3. Statistical computing is very central , but data
science is more than statistics
Activities of data scientists:
collection and generation,
preparation,
analysis,
visualization,
management and preservation of large collections of
data
Jeffrey Stanton, Introduction to Data Science, free e-book
3
4. Ask interesting question
Why is it important?Which number answers your question?
Get or generate the data
Which data will help answering you question? How is the data
generated? Are their any sampling biases? Ethical issues?
Analyze the data
Are there any anomalies or regularities?
Which hidden process has generated the data?
Fit a model to the data and validate it
Visualize and communicate results
What does 75% probability mean?
Preserve and share the data to make results reproducible
4
5. Data is a collection of facts
Facts can be numbers, words,
measurements, observations or even just
descriptions of things
Qualitative data (e.g., “it was great”)
Quantitative data
Discrete (e.g., 5)
Continuous (e.g., 3.723)
5
6. 6
Stevens, S. S. (1946). "On theTheory of Scales of Measurement". Science 103 (2684):
677–680.
Nominal (e.g., ethnic group, sex, nationality)
Ordinal (e.g., status)
Interval (e.g., temperature in Celsius)
Ratio (e.g., weight)
Observations are
only named
Observations can be ordered
Distance is meaningful
Absolute zero
8. Random sample of Twitter users
Random sample of tweets from the public timeline
More active users are more likely to be included
Friendship Paradox
Select a random sample of people and ask them to list
the people they know. Contact a sample of the listed
friends and repeat the survey.
Sampling bias: people with more friends are more
likely to show up in the friend lists which we generate
at the first stage
8
9. A study found that the profession with the
lowest average age of death was student.
Being a student does not cause you to die at an early
age. Being a student means you are young.This is
what makes the average of those that die so low.
Amount of ice cream consumed per day is highly
correlated with number of drownings per day
Both variables are correlated with the daily
temperature
9
"Teaching Statistics:A Bag ofTricks," by Gelman and Nolan (2002)
10. A study found that only 1.5% of drivers in accidents
reported that they were using a cell phone, whereas
10.9% reported that they were distracted by another
occupant in the car.
Can we conclude that using a cell phone safer than
speaking with another occupant?
P(cellphone | accident) != P(accident | cellphone)
Compare P(accident|cellphone) and P(accident|occupant)
We need to know the prevalence of cell phone use
It is likely that much more people talk to another occupant
in the car while driving than talking on the cell phone
10
Jessica Utts, What Educated Citizens Should Know about Statistics and Probability,The American
Statistician, Vol. 57, No. 2 (May, 2003), pp. 74-79
11. Ecological Fallacy
Illiteracy rate in each US state and the
proportion of immigrants per state
Negative correlation of −0.53
▪ The greater the proportion of immigrants in a state,
the lower its average illiteracy.
When individuals are considered, the
correlation was +0.12 — immigrants were on
average more illiterate than native citizens.
11
Robinson, W.S. (1950). "Ecological Correlations and the Behavior of Individuals". American
Sociological Review (American Sociological Review, Vol. 15, No. 3) 15 (3): 351–357.
13. Found data or observational data
Are observational data enough?
Are such data available?
Generate Data
Designs the data generation process
▪ E.g., via surveys, experiments, crowdsourcing
13
15. Two general types of traces:
15
Accretion - a build-up
of physical traces
Erosion - the wearing away
of material
Webb, Eugene J. et al. Unobtrusive Measures: nonreactive research in the social
sciences. Chicago: Rand McNally, 1966
16. Bulk downloads
Wikipedia, IMDB, Million Song Database, etc.
API access
NYTimes,Twitter, Facebook, Foursquare, etc.
Web scraping
Tools e.g., http://scrapy.org/
What data is ok to scrap?
▪ Public, non-sensitive, anonymized, fully referenced
information, Check terms of conditions!
16
17. Takes time to accumulate
Conservative estimate
Only what happened counts! Intentions,
motivations or internal states don’t count.
Inferentially weak
Cannot answer “what-if” questions
17
18. Surveys
Simulations
Model behavior of users/agents on a micro-level
Simulate what happens under different conditions
Empirical validation
Experiments
Keep all variables constant and only manipulate one
variable (e.g., emotions)
18
19. Simulations
Study of macro-phenomena
Difficult to validate empirically
Surveys and/or Experiments
We only get data from those who are accessible and
willing to respond or participate
Responders provide answers that are in line with self-
image and researcher’s expectations
Hawthorne effect, etc.
