Statistical Thinking for Data Science

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Statistical Thinking for Data Science Chris Fonnesbeck Vanderbilt University

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21/22 falling 7+ stories survived

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2 fell together

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40% at night

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“Even more surprising, the longer the fall, the greater the chance of survival.”

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2 to 32 stories (average = 5.5)

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"... 132 such victims were admitted to the Animal Medical Center on 62nd Street in Manhattan ..."

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"Found" Data

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convenience sample

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Missing Data

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Representative

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Statistical Issues

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Big Data

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“With enough data, the numbers speak for themselves ” Chris Anderson, Wired

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Alfred Landon

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Literary Digest Straw Poll

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"Next week, the first answers from these ten million will begin the incoming tide of marked ballots, to be triple-checked, verified, five-times cross-classified and totalled."

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2.4 million returns

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41 - 55

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George Gallup

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Sampled 50,000

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66%

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Random Sampling

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Bias

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Self-selection Bias

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For some estimate of unknown quantity ,

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p = 0.5 sample_sizes = [10, 100, 1000, 10000, 100000] replicates = 1000 biases = [] for n in sample_sizes: bias = np.empty(replicates) for i in range(replicates): true_sample = np.random.normal(size=n) negative_values = true_sample<0 missing = np.random.binomial(1, p, n).astype(bool) observed_sample = true_sample[~(negative_values & missing)] bias[i] = observed_sample.mean() biases.append(bias)

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Accuracy Mean Squared Error

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“The numbers have no way of speaking for themselves” Nate Silver

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White House Big Data Partners Workshop

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White House Big Data Partners Workshop 19 Participants 0 Statisticians

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NSF Working Group on Big Data

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NSF Working Group on Big Data 100 experts convened 0 statisticians

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Moore Foundation Data Science Environments

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Moore Foundation Data Science Environments 0 directors with statistical expertise

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NIH BD2K Executive Committee

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NIH BD2K Executive Committee 17 committee members 0 statisticians

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Feeling left out?

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It's our own fault

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“Almost everything you learned in your college statistics course was wrong”

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Typical introductory statistics syllabus 1.Descriptive statistics and plotting

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Typical introductory statistics syllabus 1.Descriptive statistics and plotting 2.Basic probability

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Typical introductory statistics syllabus 1.Descriptive statistics and plotting 2.Basic probability 3.Hypothesis testing

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Typical introductory statistics syllabus 1.Descriptive statistics and plotting 2.Basic probability 3.Hypothesis testing 4.Experimental design

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Typical introductory statistics syllabus 1.Descriptive statistics and plotting 2.Basic probability 3.Hypothesis testing 4.Experimental design 5.ANOVA

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Statistical Hypothesis Testing

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Test Statistic

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T-statistic

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p-value

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false positive rate

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"The value for which , or 1 in 20, is 1.96 or nearly 2; it is convenient to take this point as a limit in judging whether a deviation ought to be considered signiﬁcant or not." R.A. Fisher

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p-value

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the probability that the observed differences are due to chance

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the probability that the observed differences are due to chance

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a measure of the reliability of the result

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a measure of the reliability of the result

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the probability that the null hypothesis is true

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the probability that the null hypothesis is true

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"If an experiment were repeated inﬁnitely, p represents the proportion of values more extreme than the observed value, given that the null hypothesis is true."

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H0 : Mean duckling body mass did not differ among years.

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H0 : Mean duckling body mass did not differ among years.

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H0 : The prevalence of autism spectrum disorder for males and females were equal.

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H0 : The prevalence of autism spectrum disorder for males and females were equal.

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H0 : The density of large trees in logged and unlogged forest stands were equal

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H0 : The density of large trees in logged and unlogged forest stands were equal

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Statistical Straw Man

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Statistical hypotheses are not interesting

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Hypothesis tests are not decision support tools

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Multiple Comparisons

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Family-wise Error Rate >>> 1. - (1. - 0.05) ** 20 0.6415140775914581

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import seaborn as sb import pandas as pd n = 20 r = 36 df = pd.concat([pd.DataFrame({'y':np.random.normal(size=n), 'x':np.random.random(n), 'replicate':[i]*n}) for i in range(r)]) sb.lmplot('x', 'y', df, col='replicate', col_wrap=6)

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Statistically Signiﬁcant!

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"Despite a large statistical literature for multiple testing corrections, usually it is impossible to decipher how much data dredging by the reporting authors or other research teams has preceded a reported research ﬁnding."

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What's the Alternative?

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Build models and use them to estimate things we care about

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Effect size estimation

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Data-generating Model

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Florida manatee Trichechus manatus

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occupied?

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occupied? available?

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occupied? available? seen?

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Estimating visibility

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Bayesian Statistics

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Bayes' Formula

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Probabilistic Modeling

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Evidence-based Medicine

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ASD Interventions Research 19 independent studies 27 different interventions

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“While everyone is looking at the polls and the storm, Romney’s slipping into the presidency. ”