Elementary Statistics Lecture Notes PDF

Elementary Statistics WINTER 2024 Copyright © 2011 Pearson Education Canada Inc.Canada 1.1 - 1 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 2 Copyright © 2010, 2007, 2004 Pearson Educatio...

Elementary Statistics WINTER 2024 Copyright © 2011 Pearson Education Canada Inc.Canada 1.1 - 1 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 2 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 3 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 4 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 5  Recap In this section we have looked at:  Basic definitions and terms describing data  Parameters versus statistics  Types of data (quantitative and qualitative)  Levels of measurement 1.1 - 6 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 7 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 8 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 9 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 10  Abuses of Statistics  Data can often be presented in ways that may be misleading.  Some abuses of statistics are unintentional, such as people who are ignorant or careless.  In other cases, the abuses of statistics are intentionally in order to support personal objectives.  We should learn to distinguish between statistical conclusions that are likely to be valid and those that are seriously flawed. Copyright © 2011 Pearson Canada Inc. 1.1 - 11 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 12 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 13 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 14 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 15  This visualization paints an entirely different picture and shows that Argentina is nowhere close to testing as much as the US and other countries. But who wants to see the bad news, right? Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 16 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 17 1.1 - 18 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 19 Self-Interest Study 1.1 - 20  Precise Numbers  Sometimes the numbers themselves can be deceptive. A very precise figure can often be misinterpreted as being accurate.  Example: A sample of 2500 students from a Canadian university produced an average salary of $25,542.64.  A precise figure can be an estimate (sample statistic) rather than a population parameter. When it is an estimate, this fact should be emphasized to avoid confusion. Copyright © 2011 Pearson Canada Inc. 1.1 - 21  Guesstimates  Some estimates are really just guesses and can be in error by substantial amounts.  As such, it is important for us to consider the source of the estimate and how it was developed.  Example: Your friend asks you “How many people were at the party on Saturday?” You answer, “About 30 people.” However, you didn’t actually count the number of people at the party. Also, you were only there for one hour and the party lasted for six hours. Copyright © 2011 Pearson Canada Inc. 1.1 - 22 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 23 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 24  Deliberate Distortion  Some studies or surveys are distorted on purpose. The distortion can occur within the context of the data, the source of the data, the sampling method, or the conclusions.  Example: A website catering to dog owners posts an online survey to determine the most popular type of pet. Copyright © 2011 Pearson Canada Inc. 1.1 - 25  Loaded Questions  If survey questions are not worded carefully, the results of a study can be misleading. Survey questions can be “loaded” or intentionally worded to elicit a desired response. Copyright © 2011 Pearson Canada Inc. 1.1 - 26 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 27 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 28 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 29  Graphs To correctly interpret a graph, you must analyze the numerical information given in the graph, so as not to be misled by the graph’s shape. READ labels and units on the axes! 1.1 - 30  Pictographs Part (b) is designed to exaggerate the difference by increasing each dimension in proportion to the actual amounts of oil consumption. 1.1 - 31 1.1 - 32 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 33 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 34 1.1 - 35  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 © 2011 Pearson Canada Inc. 1.1 - 36  Collecting Data  We typically obtain our data from two common sources; observational studies and experiments.  In an observational study, we observe and measure specific characteristics but we don’t attempt to manipulate or modify the subjects being studied.  Example: Surveys.  In an experiment, we apply some treatment and then proceed to observe its effects on the subjects.  Example: Clinical drug trials. Copyright © 2011 Pearson Canada Inc. 1.1 - 37  Observational Study  Observational study observing and measuring specific characteristics without attempting to modify the subjects being studied 1.1 - 38  Experiment  Experiment apply some treatment and then observe its effects on the subjects; (subjects in experiments are called experimental units) 1.1 - 39  Design of Experiments  When designing an experiment, one should follow the steps below. 1. Identify your objective. What question are you trying to answer? What is the population of interest? 2. Collect sample data. The sample must be large enough to detect the treatment effect, representative of the population under consideration, and unaffected by extraneous factors. 3. Use a random procedure to avoid bias. 4. Analyze the data and form conclusions. Copyright © 2011 Pearson Canada Inc. 1.1 - 40  Treatment and Control Groups Copyright © 2011 Pearson Canada Inc. 1.1 - 41  The Placebo Effect Copyright © 2011 Pearson Canada Inc. 1.1 - 42 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 43 1.1 - 44  Design of Experiment Copyright © 2011 Pearson Canada Inc. 1.1 - 45  Confounding Copyright © 2011 Pearson Canada Inc. 1.1 - 46  Replication Copyright © 2011 Pearson Canada Inc. 1.1 - 47 1.1 - 48 1.1 - 49  Randomization Copyright © 2011 Pearson Canada Inc. 1.1 - 50 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 51  Random Sampling selection so that each individual member has an equal chance of being selected 1.1 - 52  Simple Random Sample  A simple random sample of n subjects is selected in such a way that every possible sample of size n has the same chance of being chosen.  Example: When pollsters and telemarketers, generate a phone number at random so that all phone numbers are possible, they are using random sampling. If they generate 100 such phone numbers, they have obtained a simple random sample of size 100. Copyright © 2011 Pearson Canada Inc. 1.1 - 53 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 54 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 55  Systematic Sampling Select some starting point and then select every kth element in the population 1.1 - 56 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 57 Convenience Sampling use results that are easy to get 1.1 - 58  Convenience Sampling  In convenience sampling, we simply use results that are readily available.  Convenience sampling does not employ randomization and can be heavily biased. Copyright © 2011 Pearson Canada Inc. 1.1 - 59 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 60  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) 1.1 - 61 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 62  Cluster Sampling divide the population area into sections (or clusters); randomly select some of those clusters; choose all members from selected clusters 1.1 - 63 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 64  Stratified Sampling versus Cluster Sampling  In stratified sampling, we select some of the objects from every strata.  In cluster sampling, we select all of the objects from some of the clusters. Copyright © 2011 Pearson Canada Inc. 1.1 - 65 Methods of Sampling - Summary  Random  Systematic  Convenience  Stratified  Cluster 1.1 - 66 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 1.1 - 67