19
21. 21
Data cleaning
Fill in missing values
Smooth noisy data
Identify or remove outliers
Resolve inconsistencies
Data integration
Integration of multiple databases, or files
22. 22
Data transformation
Normalization: scaled to fall within a small, specified range
Standardization: how many standard deviations from the mean
lies each data point
Discretization: divide the range of a continuous attribute into
intervals some algorithms require discrete attributes.
Data reduction
Dimensionality reduction (remove unimportant attributes via
feature selection, group features into factors e.g. PCA, SVD)
Aggregation and clustering
Sampling
23. Data Collection
Data Preprocessing Data Mining
DataAnalysis Statistical Inference
DataVisualization Machine Learning
Data Preservation
24. Problem:
Given high dimensional space (e.g., fb-user which
are described via various attributes such as
locations they visited)
Find pairs of data points (𝒙, y) that are within
some distance threshold 𝒅(𝒙, y) ≤ 𝒔
We first need to decide what „distance“
means
24
26. Goal: Given a set of items group the items
into some number of clusters, so that
Members of a cluster are similar to each other
Members of different clusters are dissimilar
26Anand Rajaraman, Jeffrey Ullman, Jure Leskovec, Mining of Massive Datasets, Cambridge University Press
27. Not-Hierarchical / Point assignment:
Maintain a set of clusters
Point belong to “nearest” cluster
Hierarchical:
Agglomerative (bottom up):
▪ Initially, each point is a cluster
▪ Repeatedly combine the two “nearest” clusters into one
Divisive (top down):
▪ Start with one cluster and recursively split it
27Anand Rajaraman, Jeffrey Ullman, Jure Leskovec, Mining of Massive Datasets, Cambridge University Press
33. Try different k, looking at the change in the
average distance to centroid as k increases
Average falls rapidly until right k, then
changes little
33
Average
Diameter
k
best k
34. Aim: Find hidden concepts/groups in a matrix
Method: SingularValue Decomposition (SVD)
34
Lescovec et al., Mining of Massive Datasets, p. 418
35. Rank = 2
Rank denotes the
information content of
the matrix.
For instance, a rank-1
matrix can be written as a
product of one column and
one vector
35
37. 37
Lescovec et al., Mining of Massive Datasets, p. 418
Relates users
and concepts
Relates movies to
concepts
Strength
of
concepts
38. Data Collection
Data Preprocessing Data Mining
DataAnalysis Statistical Inference
DataVisualization Machine Learning
Data Preservation
39. Estimate population parameter from sample statistics
Sampling Distribution of statistic:
Draw a finite set of samples of size n from the population
Computing the statistic on the sample
Repeat this process
The mean of the sampling distribution is the expected
value of the statistic in the true population
SD of the sampling distribution is the standard error
39
41. Some descriptive statistics such as mean or
median are unbiased estimators of central
tendency
Expected value of the statistic is the true
population parameter
Expected value of dispersion in a sample is an
underestimate of the true population value
41
42. True population size is N
Sample size n < N (e.g., n=100)
Correction factor :
𝑛
𝑛−1
For n=100 the correction factor is ~ 1.01
For n=100.000 our correction factor is
~1.00001
Estimate PopulationVar:
(
𝑛
𝑛−1
) ∗ (𝑥 𝑖−𝜇𝑛
𝑖=1 )
𝑛
42
43. Specify the range of values that have a high
probability of containing the true population
parameter
Confidence level α: the probability that
confidence interval contains true population
parameter
43
44. CI = sample statistic + MOE
MOE = SE * Critical value
MOE =
𝜎
𝑛
∗ 𝑧 𝛼/2
CriticalValue: how far away from the mean
must a point lie in order to be considered as
“extreme” or “unexpected”?
