intro to statistics and data analysis.pptx
- 1. Why are we here? Statistics: The science of collecting, manipulating, and analyzing empirical data. -Statistics enables us to use environmental data to follow the scientific method.
- 2. The scientific method: Example Step one: Make an observation (cool, doesn't need stats) Ex: When Mt. Pinatubo erupted in 1991, much less sunlight was available for plants... •20 Mt of sulfur dioxide ⟶ increased stratospheric sulfate aerosols, ⟶ decreased sunlight reaching Earth's surface
- 3. The scientific method: Example Step two: Ask a question (also doesn't need stats) Ex: I wonder if these aerosols could decrease crop yields?
- 4. The scientific method: Example Step three: Form a hypothesis / testable explanation (sounding somewhat stats-like, but still no pre-req's here) Ex: Did less sunlight from Mt. Pinatubo's aerosols lead to lower crop yields?
- 5. The scientific method: Example Steps four/five: Analyze data & test the hypothesis ( NEED STATISTICS!! ) Ex: Assemble spatio-temporal dataset, run multivariate linear regression, test statistical significance of regression parameters
- 6. The scientific method: Example Step six: Report conclusions & what they mean for your question Ex: Run simulation to consider the implications for solar radiation management (a form of geo-engineering)
- 7. Statistics and the scientific method •Statistics will enable us to test hypotheses, analyze data, and draw conclusions about the world from the process •Otherwise, we'd be stuck at observing and forming hypotheses •... and we'd have a lot of unanswered empirical questions!
- 8. This course This course is: •Designed to build your fundamental statistical toolkit •Designed to teach you to apply statistics in R •Designed to show you key univariate, multivariate and modeling methods that come up frequently in environmental data science •Designed to show you key spatio-temporal methods that come up in environmental data science (If enough time left!!). •Still new! ⟶ We are actively adjusting based on student ⟶ feedback. Your input will help shape the curriculum!
- 9. Sample versus population Consider a potential research question: What is the average mercury content in swordfish in the Atlantic Ocean? Some definitions •Population: The entire target population of interest. •Ex: All swordfish in the Atlantic Ocean •Census: A data collection including all individuals in the population •Ex: Collect mercury data for every single swordfish in the Atlantic Ocean (hard and ) 💰 •Sample: A subset of the target population for which we actually have data • Ex: 60 tagged swordfish from a government survey in the Atlantic Ocean
- 10. Parameters and statistics Usually we are interested in a numerical summary of the population (e.g., mean, slope, intercept, variance) •Parameter: A numerical summary of the population • Ex: average mercury content in swordfish in the Atlantic Ocean •Statistic: A numerical summary of the sample • Ex: average mercury content of the 60 swordfish collected in a government survey in the Atlantic Ocean
- 11. Parameters and statistics We use statistics (from a sample) in hopes of learning about parameters (from the population) This means that every time you do "statistics", you should be thinking... What is the population of interest? What is my sample? How are they different?
- 12. All samples are not created equal From IMS: Suppose we want to estimate time to graduation for Duke undergraduates in the last five years using a sample of recent students. •Q: Who is the population? Suppose we take a random sample (i.e., every individual in the population has the same probability of being selected)
- 13. All samples are not created equal Suppose we ask a nutrition major to pick a few of her friends for the sample. •What might go wrong here? Asked to pick a sample of graduates, a nutrition major might inadvertently pick a disproportionate number of graduates from health-related majors.
- 14. Four (random) sampling strategies Nearly all statistical methods are based on assumptions of randomness. If data are not collected randomly from the population, estimates are likely to be biased. Strategy 1: Simple random sampling •As simple as it sounds! •To consider for later classes: What problems might arise if your (simple random) sample is small?
- 15. Four (random) sampling strategies Strategy 2: Stratified sampling •More complex to analyze sample to construct estimates of population parameters (but still possible) •Helpful when individuals within a strata are quite similar •Used often as a method to reduce "noise" in your data (we'll discuss this later)
- 16. Four (random) sampling strategies Strategy 3: Cluster random sampling •Helpful when individuals within a cluster are quite different from one another •Used often when costs of data collection are high per cluster (e.g., Demographic and Health Surveys) •Also more complex to estimate population parameters
- 17. Four (random) sampling strategies Strategy 4: Multi-stage sampling •Very similar to cluster sampling, just take fewer samples (randomly)
- 18. Study design When we conduct statistical analyses, where do our samples come from? •Experimental studies • Sample is collected to fit the study's needs •Observational studies • Sample exists, design your study to make best use of available data
- 19. Study design Q: Does sunscreen lower risk of skin cancer?
- 20. Study design Q: Does sunscreen lower risk of skin cancer? •Experiment •Randomly sample 50% of individuals and assign them the sunscreen "treatment", require the other 50% to wear no sunscreen •Follow individuals for 20 years, compare cancer outcomes
- 21. Study design Q: Does sunscreen lower risk of skin cancer? Observational study Collect data on sunscreen use, skin cancer, and sun exposure Compare cancer rates for individuals with different sunscreen use habits
- 22. Types of variables A variable is a representation of something we care about in a population (e.g., nitrate concentration of groundwater). Numerical variables Object class numeric in R •Can take on a wide range of possible values •Makes sense to add, subtract, multiply, etc. •Examples: •Height of the tree canopy across the Amazon •Length of Atlantic swordfish •Daily average temperature
- 23. Types of variables Numerical variables Discrete numerical variables take on only a limited set of values, often counts (e.g., population) Continuous numerical variables: can take on infinite values within a range (e.g., arsenic concentration in groundwater)
- 24. Types of variables Categorical variables Object class factor in R •Values correspond to one of a fixed number of categories •Possible values are called levels •Examples: •Land use type •Species of tree •Age group (e.g., <15, 15-64, 65+) (watch out! continuous numerical data can often be stored as a categorical variable!)
- 25. Types of variables Categorical variables Nominal variables are unordered descriptions Ordinal variables are categories with a natural ordering Binary variables only take on 0 or 1
- 26. Things to do 1- Install R https://www.r-project.org/ 2- Install RStudio https://posit.co/download/rstudio-desktop/ 3- Access to course material on Olat https://olat.vcrp.de/url/RepositoryEntry/4703814428 Code: ETX3