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Overview of Data Summarization: Observational vs. Experimental Studies in Statistics

This overview explores the key differences between observational and experimental studies in statistics. Observational studies focus on summarizing data to identify patterns and characteristics without controls, typically using descriptive statistics. In contrast, experimental studies involve control groups and aim to determine if observed differences in treatments are statistically significant through inferential statistics. The document also illustrates these concepts with examples of tree height measurements from two forests, providing insights into measures of central tendency and variation.

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Overview of Data Summarization: Observational vs. Experimental Studies in Statistics

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  1. LA 10001 – SOS Version LEC-01 Althoff Statistics- Overview How Do We Summarize/Communicate Data?

  2. Observational vs. Experimental Studies • Observational: no controls (usually), trying to determine basics, learn patterns, trends, characteristics • Experimental: control (usually), have basic knowledge of subject that enables one to “separate” into treatment groups

  3. Observational vs. Experimental Studies • Observational: generally summarize data using descriptive statistics • Experimental: determine if differences between treatments are “real” using inferential statistics

  4. Forest A a

  5. Tree Height in meters • 45 • 42 • 42 • 46 • 40 • 42 • 43 • 32 • 52 • 35 • 36 • 34 • 38 b

  6. Tree Height in meters • 45 • 42 • 42 • 46 • 40 • 42 • 43 • 32 • 52 • 35 • 36 • 34 • 38 • Mean = 40.5 c

  7. Tree Height in meters Low-to-high • 45 32 (8) • 42 34 (12) • 42 35 (10) • 46 36 (11) • 40 38 (13) • 42 40 (5) • 43 42 (2) • 32 42 (3) • 52 42 (6) • 35 43 (7) • 36 45 (1) • 34 46 (4) • 38 52 (9) • Mean = 40.5 • Median = 42 d

  8. Tree Height in meters Low-to-high • 4532 (8) • 42 34 (12) • 42 35 (10) • 46 36 (11) • 40 38 (13) • 42 40 (5) • 43 42 (2) • 32 42 (3) • 52 42 (6) • 35 43 (7) • 36 45 (1) • 34 46 (4) • 3852 (9) • Mean = 40.5 • Median = 42 • Min = 32 • Max = 52 • Range = 32 -52 • or 20 e

  9. Tree Height in meters • 45 • 42 • 42 • 46 • 40 • 42 • 43 • 32 • 52 • 35 • 36 • 34 • 38 • Variance ( ) = 30.6 • Standard deviation (S ) = 5.5 s2 SD f

  10. Forest A Descriptive Statistics • Mean = 40.5 • Median = 42 • Min = 32 • Max = 52 • Range = 32 – 52 or 20 • Variance ( ) = 30.6 • Standard deviation (S ) = 5.5 Measures of CENTRAL tendency Measures of VARIATION s2 SD g

  11. Forest B Forest A h

  12. Tree Height in meters • 53 • 34 • 32 • 51 • 33 • 38 • 38 • 32 • 52 • 35 • 56 • 34 • 38 Forest B Forest A MEAN 40.5 38 40.5 42 MEDIAN i

  13. Tree Height in meters • 53 • 34 • 32 • 51 • 33 • 38 • 38 • 32 • 52 • 35 • 56 • 34 • 38 Forest B Forest A MIN 32 52 32 – 52 or 20 32 56 32-56 or 24 MAX RANGE j

  14. Tree Height in meters • 53 • 34 • 32 • 51 • 33 • 38 • 38 • 32 • 52 • 35 • 56 • 34 • 38 Forest B Forest A Variance (s2) 81.1 9.0 30.6 5.5 Standard Deviation (s) k

  15. Forest B Forest A l

  16. In Summary: Descriptive Statistics • central tendency: mean (average) median mode • spread / variation: range variance standard deviation standard error

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