44
n … sample size
σ … standard deviation
z α/2 … confidence coefficient
47. Select 1000 fb-user randomly
Average number of bar visits per year X = 78
Standard Deviation:
(𝑥 𝑖−𝜇𝑛
𝑖=1 )
2
𝑛
= 30
Confidence level is 95% divide 0.95 by 2 to get
0.475
Check out the z table z = 1.98
MOE =
𝜎
𝑛
∗ 𝑧 𝛼/2 =
30
1000
∗ 1.98= 1.88
78 +/- 1.88 CI: [76.12 ; 79.88]
47
48. Exact CI can only be computed when the
sampling distribution and SD of sampling
distribution (i.e., SE) are known
Otherwise we have to estimate the Standard
Error (SE) Bootstrap
48
49. Sampling with replacement
Population is unknown
But we observe one sample from the population of
size n=4: {2, 3, 8, 8}
We use this sample to generate a large number of
bootstrap samples of size n:
▪ 8, 8, 8, 3
▪ 3, 3, 8, 2
▪ …
Compute statistic (e.g. ,mean) for each
bootstrap sample
Estimate SE from the bootstrap distribution
49
51. Randomly selected sample of fb-user
Have they ever checked in at a nightclub?
Democrats: 100/1000 yes
Republican: 90/1000 yes
Do the nightlife preferences differ
significantly across political parties?
Give 95% CI for difference in proportions
51
53. H1: political party affects the nightlife-preferences
H0: political party does not affects the nightlife-
preferences
Proportion of users who visited nightclubs not matter
which party they belong to: 190/2000 = 0.095
If political affinities have no effect, we would expect
the following frequencies:
53
Democrats Republicans
yes 100 90 190
no 900 910 1810
Democrats Republicans
yes 95 95 190
no 905 905 1810
54. χ2=
𝑜−𝑒 2
𝑒
= 0.5815
DF = (number of rows – 1) x (number of columns – 1) = 1
Critical value of χ2 at 5% significance and 1 DF is
3.84
Our χ2 does not exceed the critical value
We cannot reject H0
54
Democrats Republicans
yes 100 90 190
no 900 910 1810
55. If α=0.05 then 95%
of all values fall in
this interval
Two-tail test:
2.5% of values in the
upper tail and 2.5%
of the lower tail are
considered as so
extreme that we
reject H0 if we
observe them
55
56. Test if democrats on fb, on average, have more
than 60 bar visits per year
H1: µ > 60
H0: µ <= 60
Random sample of 20 democratic fb-user:
{65 73 51 67 48 80 69 53 59 62 71 67 64 78 65 490
80 60 51 70}
Sample mean 𝜇=64.1
Assume we know SD in population = 10
𝑧 =
𝜇− 𝜇
𝑆𝐸
𝑆𝐸 =
𝑆𝐷
𝑛
𝑧 =
64.1−60
10/ 20
= 1.8336
56
57. Would we expect that? How extreme is
this observation?
If H0 is true (mean<=60) in which area
around the mean do 95% of all points lie
Pick alpha level α=0.05 that’s the
maximum probability where you reject
the null hypothesis if the null hypothesis
is true
Right-tail test: find our critical value for
0.45 using the z-distribution
If the z-score of our observed data exceed
this value we have to reject H0
57
1.8336 > 1.645 reject
the null hypothesis
58. Large Effects, Small Samples:
In small samples it is easy to overestimate an effect which
might have happened by chance
Small Effects, Large Samples:
The smaller the effect you want to measure the larger the
sample size you need to prove it significant!
Example: Assume a coin is biased: 10% head and 90% tail
Tossing the coin 10 times should be enough to convince people
that the coin is biased.
Example: Assume a coin is biased: 51% head and 49% tail
Minimum sample size increases with decreasing effect size
which one wants to demonstrate
58
59. The more we analyze, the more we find by
chance!
If you calculate correlation between 10 variables
(i.e., 44 different correlation coefficients) you
should expect that at least 2 correlations are
significant with p < 0.05 by chance (one in every
20)
Corrections or adjustments for the total number
of comparison are needed!
59
60. Many tests such as z-test, t-test, ANOVA make the
normality assumption.
If true population is very skewed (e.g. power law) the
sampling distribution of the statistic will not be normal
Nonparametric methods like sign-test use e.g. median
rather than the mean
Hypothesis about the median of the true population (e.g. H1:
median < 100, H0: median = 100)
Count number of measurements that favor the null hypothesis
If H0 is true half of the measurement should fall on each side.
