© 2008 McGraw-Hill Higher Education The Statistical Imagination Chapter 1. The Statistical Imagination

© 2008 McGraw-Hill Higher Education The Field of Statistics As a field of study, statistics is a set of procedures for gathering, measuring, classifying, coding, computing, analyzing, and summarizing systematically acquired numerical information

© 2008 McGraw-Hill Higher Education Applications of Statistics Scientific applications: A tool for testing scientific theories Practical applications : Used by marketing advertisers, policy makers, public health officials, insurance underwriters, educators, survey firms, stock investors and analysts, and odds makers

© 2008 McGraw-Hill Higher Education The Statistical Imagination An appreciation of how usual or unusual an event, circumstance, or behavior is in relation to a larger set of similar events, and an appreciation of an event’s causes and consequences

© 2008 McGraw-Hill Higher Education Features of the Statistical Imagination It is a balanced way of observing the world It involves the ability to think through a problem and maintain a sense of proportion when weighing evidence against preconceived notions It helps us to understand that most events are predictable

© 2008 McGraw-Hill Higher Education Linking The Statistical and Sociological Imaginations Social reality is normative: interpretation depends on the place, time, and culture Statistical norms are measurements of social norms Statistical ideals often reflect social values

© 2008 McGraw-Hill Higher Education Tools for Proportional Thinking Data: Systematically acquired information, following the procedures of science and statistics Statistical error: Known degrees of imprecision in procedures used to gather information

© 2008 McGraw-Hill Higher Education Two Purposes of Statistics Descriptive statistics: Used to tell us how many observations were recorded and how frequently each score or category occurred Inferential statistics: Used to show cause and effect relationships and to test hypotheses and theories

© 2008 McGraw-Hill Higher Education What is Science? Science is the systematic study of empirical phenomena Empirical means observable and measurable Phenomena are facts, happenstances, events, or circumstances

© 2008 McGraw-Hill Higher Education The Purpose of Science The purpose of scientific investigation is to explain things These explanations take the form of theory : A set of interrelated, logically organized statements that explain a phenomenon of special interest, and that have been corroborated through observation and analysis

© 2008 McGraw-Hill Higher Education The Limitations of Science Restricted to examining empirical phenomena Many sound, factually based scientific arguments lack political or taxpayer support Ethical dilemmas often arise creating resistance to its application

© 2008 McGraw-Hill Higher Education Data and Variables Data: Systematically acquired information Variables: Measurable phenomena that vary or change over time, or that differ from place to place or from individual to individual Constants: Characteristics of study subjects that do not vary

© 2008 McGraw-Hill Higher Education Study subjects Study subjects: The people or objects under scientific observation Variation: How much the measurements of a variable differ among study subjects

© 2008 McGraw-Hill Higher Education A Hypothesis A prediction about the relationship between two variables, asserting that differences among the measurements of an independent variable will correspond to differences among the measurements of a dependent variable

© 2008 McGraw-Hill Higher Education Independent and Dependent Variables Dependent variable: The variable whose variation we wish to explain Independent variables: The predictor variables that are related to, or predict variation in, the dependent variable

© 2008 McGraw-Hill Higher Education Relationships Between Independent and Dependent Variables Cause → Effect Predictor → Outcome Stimulus → Response Intervention → Result (action taken) Correlation: measures of the two variables fluctuate together

© 2008 McGraw-Hill Higher Education The Research Process Involves organizing ideas into a theory, making empirical predictions that support the theory, and then gathering data to test these predictions Cumulative process – a continual process of accumulation of knowledge

© 2008 McGraw-Hill Higher Education 7 Steps of the Research Process Specify the research question Review the scientific literature Propose a theory and state hypotheses Select a research design Collect the data Analyze the data and draw conclusions Disseminate the results

© 2008 McGraw-Hill Higher Education Mathematical Proportions Division problems that weigh a part (the numerator) against a whole (the denominator) Proportional thinking: placing an observation into a larger context A sense of proportion: to see things objectively, make fair judgements about behavior, and give the correct amount of attention to things that really matter

© 2008 McGraw-Hill Higher Education Calculating Proportions and Percentages Start with a fraction Divide the fraction to obtain a proportion (in decimal form) The quotient will always have values between 0 and 1 Multiply the proportion by 100 to change it into a percentage

© 2008 McGraw-Hill Higher Education Transforming Fractions, Proportions, and Percentages To change a fraction into a proportion: Divide to “decimalized” A proportion into a percentage: Multiply by 100 A percentage into a proportion: Divide the percentage by 100 To express a proportion as a fraction: Observe the decimal places (See Appendix A)

© 2008 McGraw-Hill Higher Education Rates A rate is the frequency of occurrence of a phenomenon per a specified, useful “base” number of subjects in a population Rate of occurrence = (p) (a base number) Rates standardize comparisons for “populations at risk” The choice of a base number depends on the phenomenon being measured

© 2008 McGraw-Hill Higher Education Presenting Answers to Encourage Proportional Thinking Symbol = Formula = Contents of formula = Answer

© 2008 McGraw-Hill Higher Education How to Succeed in This Course and Have Fun Never miss class and keep up Organize materials in a three-ring binder Use proper reading techniques Closely follow formulas, calculation spreadsheets, and procedures Ask for assistance as it is needed

© 2008 McGraw-Hill Higher Education Statistical Follies Watch out for small denominators, especially when “percentage change” data is reported A few new cases in a small group can appear as a large percentage change