1: Sampling and Data
- Page ID
- 4546
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 1.0: Introduction to Sampling and Data
- This page highlights the prevalence of statistics in everyday life through media and its significance in informed decision-making. It discusses the necessity of understanding statistics across various professions and introduces basic concepts of probability and data analysis, stressing the importance of quality data in this process.
- 1.1: Definitions of Statistics, Probability, and Key Terms
- This page discusses a statistics course that focuses on data collection, analysis, interpretation, and presentation. It highlights descriptive and inferential statistics, emphasizing the importance of statistical inference and sampling. Examples illustrate key statistical concepts such as population, sample, parameter, and variable through practical cases, including automobile safety and malpractice lawsuits.
- 1.2: Data, Sampling, and Variation in Data and Sampling
- This page provides an overview of data types, focusing on qualitative and quantitative distinctions. It emphasizes effective data representation through various graphs and highlights the importance of sampling methods. Key concepts include sampling errors and biases, while stressing the need for representative samples to ensure accurate conclusions. Additionally, variability in measurements is discussed, showcasing how sampling techniques can impact results.
- 1.3: Levels of Measurement
- This page offers guidance on organizing and analyzing data through frequency calculations and levels of measurement: nominal, ordinal, interval, and ratio. It includes examples and exercises related to soccer players' heights and rainfall data calculations, emphasizing rounding in frequency. The text also discusses data gathering methods and includes statistics from earthquakes and vehicle crashes to encourage frequency and percentage analysis.
- 1.4: Experimental Design and Ethics
- This page outlines essential principles of experimental design for scientific studies, focusing on independent and dependent variables, random assignment to minimize lurking variables, and establishing cause-and-effect. It emphasizes the significance of control groups and blinding to reduce bias, highlighting how expectations can affect outcomes.
- 1.5: Sampling Experiment (Worksheet)
- A statistics Worksheet: The student will demonstrate the simple random, systematic, stratified, and cluster sampling techniques. The student will explain the details of each procedure used.
- 1.6: Key Terms
- This page defines key statistical and research methodology terms, covering averages, types of variables, sampling methods (cluster, stratified, convenience), experimental units, control groups, and informed consent. It also addresses data types and sampling errors, emphasizing foundational principles for data analysis and interpretation.
- 1.7: Review
- This page introduces key statistical concepts, covering data types (qualitative and quantitative) and sampling methods for reliable representation. It details the four measurement levels (nominal, ordinal, interval, ratio) and stresses accurate data reporting and organization. It also highlights the significance of experimental design, including random assignment and control groups, while addressing ethical considerations in statistics.
- 1.8: Homework
- This page covers exercises in statistics and sampling methods, detailing definitions like populations, samples, and data types. It includes examples from fitness centers and marketers regarding behaviors and opinions. The text explores sampling methodologies, biases, and issues like survey reliability and sampling errors, with historical polling references.
- 1.9: References
- This page compiles references on statistics, probability, data sampling, experimental design, and research ethics. It features links to data sources and studies, discussing concepts such as the Gallup-Healthways Well-Being Index and historical polling methods. The aim is to clarify key terms and issues in data analysis and interpretation across various fields, highlighting the significance of methodology and ethical practices.
- 1.10: Solutions
- This page discusses scenarios in statistical data collection, covering populations, sample means, and characteristics like age and health costs. It emphasizes the importance of representative sampling, identifies potential biases, and explains factors influencing response rates. The text highlights the distinction between correlation and causation, noting the impact of confounding variables. Finally, it offers suggestions for enhancing survey accuracy.
Curated and edited by Kristin Kuter | Saint Mary's College, Notre Dame, IN