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Introduction to Statistics: Understanding Data Analysis and Statistical Thinking

This section covers the foundational concepts of statistics, including definitions of key terms such as population, sample, parameter, and statistic. It emphasizes the importance of statistical thinking, urging critical evaluation of data sources, sampling methods, and conclusions drawn from analysis. Readers are encouraged to consider the context of data, potential biases in sources, and the practical implications of findings. By understanding these principles, individuals can make informed decisions based on statistical results and avoid the pitfalls of blindly accepting numerical conclusions.

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Introduction to Statistics: Understanding Data Analysis and Statistical Thinking

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  1. Sections 1.1 and 1.2 Review and Preview and Statistical Thinking

  2. WHAT IS STATISTICS? • Actual and specific numbers derived from data. • Definition: A collection of methods for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data.

  3. SOME IMPORTANT DEFINITIONS • Population: the entire group of subjects or complete collection of measurements to be studied. • Census: the collection of data from every element in a population. • Sample: a subset of, or sub-collection, from a population. • Parameter: a numerical measurement describing a characteristic or attribute of a population. • Statistic: a numerical measurement describing a characteristic or attribute of a sample.

  4. STATISTICAL THINKING This section introduces basic principles of statistical thinking used throughout this book. Whether conducting statistical analysis of data that we have collected, or analyzing a statistical analysis done by someone else, we should not rely on blind acceptance of mathematical calculation. We should consider these factors: • Context of Data • Source of the Data • Sampling Method • Conclusions • Practical Implications

  5. CONTEXT • What do the values represent? • Where did the data come from? • Why were they collected? • An understanding of the context will directly affect the statistical procedure used.

  6. SOURCE OF DATA • Is the source objective? • Is the source biased? • Is there some incentive to distort or spin results to support some self-serving position? • Is there something to gain or lose by distorting results? • Be vigilant and skeptical of studies from sources that may be biased.

  7. SAMPLING METHOD • Does the method chosen greatly influence the validity of the conclusion? • Voluntary response (or self-selected) samples often have bias (those with special interest are more likely to participate). These samples’ results are not necessarily valid. • Other methods are more likely to produce good results.

  8. CONCLUSIONS • Make statements that are clear to those without an understanding of statistics and its terminology. • Avoid making statements not justified by the statistical analysis.

  9. PRACTICAL IMPLICATIONS • State practical implications of the results. • There may exist some statistical significanceyet there may be NOpractical significance. • Common sense might suggest that the finding does not make enough of a difference to justify its use or to be practical.

  10. STATISTICAL SIGNIFICANCE • Consider the likelihood of getting the results by chance. • If results could easily occur by chance, then they are not statistically significant. • If the likelihood of getting the results is so small, then the results are statistically significant.

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