DATA ANALYTICS REFERENCE DOCUMENT
|Document Title:||52446 - Fundamentals of Data Analysis summary document|
|Contributor(s):||Rita Raher, Gerhard van der Linde|
Details of Modification(s)
Reason for modification
|0||Draft release||Referene document to summerise module coverage||2018/10/22 10:37||Gearoid O'Gcrannaoil|
On completion of this module the learner will/should be able to:
The following is a list of topics that will likely be covered in this module. Note that the topics might not be presented in this order and might not be explicitly referenced in course materials.
Searching for data sets, file formats, data structures.
Calculating summary statistics, programmatically generating plots, histograms, scatter plots, box plots.
Character sets, search and replace, regular expressions, outlier identification.
Ordinary linear regression, classification.
Programmatically applying data analysis techniques, automating data analysis workflows.
This week you'll play a simple game of chance in Python.
Jupyter is a piece of software written in Python for displaying and presenting Python code, it's outputs and some documentation. In later lectures you will learn to create your own notebooks. For now, just watch the accompanying video, run this notebook on your own machine, and submit the result of running it in to the link below as specified in the notebook itself.
This week we'll analyse the Win a car problem.
Running the game file from link above for 10,000 cycles produces two datasets with very different outcomes.
There seems to be a clear probability advantage changing your choice once the goat was revealed.
This week we'll look at the problem that founded modern hypothesis testing.
This approach in my opinion assumes a very good grasp and knowledge of mathematics and an intuitive feel for factorials4) I could eventually figure out the flow of the math and reproduce the results but if I have to come up with the algorithm from scratch without references to the article I am afraid that might just fail.
Playing with itertools5) however and some basic python code made much more sense to me and analysing this all more from a language perspective started to make much more sense form me at least.
In : n=list(range(4)) In : n Out: [0, 1, 2, 3] In : list(iter.combinations(n,3)) Out: [(0, 1, 2), (0, 1, 3), (0, 2, 3), (1, 2, 3)] In : list(iter.permutations(n,3)) Out: [(0, 1, 2), (0, 1, 3), (0, 2, 1), (0, 2, 3), (0, 3, 1), (0, 3, 2), (1, 0, 2), (1, 0, 3), (1, 2, 0), (1, 2, 3), (1, 3, 0), (1, 3, 2), (2, 0, 1), (2, 0, 3), (2, 1, 0), (2, 1, 3), (2, 3, 0), (2, 3, 1), (3, 0, 1), (3, 0, 2), (3, 1, 0), (3, 1, 2), (3, 2, 0), (3, 2, 1)]
So essentially combinations does not repeat the same numbers and permutations cares about the order too, so repeats the numbers as long as the exact sequence is not repeated.
So then having cleared this up, it makes sense then, to me at least, that from a list of eight cups I can make 70 unique selections of 4 as confirmed by my python function.
In : len(list(iter.combinations(cups,4))) Out: 70
So the correct sequence of cups is one of the set of 70, therefore theodds of randowmly select this correct sequence is 1/70.
The last part of the notebook then explains the overlap scenario and the logic for rejecting a three out of four selection because of the overlap probabbility count of 15 item out of 70, i.e. . So even worse for 2 out of for with a 50% chance.
So testing for overlap in a set to determine the frequency of a subset to decide if the occurance can justify rejecting the null hypotheses8).
This week we'll use Bayes' theorem to analyse tests.
This week we'll look at simple linear regression and noise in simulated data.
# import the libraries we need for number crunching and plotting import numpy as np import matplotlib.pyplot as pl #generate random data for the experiment #generate a series w from zero to 20 w = np.arange(0.0, 21.0, 1.0) #generate a linear series y=mx+c using m=5 and c=10 and add some random offsets to it d = 5.0 * w + 10.0 + np.random.normal(0.0, 5.0, w.size) # find thevalues of m and c from the randowm data generated m,c=np.polyfit(w,d,1) #plot the dataset and the linear fit derived above pl.plot(w, m * w + c, 'b-', label='Best fit line') pl.plot(w,d,'k.') pl.show()
This week we'll look into Classification.
