MXB107_Lec3_216 - WHATS ON TODAY Data Visualisation and...

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WHAT’S ON TODAY Data Visualisation and Description 1. Basic Principles of Description Separating “Signal” from “Noise” Central Tendency, Spread, Shape, Inter-relationship Numerical vs Graphical Techniques 2. Basic Principles of Graphical Presentation Information Density and Extraneous Components Assessing Model Assumptions 3. Application to Univariate Data Discrete (Nominal/Ordinal) vs Continuous 4. Application to Bivariate/Multivariate Data Cross-Tabulation, ANOVA, ANCOVA and Regression settings
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Basic Principles 1. Summarisation is “Compression” a. Interpretability vs Loss of Information b. Over- and Under-smoothing Too much compression obscures key details Too little compression leaves noisy image DATA SUMMARISATION
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Basic Principles 2. Key Features of Datasets a. Central Tendency (sometimes termed “Location”) b. Spread c. Shape (Most common focuses: Symmetry and Multi-modality) d. Inter-relationships (for Bivariate or Multivariate) DATA SUMMARISATION
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Basic Principles 3. “A (Good) Picture is Worth 1000 [Data Points]” a.“Information Density” – Are too many or too few aspects of data depicted? (see “smoothing”) b.Avoid extraneous information and adornment (e.g., 3D Pie Charts! See this week’s Workshop) 4. Identification of Aberrant Features a. Outliers and Artefacts DATA SUMMARISATION
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DATA SUMMARISATION We will break down our discussion by: Univariate vs Bivariate vs Multivariate Data Discrete vs Continuous Data Graphical vs Numerical Summary
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DATA SUMMARISATION Univariate – Discrete – Graphical Key aspect is distribution among possible values Use Pie Charts & Bar Charts Percentage of observations in each “category” is: Area of Sector (Pie Charts) Height of Bar (Bar Charts) Combining small categories aids visualisation (loses info) Advantages/Disadvantages Pie Charts hard to compare individual categories, but readily show majority category (or group of categories)
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DATA SUMMARISATION Univariate – Discrete – Graphical EXAMPLE: A random sample of the characteristics of 93 different makes and models of automobiles on sale in 1993 was gathered. Among the collected characteristics for each car was the number of engine cylinders. Let’s investigate the distribution of number of cylinders in the sample.
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DATA SUMMARISATION Univariate – Discrete – Graphical EXAMPLE: Car Engine Cylinders QUESTIONS: Which most prevalent? Is it majority (i.e., > 50%)? More 3 cylinder than 5 cylinder engines in Cylinders Count 3 3 4 49 5 2 6 31 8 7 Rotary 1
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DATA SUMMARISATION Univariate – Discrete – Graphical EXAMPLE: Car Engine Cylinders QUESTIONS: Which most prevalent? Is it majority (i.e., > 50%)? More 3 cylinder than 5 cylinder engines in
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DATA SUMMARISATION Univariate – Discrete – Graphical EXAMPLE: Car Engine Cylinders ISSUE: Combining small categories may give more insight to main pattern
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DATA SUMMARISATION Univariate – Discrete – Numerical 1. Location a. Categorical (i.e., Nominal/Ordinal) Mode = Most Common Category (be careful if merged!)
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