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Probability and data 1w
1. ALLPPT.com _ Free PowerPoint Templates, Diagrams and Charts
윤 경 일 연구원
Introduction to Probability and Data
2. Introduction to Statistics With R
Statistics with R
Introduction to Data and Probability
Statistical Inference
Modeling and Linear Regression
Bayesian Statistics
Statistics Capstone Project
How to:
Make use of data
Collect data
Analyze data
Make inferences
Draw conclusions
3. Introduction to Data
Data
Collected from likes field notes, surveys, and experiments
Backbone of a statistical investigation
General process of investigation
1. Identify a question or problem
2. Collect relevant data on the topic
3. Analyze the data
4. Form a conclusion
Statistics
How best to collect data
Analyze data
Draw conclusions from data
3 primary components of Statistics
1. How best can we collect data?
2. How should it be analyzed?
3. What can we infer from the analysis?
4. Introduction to Data
Approach
Population
Defining populations
of interest
Sample
Methods of taking
sample from population
Design
Best answer
research questions
Scope
Scope of inference
for a study
Exploratory
data
analysis
Data visualizations
,Summary statistics
inference
Wrap up with simulation-based
Introduction to statistical inference
5. Data basics
Observations, variables, and data matrices
Years Boys girls
1997 351 154
… … …
Data matrix of birth
Observation(case)
variable
Types of variables
All variables
Numerical
(quantitative)
Categorical
(qualitative)
Continuous
Discrete
Infinite number of
value within range
Specific set of
numeric values
ex)height
ex)number of cars
a household owns
Ordinal
Regular
categorical
Levels have an
inherent ordering
ex) satisfied of survey
Not have an
inherent ordering
ex) morning personorafternoon person
6. Data basics
Relationships between variables
• Two variables that show some connection with one another are called associated(dependent)
• Association can be further described as positive or negative
• If two variables are not associated, they are said to be independent
7. Observational studies & experiments
Define observational studies and experiments
Studies
observational
experiment
Merelyobserve
Onlyestablishanassociation
Retrospective: uses past data
Prospective: collectedthroughoutthestudy
Randomlyassignsubjectstotreatments
Establishcausalconnections
Observational Experiment
Work out
Don’t
work out
Average
energy
level
Average
energy
level
Work out
Don’t
work out
Random
assignment
8. Observational studies & experiments
Confounding variable
• which is a variable that is correlated with both the explanatory and response variables.
• also called a lurking variable, confounding factor or a confounder
Correlation vs Causation
• correlation does not imply causation
• just correlation is the type of study that we’re basing our conclusion
9. Sampling & sources of bias
Census vs. sample
• Some individuals are hard to locate or measure
• Be different from the rest of the population
• Populations rarely stand still
A few sources of sampling bias
Census Sample
• exploratory analysis
• inference
• representative sample
• Convenience sample : Individuals who are easily accessible are more likely to be included in the sample
• Non-response : If only a (non-random) fraction of the randomly sampled people respond to a survey
such that the sample is no longer representative of the population
• Voluntary response : Occurs when the sample consists of people who volunteer to respond because
they have strong opinions on the issue
10. Sampling & sources of bias
Sampling methods
Simple random sample(SRS) Stratified sample
Cluster sample Multistage sample
11. Experimental design
Principles of experimental design
• Control : compare treatment of interest to a control group
• Randomize : randomly assign subjects to treatments
• Replicate : collect a sufficiently large sample, or replicate the entire study
• Block : block for variables known or suspected to affect the outcome
Experimental design terminology
Blocking vs. explanatory variables
• explanatory variables ( factors ) – conditions we can impose on experimental units
• blocking variables – characteristics that the experimental units com with, that we would like to control for
• blocking is like stratifying:
• blocking during random assignment
• stratifying during random sampling
• Placebo : fake treatment often used as the control group for medical studies
• Placebo effect : showing change despite being on the placebo
• Blinding : experimental units don’t know which group they’re in
• Double-blind : both the experimental units and the researchers don’t know the group assignment
12. Experimental design
Random sampling vs. random assignment
• Random sampling : subjects are being selected
• Random assignment : subjects are being assigned to various treatments
Difference
Important to think about the nature of the variable and not just the observed values when determining if the numerical variable is continuous or discrete
For example, height is a continuous variable. However we tend to report our height rounded to the nearest unit of measure like inches or centimeters
Difference
Important to think about the nature of the variable and not just the observed values when determining if the numerical variable is continuous or discrete
For example, height is a continuous variable. However we tend to report our height rounded to the nearest unit of measure like inches or centimeters
If you're going to walk away with one thing from this class, let it be correlation does not imply causation. And what determines whether we can infer causation or just correlation is the type of study that we're basing our conclusions. Observational studies for the most part, allow us to make only correlational statements. While experiments, allow us to infer causation. We said for the most part, because there are actually more advanced methods broadly titled causal inference that allow for making causal inferences for observational studies, but those studies are beyond the methods for this course.