60
61. Data Collection
Data Preprocessing Data Mining
DataAnalysis Statistical Inference
DataVisualization Machine Learning
Data Preservation
62. Aim
Find a function that describes the relation between X
(e.g. bar visits) andY (e.g. new friends)
Given X predictY
Problem
Infinite number of ways X andY could be related
Idea
Reduce space of possible function and start with the
simplest one (linear relation)
Y= 𝑏0 + 𝑏1 𝑋
62
64. Use Gradient Descent to minimize Cost
function C 𝑏0, 𝑏1
C 𝑏0, 𝑏1 =
1
2𝑁
(𝑌𝑖−𝑌𝑖)2𝑁
𝑖=1
C 𝑏0, 𝑏1 =
1
2𝑁
(𝑌𝑖 − 𝑏0 − 𝑏1 𝑋)2𝑁
𝑖=1
Start with some guess for 𝑏0, 𝑏1
Keep changing 𝑏0, 𝑏1 to reduce C 𝑏0, 𝑏1 until
we hopefully end up at a minimum
64
65. 𝑏0 ≔ 𝑏0 − 𝛼
𝜕
𝜕𝑏 𝑗
C 𝑏0, 𝑏1
𝑏1 ≔ 𝑏1 − 𝛼
𝜕
𝜕𝑏 𝑗
C 𝑏0, 𝑏1
Simultaneous updates of b0 and b1
65
Derivative of cost function
informs us about the slope of
the cost function
Learning rate
67. Residuals: deviation between the observed
and the predicted values
Residual sum of squares:
67
Is this a good
measure?
No it depends on
the number of
observations N
What if we
multiply it with
1/N?
68. 𝑦𝑖… observed value
𝑦 … value predicted by the model
𝑦 … mean of observed data
68
Total variability
in the outcome
that needs to be
explained
Unexplained variability!
Residuals: difference
between the observed value
and the estimated value
Proportion of the total variability
unexplained by the model
69. Independent variable is binary (e.g., went to nightclub
or not)
We can group users by number of new friends year
(20-25, 25-30, 30-35, etc.) and compute the proportion
of people with high “nightclub-probability”
69
70. Logistic Regression:
Maximum Likelihood Estimator
Estimate unknown coefficients by
maximizing the log likelihood function
Coefficient is interpreted as the rate of
change in the "log odds" as X changes
70
ln
𝑃(𝑌 = 1)
1 − 𝑃(𝑌 = 1)
= 𝑏0 + 𝑏1X + ϵ
71. Simple Example:
You have a coin that you know is biased towards
heads and you want to know what the probability of
heads (p) is.
We want to estimate the unknown parameter p!
71
72. You flip the coin 10 times and the coin comes
up head 7 times.
What’s your best guess for p?
72
81. Be careful when drawing conclusions from
graphs
Size of effect shown in graphic != Size of
effect in sample data != Size of the effect
in the true population
Scale Disorting (e.g., bar charts not starting with
zero)
Snapshot
…
81
83. GESIS Data Archives & Data Centers
Preserve research data and make them accessible for
reuse.
Competencies and infrastructure
▪ e.g. https://datorium.gesis.org/xmlui/
CESSDA:
umbrella organisation for the European national data
archives (http://www.cessda.net/)
Re3data
browse data archives by topic: http://www.re3data.org/
83
DPC Digital Preservation Handbook:
http://www.dpconline.org/advice/preservationhandbook
84. Legal and regulatory framework
including open access and licenses
Incentives to share data
Credentials? Citation principles under development (see
e.g. http://www.datacite.org/).
Long term preservation strategies
software and hardware changes, documentation,
metadata and retrieval/access
Data preservation starts at an individual level
Reasons for data loss often on an individual level,
e.g. broken hardware, researchers leaving a
group.
84
86. Vasant Dhar. Data Science and Prediction. In: Communications of
the ACM, December 2013,Vol. 56, No. 12, pp. 64-73
Anand Rajaraman, Jeffrey Ullman, Jure Leskovec, Mining of
Massive Datasets, Cambridge University Press (free download)
Jeffrey Stanton, Introduction to Data Science (free download)
Steffen Staab, Data Science Course University Koblenz-Landau,
https://www.uni-koblenz-landau.de/campus-
koblenz/fb4/west/teaching/ss14/data-science/data-science1
Serious Stats,Thom Baguley
86