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Elementary Statistics M A R I O F. T R I O L A Copyright © 1998, Triola, Elementary Statistics Copyright © 1998, Triola, Elementary Statistics Addison Wesley Wesley Longman Longman Addison 1 Introduction To Statistics Chapter 1 M A R I O F. T R I O L A Copyright ©Copyright 1998, Triola, Elementary Statistics © 1998, Triola, Elementary Statistics Addison Wesley Longman Addison Wesley Longman 2 Chapter 1 Introduction to Statistics 1-1 Overview 1-2 The Nature of Data 1-3* Uses and Abuses of Statistics 1-4 Design of Experiments Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 3 1-1 Overview Statistics Two Meanings Actual numbers Methods of analysis Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 4 Statistics Actual numbers numerical measurements determined by a set of data Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 5 Statistics Methods of analysis a collection of methods for planning experiments, obtaining data, and then analyzing, interpreting, and drawing conclusions based on the data Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 6 Definitions Population the complete collection of elements (scores, people, measurements, etc.) to be studied Sample Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 7 Definitions Population the complete collection of elements (scores, people, measurements, etc.) to be studied Sample a subset of a population Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 8 Definitions Parameter a numerical measurement describing some characteristic of a population Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 9 Definitions Parameter a numerical measurement describing some characteristic of a population population parameter Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 10 Definitions Statistic a numerical measurement describing some characteristic of a sample Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 11 Definitions Statistic a numerical measurement describing some characteristic of a sample sample statistic Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 12 Definitions • Population Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 13 Definitions Population Parameter Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 14 Definitions Population Parameter Sample Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 15 Definitions Population Parameter Sample Statistic Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 16 Definitions Population Parameter Sample Statistic Census Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 17 1-2 The Nature of Data Definitions Quantitative data numbers representing counts or measurements Qualitative (attribute) data nonnumeric data that can be separated into different categories Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 18 Definitions Discrete data which results from either a finite number of possible values or a countable number of possible values 0, 1, 2, 3, . . . Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 19 Definitions Discrete data which results from either a finite number of possible values or a countable number of possible values 0, 1, 2, 3, . . . Continuous data which results from infinitely many possible values that can be associated with points on a continuous scale in such as way that there are no gaps or interruptions 3 Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 4 20 Quantitative Data Discrete - Countable Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 21 Quantitative Data Discrete - Countable Continuous - Measurements with no gaps Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 22 Definitions nominal level of measurement characterized by data that consist of names, labels, or categories only. Data cannot be arranged in an ordering scheme (such as low to high) E.g. Blood types: O, A, B, AB Genders: Male & Female Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 23 Definitions 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 E.g. Taste of food: bad, so-so, good, delicious Grades: A, B, C, D, F Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 24 Definitions interval level of measurement like the ordinal level, with the additional property that we can determine meaningful amounts of differences between data. However, there is no inherent (natural) zero starting point (where none of the quantity is present.) E.g. year 2000, temperature 96.2 F etc. Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 25 Definitions ratio level of measurement the interval level modified to include the inherent zero starting point where zero indicates that none of the quantity is present. For values at this level, differences and ratios are meaningful. E.g. weights of grains, heights of people Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 26 Levels of Measurement Nominal - names only Ordinal - names with some order Interval - differences but no ‘zero’ Ratio - differences and a ‘zero’ Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 27 Levels of Measurement Nominal - names only Ordinal - names with some order Interval - differences but no ‘zero’ Ratio - differences and a ‘zero’ Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 28 Design of Experiments Section 1-4 M A R I O F. T R I O L A Copyright ©Copyright 1998, Triola, Elementary Statistics © 1998, Triola, Elementary Statistics Addison Wesley Wesley Longman Longman Addison 29 Steps for Designing an Experiment 1. Identify the exact question and exact 2. Develop a plan for collecting data that is representative of the population 3. Collect data minimizing errors that result in biased data 4. Analyze the data and draw conclusions Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman population 30 Definitions Observational Study Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 31 Definitions Observational Study observing and measuring specific characteristics Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 32 Definitions Experiment Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 33 Definitions Experiment application of some treatment and then observe its effects on the subject Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 34 Definitions Experiment application of some treatment and then observe its effects on the subject Treatment Group Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 35 Definitions Experiment application of some treatment and then observe its effects on the subject Treatment Group Control Group E.g. Drug v.s. placebo Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 36 Designing an Experiment Experimental units (blocks) Completely randomized design Rigorously controlled design Replication Study the text book Section 1-4 for the details Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 37 Definitions Confounding Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 38 Definitions Confounding effects from two or more variables that cannot be distinguished from each other Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 39 Data carelessly collected may be so completely useless that no amount of statistical torturing can salvage them. Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 40 Random Sampling - selection so that each has an equal chance of being selected Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 41 Stratified Sampling - subdivide population and draw sample from each stratum Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 42 Systematic Sampling Every K th element Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 43 Cluster Sampling - divide into sections; choose a few of those sections; choose all from selected sections Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 44 Convenience Sampling - use readily available results Hey! Do you believe in the death penalty? Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 45 Methods of Sampling Random Stratified Systematic Cluster Convenience Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 46 Definitions Sampling Error the difference between a sample result and the true population result due to chance sample fluctuations Non-sampling Error sample data that is incorrectly collected, recorded, or analyzed Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 47