuses of Statistics  Misleading Graphs  Bad Samples  Small Samples Conclusions should not be based on samples which are far too small Bar graphs and pie charts can be used to exaggerate or understate the true nature of data

Slide 28 Copyright © 2004 Pearson Education, Inc. Figure 1-1

Slide 29 Copyright © 2004 Pearson Education, Inc. To correctly interpret a graph, we should analyze the numerical information given in the graph instead of being mislead by its general shape.

Slide 30 Copyright © 2004 Pearson Education, Inc. Misuses of Statistics  Bad Samples  Small Samples  Misleading Graphs  Pictographs Drawing of objects, called Pictographs, may also be misleading

Slide 31 Copyright © 2004 Pearson Education, Inc. Figure 1-2 Double the length, width, and height of a cube, and the volume increases by a factor of eight

Slide 32 Copyright © 2004 Pearson Education, Inc. Misuses of Statistics  Bad Samples  Small Samples  Misleading Graphs  Pictographs  Distorted Percentages  Loaded Questions Misleading or unclear percentages are often used Survey questions can be “loaded” or intentionally worded to elicit a desired response

Slide 33 Copyright © 2004 Pearson Education, Inc. 97% yes: “Should the President have the line item veto to eliminate waste?” 57% yes: “Should the President have the line item veto, or not?”

Slide 34 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  Partial Pictures  Deliberate Distortions Misuses of Statistics Sometimes survey questions can be unintentionally loaded by such factors as the order of the questions being considered Even if there is statistical association between two variables, we may not conclude that one of the variable is the cause (or directly affects) the other. Studies are sometimes sponsored by parties with specific interest about the outcome When a precise figure is used, many people incorrectly assume that it is also accurate Claims can be technically correct but misleading if they do not present the complete picture When results were created without data to back them up

Slide 35 Copyright © 2004 Pearson Education, Inc. Recap  Reviewed 13 misuses of statistics.  Illustrated how common sense can play a big role in interpreting data and statistics In this section we have:

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.  Observational Study observing and measuring specific characteristics without attempting to modify the subjects being studied Broadly, there could be two kinds of study in Statistics

Slide 38 Copyright © 2004 Pearson Education, Inc.  Experiment apply some treatment and then observe its effects on the subjects Definitions

Slide 39 Copyright © 2004 Pearson Education, Inc.  Cross Sectional Study Data are observed, measured, and collected at one point in time.  Retrospective (or Case Control) Study Data are collected from the past by going back in time.  Prospective (or Longitudinal or Cohort) Study Data are collected in the future from groups (called cohorts) sharing common factors. Different types of Observational Studies

Slide 40 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 Definitions  Simple Random Sample (of size n ) subjects selected in such a way that every possible sample of the same size n has the same chance of being chosen

Slide 41 Copyright © 2004 Pearson Education, Inc. Random Sampling selection so that each has an equal chance of being selected

Slide 42 Copyright © 2004 Pearson Education, Inc. Systematic Sampling Select some starting point and then select every K th element in the population

Slide 43 Copyright © 2004 Pearson Education, Inc. Convenience Sampling use results that are easy to get

Slide 44 Copyright © 2004 Pearson Education, Inc. Stratified Sampling subdivide the population into at least two different subgroups that share the same characteristics, then draw a sample from each subgroup (or stratum)

Slide 45 Copyright © 2004 Pearson Education, Inc. Cluster Sampling divide the population into sections (or clusters); randomly select some of those clusters; choose all members from selected clusters

Slide 46 Copyright © 2004 Pearson Education, Inc.  Random  Systematic  Convenience  Stratified  Cluster Methods of Sampling

Slide 47 Copyright © 2004 Pearson Education, Inc.  Sampling Error the difference between a sample result and the true population result; such an error results from chance sample fluctuations  Nonsampling Error sample data that are incorrectly collected, recorded, or analyzed (such as by selecting a biased sample, using a defective instrument, or copying the data incorrectly) Definitions