part2 - Public Health 6450 Fall 2011 Andrew Mugglin and...

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Public Health 6450 – Fall 2011 Andrew Mugglin and Lynn Eberly Division of Biostatistics School of Public Health University of Minnesota [email protected] Part 02
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Review Univariate EDA with Descriptive Statistics Multivariate EDA with Tables and Plots Where are we going? Previously: I Univariate Exploratory Data Analysis (EDA) with plots I Categorical Variable: Frequency Table, Bar chart, Pie Chart I Continuous Variable: Stemplot, Histogram Current topics: I Univariate EDA with descriptive statistics I Multivariate EDA with tables and plots Mugglin and Eberly PubH 6450 Fall 2011 Part 02 2 / 51
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Review Univariate EDA with Descriptive Statistics Multivariate EDA with Tables and Plots Measures of Central Tendency and Shape Measures of Dispersion Data Exploration Strategy Measures of central tendency I Mean I Median I Mode I Skew Mugglin and Eberly PubH 6450 Fall 2011 Part 02 3 / 51
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Review Univariate EDA with Descriptive Statistics Multivariate EDA with Tables and Plots Measures of Central Tendency and Shape Measures of Dispersion Data Exploration Strategy Summation notation Setup: dataset consists of { 8 , 2 , 3 , 5 } . These numbers are denoted as x i x 1 = 8 , x 2 = 2 , x 3 = 3 , x 4 = 5 . Sum = 4 X i =1 x i = x 1 + x 2 + x 3 + x 4 = 8 + 2 + 3 + 5 = 18 where the captial Greek letter sigma is the summation sign. Mugglin and Eberly PubH 6450 Fall 2011 Part 02 4 / 51
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Review Univariate EDA with Descriptive Statistics Multivariate EDA with Tables and Plots Measures of Central Tendency and Shape Measures of Dispersion Data Exploration Strategy Mean Definition For a set of n observations x 1 , x 2 , . . . , x n , the mean ¯ x is defined as: ¯ x = x 1 + x 2 + · · · + x n n , or ¯ x = 1 n n X i =1 x i . Mugglin and Eberly PubH 6450 Fall 2011 Part 02 5 / 51
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Review Univariate EDA with Descriptive Statistics Multivariate EDA with Tables and Plots Measures of Central Tendency and Shape Measures of Dispersion Data Exploration Strategy Median Definition For a set of n observations x 1 , x 2 , . . . , x n , the median M is the midpoint, i.e., half the observations take that value or a smaller value. Let x (1) , x (2) , . . . , x ( n ) denote the increasingly ordered observations: x (1) is the minimum (the smallest) x (2) is the second smallest, x (3) is the third smallest, . . . x ( n ) is the maximum (the largest). Then M = ( x ( n +1) / 2 if n is odd , 1 2 ( x n / 2 + x ( n +2) / 2 ) if n is even . Mugglin and Eberly PubH 6450 Fall 2011 Part 02 6 / 51
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Review Univariate EDA with Descriptive Statistics Multivariate EDA with Tables and Plots Measures of Central Tendency and Shape Measures of Dispersion Data Exploration Strategy Mode Definition The mode: The value that occurs most frequently in the data set. Example: { 8 , 2 , 3 , 5 } . What is the mode? A dataset can be multi-modal, i.e. , have several modes occurring at the same frequency. Example: { 2 , 3 , 5 , 5 , 5 , 7 , 9 , 10 , 10 , 10 , 12 , 21 } What is the mode? Mugglin and Eberly PubH 6450 Fall 2011 Part 02 7 / 51
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Review Univariate EDA with Descriptive Statistics Multivariate EDA with Tables and Plots Measures of Central Tendency and Shape Measures of Dispersion Data Exploration Strategy Example How many hours of television do you watch every week?
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