Understanding Statistics: Measures and Analysis Techniques
Explore the fundamentals of statistics, including measures of location and spread, using statistical analysis tools like R to interpret data effectively. Learn how to summarize and interpret data sets to derive valuable insights for decision-making.
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Introduction to Statistics (CVEN 5454) Lecture 2 Mikaela DeRousseau Jan 16, 2020 1
Personal Introduction Ph.D. student with Civil Systems focus Research: Developing a new (computational) method for designing concrete that minimizes carbon dioxide emissions of the built environment Advised by Joe Kasprzyk and Wil Srubar 2
Lecture Outline Part I (normal lecture, brief) Introduce basic statistical measures (mean, median, standard deviation, IQR, skew, etc.) Part II (using R) Basic concepts of using R Show how to calculate above statistical measures in R Generate boxplots, histograms, and scatterplots in R and understand their meaning Extra tips for succeeding in this class 3
Statistics: figuring out what we can learn from a dataset Measurements of total organic carbon (TOC) values in ppm: [21 18 43 21 11 18 22 19 24 25 15 20 26 23 22 18 27] We can use simple statistical measures to characterize/summarize the data 4
Measures of Location ? Median = the 50th percentile of the data (P.50) (Central value of the distribution when data are ranked in order of magnitude) Mean ( ?) = ?=1 ?? ? (xi = each data value, n = sample size) TOC Values (ppm) Mean Median [21 18 43 21 11 18 22 19 24 25 15 20 26 23 22 18 27] [2000 18 43 21 11 18 22 19 24 25 15 20 26 23 22 18 27] Mean 21.9 Median 21 138.4 22 When might it be important to show both measures of location? 5
Measures of Spread \ ? (?? ? )2 ? 1 Variance (s2) = ?=1 Standard deviation (s) = ?2 *Note: when you start talking about populations (as opposed to samples, you ll see the notation: . 6
Measures of Spread, continued \ Interquartile range (IQR) = range of the central 50% of the data Outlier-resistant! (75th percentile 25th percentile) TOC Values (ppm) St. Dev. IQR [21 18 43 21 11 18 22 19 24 25 15 20 26 23 22 18 27] [2000 18 43 21 11 18 22 19 24 25 15 20 26 23 22 18 27] Mean 6.75 Median 6 479.8 7 When would it be important to show both measures of spread? 7
Measures of Skewness How would you describe a skewed dataset? Extreme values extending out further in one direction ? (?? ?)2 ?3 Skew (g) = ?=1 Symmetric data Positively skewed data Do you expect water resources and environmental concentration data to tend to be positively or negatively skewed? 8
Introduction to R and R Studio Download R: https://www.r-project.org/ Download R Studio: https://rstudio.com/products/rstudio/download/ Supplementary R tutorials and information: Online Book, R for Data Science - https://r4ds.had.co.nz/ R cheatsheet https://rstudio.com/wp-content/uploads/2016/10/r-cheat- sheet-3.pdf When all else fails, google it! 9
