Goal: Describe a set of data

• The first kind of data analysis performed
• Commonly applied to census data
• The description and interpretation are different steps
• Descriptions can usually not be generalized without additional statistical modeling

Goal: Find relationships you didn’t know about

• Exploratory models are good for discovering new connections
• They are also useful for defining future studies
• Exploratory analysis are usually not the final say
• Exploratory analysis alone should not be used for generalization/predicting
• Correlation does not imply causation

Goal: Use a relatively small sample of data to say something about a bigger population

• Inference is commonly the goal of statistical models
• Inference involves estimating both the quantity you care about and your uncertainty about your estimate
• Inference depends heavily on both the population and the sampling scheme

Goal: To use the data on some objects to predict values for another object

• if $X$ predicts $Y$ does not mean that $X$ cause $Y$
• Accurate prediction depends heavily on measuring the right variables
• Although there are better and worse prediction models, more data and simple model works really well
• Predictive is very hard, especially about the future references

Goal: To find out what happens to one variable when you make another variable change

• Usually randomized studies are required to identify causation
• There are approaches to inferring causation in non-randomized studies, but they are complicated and sensitive to assumptions
• Causal relationships are usually identified as a average effects, but may not apply to every individual
• Causal models are usually the “good standard” for data analysis

Goal: Understand the extract changes in variables that lead to changes in other variables for individual objects

• Incredibly hard to infer, except in simple situations
• Usually modeled by a deterministic set of equations(physical/engineering science)
• Generally the random components of the data is measurement error
• If the equations are known but the paraments are not, the may be infered with data analysis