import sklearn.neighbors as nei import pandas as pd import sklearn.model_selection as mod # Load the iris data set from a URL. df = pd.read_csv("https://github.com/ianmcloughlin/datasets/raw/master/iris.csv") inputs = df[['sepal_length', 'sepal_width', 'petal_length', 'petal_width']] outputs = df['class'] knn = nei.KNeighborsClassifier(n_neighbors=5) knn.fit(inputs, outputs) knn.predict([[5.6, 2.8, 4.9, 2.0]]) n=(knn.predict(inputs) == outputs).sum() # how many out of 150 is predicted right print(n) #Split into training and test set using 'train_test_split', using a third of the set selected randomly inputs_train, inputs_test, outputs_train, outputs_test = mod.train_test_split(inputs, outputs, test_size=0.33) knn = nei.KNeighborsClassifier(n_neighbors=5) knn.fit(inputs_train, outputs_train) n=(knn.predict(inputs_test) == outputs_test).sum() print(n)
A heuristic is a rule that provides a shortcut to solving difficult problems. Heuristics are used when you have limited time and/or information to make a decision. Heuristics lead you to a good decision most of the time. Heuristics are discussed in both computer science and psychology circles.
A bat and ball cost $1.10.
The bat costs $1 more than the ball.
How much does the ball cost?
So the “obvious” answer is wrong, it is not 10c but 5c.
All roses are flowers.
Some flowers fade quickly.
Therefore some roses fade quickly.
So some roses will not necessarily form part of the some flowers collection, so as a result might not fade at all.
Linda is 31 years old, single, outspoken and very bright. She majored in philosophy. As a student she was deeply concerned with issues of discrimination and social justice and also participated in antinuclear demonstrations.
Which is more likely?
a. Linda is a bank teller.
b. Linda is a bank teller and active in the feminist movement.
Most people that answered the study chose “b”, but it's a fallacy from a mathematical perspective. B is true when A is true, so the question creates the potential for the fallacy, also the blurp suggests the answer and being a bank teller is much more likely than both….
Conjunction fallacy - The mistake is choosing the answer within another answer…
Higher chance of being right answering A.
Would you accept this gamble?
50% chance to win $150
50% chance to lose $100
Utility Theory on average win…
Most people will not take the gamble. Tipping point, twice as big gain, then people will start taking on the risk…
Risk aversion, don't like to lose…
A person who is asked “What proportion of long-distance
relationships break up within a year?” may answer as if
been asked “Do instances of swift breakups of long-distance
relationships come readily to mind?”
The availability heuristic. If asked a question, the person answering would recall recent event to answer the question and might no represent the norm, for example how many fruits eaten and think about yesterday only and l=not long term…
Sampling bias occurs when the units that are selected from the population for inclusion in your sample are not characteristic of (i.e., do not reflect) the population. This can lead to your sample being unrepresentative of the population you are interested in. For example, you want to measure how often residents in New York go to a Broadway show in a given year. Clearly, standing along Broadway and asking people as they pass by how often they went to Broadway shows in a given year would not make sense because a higher proportion of those passing by are likely to have just come out of a show. The sample would therefore be biased. For this reason, we have to think carefully about the types of sampling techniques we use when selecting units to be included in our sample. Some sampling techniques, such as convenience sampling, a type of non-probability sampling (which reflected the Broadway example above), are prone to greater bias than probability sampling techniques. We discuss sampling techniques further next.
import sqlite3 # load the SQLite library conn = sqlite3.connect('data/example.db') # open a local database file c = conn.cursor() # create a cursor c #read three csv files in person = pd.read_csv("https://github.com/ianmcloughlin/datasets/raw/master/cars-db/person.csv", index_col=0) car = pd.read_csv("https://github.com/ianmcloughlin/datasets/raw/master/cars-db/car.csv", index_col=0) county = pd.read_csv("https://github.com/ianmcloughlin/datasets/raw/master/cars-db/county.csv", index_col=0) #convert and save csv files to the database county.to_sql("county", conn) person.to_sql("person", conn) car.to_sql("car", conn) # run a query to show all the tables created above c.execute("SELECT name FROM sqlite_master WHERE type='table'") c.fetchall() # run a query with a joinbetween two tables c.execute(""" SELECT p.Name, c.Registration, p.Address FROM person as p JOIN car as c ON p.ID = c.OwnerId """) c.fetchall() # run a query with a join between three tables c.execute(""" SELECT p.Name, c.Registration, p.Address FROM person as p JOIN car as c ON p.ID = c.OwnerId JOIN county as t ON t.Name = p.Address WHERE c.Registration NOT LIKE '%-' + t.Registration + '-%' """) c.fetchall() # close the connection conn.close()
The Jupyter Notebook - How to nicely present my work
Working on the dataset
One notebook is plenty - less hassle for the reader
Note: Be more descriptive about the data when you are going through the notebook. Why is dataset interesting? Give a high level flavour about what is going on. Tell a story