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Exploring Statistics: Data Analysis & Inference Techniques

Understand the basics of statistics, including data production, analysis, probability, and statistical thinking. Learn how to draw conclusions from data and make informed decisions through real-world examples.

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Exploring Statistics: Data Analysis & Inference Techniques

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  1. What is Statistics? • Chapter “P” • YMS3e • AP Stats at LSHS • Mr. Molesky • Sept. 5, 2007

  2. Case Study • Can Magnets Help Reduce Pain? • Read the study on page 3. • What do you observe? Does there appear to be a difference between the reported Active and Inactive pain scores? • Can we “condense” the data? What can we calculate to simplify things? What do you observe? • Is this difference large enough to argue that magnets are effective in reducing pain? • Is this difference due to chance variation, or is it evidence of a real difference?

  3. Data/Statistics Inference/Conclusions Intro: What is Stats? • Statistics: • The science (and art) of learning from data. • Data: • Numbers with a contextual meaning. • We use data and Statistics to draw conclusions about a population based on sample information. Population Sample

  4. 4 Themes of Stats • Part I: Exploratory Data Analysis • The tools and strategies for organizing, displaying, describing, and analyzing data. • Part II: Producing Data • Designing surveys, experiments, and observational studies that will yield the data necessary to answer a question of interest. • Part III: Probability • The study of chance behavior. How likely are certain outcomes? • Part IV: Inference • Draw conclusions about the population based on samples. Test claims and compute estimates.

  5. II. Data Production • When answering a question, where the data come from is important. • Data beat personal experiences (anectodal). • Data Sources • Available Data • Surveys • Observational Studies • Experiments • Do P.1-P.5 on page 11.

  6. I. Data Analysis • Organize, Display, Summarize, and Interpret • Individual: Objects described by data • Variable: Characteristic of an individual • Categorical: Places individuals into groups • Quantitative: Numeric measures • Distribution: Values taken on by a variable and how often it takes those values.

  7. I. Data Analysis • When analyzing data, ask the following: • Who are the individuals being described? • What are the variables? • Why were the data gathered? • When, where, how, and by whom were the data produced? • Read pp 12-18, Do 7,9,11,12

  8. III. Probability • Long-term chances of an event occuring • Chance behavior is unpredictable in the short run, but has a regular, predictable pattern in the long run. • Consider flipping a coin, rolling dice, etc. • We use probability to determine how likely certain sample values/statistics are. We want to know, “Is this value likely to be due to chance?” • See Example P.10

  9. Statistical Thinking • Data come from real-world contexts... • Doing statistics means more than just manipulating data! • Form the habit of asking “What do the data tell me?” • Statistics involves a lot of calculating and graphing. • We’ll let our calculator/computer do most of this. However, ideas and judgments can not be automated! • You learn statistics by doing statistical problems! • Read Chapter P, Do 13-16,18

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