Introduction to Statistics with Python

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INTRODUCTION TO STATISTICS WITH PYTHON @CHRISTIANBARRA - PYCON7

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MY NAME IS CHRISTIAN I’M STUDYING STATISTICS @UNIPD HELLO !!!

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THE STORY OF THIS TALK: 3 DAYS BEFORE THE CONFERENCE VALERIO: CHRISTIAN, WE HAVE A FREE SLOT AND WE NEED A TALK CHRISTIAN: I CAN’T IN 3 DAYS… VALERIO: YOU MUST.

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CONTENT 1. What is STATISTICS ? 2. Variable types 3. Univariate distribution 4. Frequencies 5. M^3 (Mean, Median, Mode) 6. Variance and Standard Deviation 7. Multivariate distribution 8. Covariance and Correlation

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1. WHAT IS STATISTICS ?

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— Oxford English Dictionary …. THE BRANCH OF SCIENCE OR MATHEMATICS CONCERNED WITH THE ANALYSIS AND INTERPRETATION OF NUMERICAL DATA AND APPROPRIATE WAYS OF GATHERING SUCH DATA. ” “

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— American Statistical Association STATISTICS IS THE SCIENCE OF LEARNING FROM DATA, AND OF MEASURING, CONTROLLING, AND COMMUNICATING UNCERTAINTY; AND IT THEREBY PROVIDES THE NAVIGATION ESSENTIAL FOR CONTROLLING THE COURSE OF SCIENTIFIC AND SOCIETAL ADVANCES ” “

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— John Tukey, Bell Labs, Princeton University THE BEST THING ABOUT BEING A STATISTICIAN IS THAT YOU GET TO PLAY IN EVERYONE ELSE'S BACKYARD. ” “

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— Mark Twain THERE ARE THREE KINDS OF LIES: LIES, DAMNED LIES, AND STATISTICS. ” “

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2. VARIABLES

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4 KINDS OF VARIABLES • QUANTITATIVE VARIABLES • CONTINUOUS • DISCRETE • CATEGORICAL VARIABLES • ORDINAL • NOMINAL

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OUR RAW DATA

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VOTES AT UNIVERSITY FROM 1 TO 30.

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QUANTITATIVE… AND DISCRETE

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THE DISTANCE BETWEEN 17 AND 18 IS THE SAME BETWEEN 27 AND 28 ?

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THE TYPE OF A VARIABLE SOMETIMES IS NOT STRICTLY RELATED TO THE VALUE THAT ASSUMES

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ANOTHER TYPICAL ERROR…

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FROM 1 TO 7 HOW MUCH DO YOU ENJOY THE CONFERENCE ?

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AFTER THE SURVEY….

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ON AVERAGE PEOPLE ENJOYED THE CONFERENCE 4.5

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DON’T RAPE YOUR VARIABLES

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4. FREQUENCIES

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DIFFERENT TYPES OF FREQUENCY • ABSOLUTE FREQUENCY (ni): number of observation for each of the “OBSERVATIONAL UNIT“ • ABSOLUTE CUMULATIVE FREQUENCY (Ni): Ni = Ni-1 + ni • RELATIVE FREQUENCY (fi): number of observations for each of the “OBSERVATIONAL UNIT“ divided by the total number of observations (N) • RELATIVE CUMULATIVE FREQUENCY (Fi): Fi = Fi-1 + fi • % FREQUENCY: fi * 100 • % CUMULATIVE FREQUENCY: Fi * 100

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3. UNIVARIATE DISTRIBUTION

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WE WORK WITH JUST 1 VARIABLE

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3 MAIN CONCEPTS • OBSERVATIONAL UNITS: entities whose characteristics we measure or observe (ALIAS ROWS) • VARIABLE: feature, characteristic of the OBSERVATIONAL UNITS (ALIAS COLUMNS) • FREQUENCY: Number of OBSERVATIONAL UNITS with the same value of a VARIABLE

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import numpy as np import pandas as pd import matplotlib.pyplot as plt %matplotlib inline univariate = pd.DataFrame(df["Product (X1)"].value_counts()) univariate.columns = ["Absolute Frequency (ni)"] univariate

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FREQUENCY TABLE

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5. MEAN, MEDIAN AND MODE

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THERE ARE DIFFERENT TYPES OF MEAN

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ARITHMETIC MEAN (MOST USED)

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df.mean() Price (X3) 28.051205 Margin (X5) 15.525602 Stock (X6) 12.293333 dtype: float64

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WHY IS THE MEAN SO IMPORTANT ?

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FOR THIS PROPERTY

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MODE: VALUE THAT APPEARS MOST OFTEN (HIGHEST FREQUENCY)

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df["Product (X1)”].mode() 0 Socks dtype: object

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MEDIAN: ALSO CALLED 50TH PERCENTILE

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THE PROPERTY OF THE MEDIAN

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YOU NEED A VARIABLE THAT YOU CAN “ORDER”

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AND WE CAN’T ORDER PRODUCTS

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df.median() Price (X3) 22.652655 Margin (X5) 12.826328 Stock (X6) 12.000000 dtype: float64

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univariate_stocks = pd.DataFrame(df["Stock (X6)"].value_counts()) univariate_stocks = univariate_stocks.sort_index() univariate_stocks.columns = ["Absolute Frequency (ni)"] univariate_stocks["Relative Frequency (fi)"] = univariate_stocks["Absolute Frequency (ni)"]/ univariate_stocks["Absolute Frequency (ni)"].sum() univariate_stocks['Relative Cumulative Frequency (Fi)'] = univariate_stocks['Relative Frequency (fi)'].cumsum() univariate_stocks

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6. VARIANCE AND STANDARD DEVIATION

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WE CALL THEM MEASURES OF DISPERSION

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MEAN AND VARIANCE ARE PROBABLY THE MOST IMPORTANT CONCEPTS IN STATISTICS

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AS MY PROFESSOR SAID… VARIANCE IS YOUR EMPLOYER

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HELLO BOSS !

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BUT IS A STRANGE CONCEPT… SQUARE OF SOMETHING

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STANDARD DEVIATION

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NOW WE HAVE A KIND OF DISTANCE

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THE DISTANCE, ON AVERAGE, FROM THE MEAN

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YOU CAN USE STD ALSO TO SAY ROMANTIC THINGS TO YOUR PARTNER

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LIKE YOU ARE 3 STD FROM THE MEAN (NERDY WAY TO SAY YOU ARE UNIQUE)

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NORMAL DISTRIBUTION

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7. BIVARIATE DISTRIBUTION

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WE WORK WITH 2 VARIABLES

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OUR VARIABLES

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BIVARIATE DISTRIBUTION

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NOW WE CAN CONSIDER A BIVARIATE LIKE AN UNIVARIATE DISTRIBUTION

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CONDITIONED DISTRIBUTION

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STOCKS (X6) | X3 = 18.95…

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PRICES (X3) | X6 = 4

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BIVARIATE DISTRIBUTION

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FOR EACH CONDITIONED DISTRIBUTION WE CAN CALCULATE MEAN AND VARIANCE

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AT THE END WE HAVE 13 CONDITIONED MEANS/VARIANCES AND 2 MARGINAL MEANS/VARIANCES