Final Exam Time and Place:Saturday, Dec 8,

9:00am - 12:00pmEN 1054

Chapter 19.1 Exploratory Data Analysis

What is Exploratory Data Analysis?

• An approach to analyze data sets to:– Discover patterns– Find a better model

• It’s an iterative process– Refine to uncover patterns

Confirmatory vs. Exploratory

Confirmatory analysis• What decision can be made?• How certain can we be?• What are values of parameters?• Sample• ONE use of a sample (data-

grinding, otherwise)• Single analysis• p-value = ?• Yes/no decision• Residuals acceptable?• Experimental design

Exploratory analysis • What is the appropriate model?• What is data telling us?• What is structure of model?• Batch of data• Repeated use of a

batch .• Iterative search for pattern• Explained variance = ?• Best model• Residuals show pattern?• Factor analysis

ExploratoryWhat is the appropriate model?

But remember, pattern ≠ cause

ConfirmatoryWhat decision can be made?

Inference

• Confirmatory– Narrow form of inference– Relate one Q to another Q

(e.g. βreg)

• Exploratory– Broader form of inference– Trying to discover a pattern

worth running through a confirmatory analysis

P corm P soilN corn ~ N soil C corn C soil ⁞ ⁞

Don’t confuse confirmatory and exploratory analyses

• Refining models using p-values ≠ exploratory analysis

• Repeated analysis of the same data set is data dredging (aka: data grinding, data mining, data fishing, data snooping…)

• Any data set has a degree of randomness, so multiple comparisons may be bound to find a false association

Characteristics of Exploratory Analyses

• Relies strongly on graphical analyses

http://gallery.r-enthusiasts.com/thumbs.php

Characteristics of Exploratory Analyses

• Simplify – determine best model for pattern

Execution

1. Define all quantities that are used – Procedure statement

– Name and Symbol

– Values with Units

2. Identify response and explanatory variables

3. Decide whether to undertake exploratory or confirmatory analysis, stating reasons for choice

4. State screening criterion to distinguish exploratory from confirmatory analysis– Visual screening

– P-value based (e.g. keep if <0.1)

Box and Arrow Diagrams Logic

• Gordon Riley is interested in aquatic productivity of Georges Bank

LightNutrients (nitrates,

phophates)

Phytoplankton Zooplankton