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An introduction to a statistics course, discussing the goals of the course, addressing common phobias, and explaining the concepts of descriptive and inferential statistics. Students are encouraged to keep up with the material and test themselves regularly.

Typology: Study notes

2009/2010

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Download Introduction to Statistics: Goals, Phobias, and Descriptive & Inferential Statistics - Pro and more Study notes Psychology in PDF only on Docsity! 1 Introduction to Statistics 1. Goals of the Course 2. The What and Why of Statistics 3. The Syllabus 2 Introduction to Statistics The Course Syllabus Available on Oncourse Note: syllabus may be subject to change, including exam dates. Changes will be announced in class and via email Syllabus is approximate only! 5 Introduction to Statistics A Word About Phobias 1. All statistical procedures were developed to serve a purpose 2. If you understand why a new procedure is needed, you will find it much easier to learn the procedure After each class/chapter, try to read the “Preview” section at the beginning of each book chapter. 6 Introduction to Statistics Why Statistics? 2. Science is based on observation - statistics allows us to organize, summarize and interpret empirical data 1. Statistics is all around us 7 Introduction to Statistics Examples 1. In a psychological experiment, we need to determine a human subject’s reaction time. The measurements we obtain vary a great deal from one trial to the next. What can we do to get a reliable estimate? 2. A drug company has developed a new substance that, they claim, reduces blood pressure. How do we test this claim? 3. The mayor of a large city must decide whether to build an extension of the downtown highway system or not. The mayor is concerned about voter support. How does the mayor find out what people think? 10 Introduction to Statistics Fundamental Logic of Statistical Reasoning samplinginference 11 Introduction to Statistics Populations and Samples Population of individuals population of scores Sample of individuals sample of scores A parameter describes a population A statistic describes a sample Observation / measurement = datum / score / raw score For instance, the mean of the population And the mean of the sample 12 Introduction to Statistics Descriptive Statistics Descriptive statistics are used to summarize, organize and simplify data some examples...
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16 Introduction to Statistics Inferential Statistics Inferential statistics study samples and allow generalizations (inferences) about the population from which the sample was obtained (assuming the sample was representative). For example: I want to use the data from 100 students to make conclusions about all of the incoming students of IU By the end of the course, you should have an understanding of why this works (and its limitations) 17 Introduction to Statistics Inferential Statistics Sampling error is the discrepancy between a sample statistic and the corresponding population parameter Keep the sampling error small: Use large samples Use random sampling 20 Introduction to Statistics Inferential Statistics Sampling error is the discrepancy between a sample statistic and the corresponding population parameter Keep the sampling error small: Use large samples Use random sampling 21 Introduction to Statistics Fundamental Logic of Statistical Reasoning: Let’s try an example! samplinginference 22 Introduction to Statistics Population: K300 Mean = 66.9 Student # Sample 1: Mean = 68.5 Sample 1: Mean = 65.8 25 Introduction to Statistics Correlational Method Correlational method: Two variables are observed and checked to see if a relationship exists 26 Introduction to Statistics Correlational Method Correlational method: Two variables are observed and checked to see if a relationship exists Does early wake-up time cause better academic performance? Correlation does not imply causation • Experimental method: Goal is to establish causal relationships between variables • Requires manipulation and control conditions • The independent variable is the one that is manipulated • The dependent variable is the one that is observed 27 Introduction to Statistics Experimental Method 30 Introduction to Statistics Discrete and Continuous Variables A discrete variable consists of separate, indivisible categories (e.g., number of male children in family). A continuous variable is divisible into an infinite number of fractional parts (e.g., weight of male children in family). 31 Introduction to Statistics Scales of Measurement Different kinds of scales: nominal ordinal interval ratio When collecting data we need to make measurements. How do we measure things? By putting them into categories: Qualitative By using numbers: Quantitative • Nominal – Set of categories that have different names – “more than” or “less than” not defined – Major = {Math, Stats, Physicis} • Ordinal – Organized in an ordered sequence – You can determine the direction of difference (i.e., order) – Groups = {lower, middle, upper socioeconomic class} 32 Introduction to Statistics Scales of Measurement 35 From Jaccard and Becker (5th ed., Fig. 1.1) Example 36 Introduction to Statistics Statistical Notation One score: X Two scores: X, Y Number of scores (sample): n Number of scores (population): N Summation: X (“sum of X”) (think of summing over a column in a spreadsheet) Note: (X-5) X-5 X2 (X)2 Example: X = {3, 1, 7, 4} X = 3 + 1 + 7 + 4 = 15 X2 = 9 + 1 + 49 + 16 = 75 37 Introduction to Statistics Statistical Notation Note: (X-5) X-5 X2 (X)2 X = {3, 1, 7, 4} X = 15 (X-5) = (-2) + (-4) + 2 + (-1) = -5 X-5 = (X)-5 = 15 – 5 – 10 (X)2 = (X) x (X) = 15 x 15 = 225 X2 = 75