Python: Getting Started with Data Analysis

Analysis with Programming has recently been syndicated to Planet Python. And as a first post being a contributing blog on the said site, I would like to share how to get started with data analysis on Python. Specifically, I would like to do the following:

1. Importing the data
   • Importing CSV file both locally and from the web;
2. Data transformation;
3. Descriptive statistics of the data;
4. Hypothesis testing
   • One-sample t test;
5. Visualization; and
6. Creating custom function.

Importing the data

This is the crucial step, we need to import the data in order to proceed with the succeeding analysis. And often times data are in CSV format, if not, at least can be converted to CSV format. In Python we can do this using the following codes:

	import pandas as pd
	# Reading data locally
	df = pd.read_csv('/Users/al-ahmadgaidasaad/Documents/d.csv')
	# Reading data from web
	data_url = "https://raw.githubusercontent.com/alstat/Analysis-with-Programming/master/2014/Python/Numerical-Descriptions-of-the-Data/data.csv"
	df = pd.read_csv(data_url)

view raw pygets1.py hosted with ❤ by GitHub

To read CSV file locally, we need the pandas module which is a python data analysis library. The read_csv function can read data both locally and from the web.

Data transformation

Now that we have the data in the workspace, next is to do transformation. Statisticians and scientists often do this step to remove unnecessary data not included in the analysis. Let's view the data first:

	# Head of the data
	print df.head()
	# OUTPUT
	Abra Apayao Benguet Ifugao Kalinga
	0 1243 2934 148 3300 10553
	1 4158 9235 4287 8063 35257
	2 1787 1922 1955 1074 4544
	3 17152 14501 3536 19607 31687
	4 1266 2385 2530 3315 8520
	# Tail of the data
	print df.tail()
	# OUTPUT
	Abra Apayao Benguet Ifugao Kalinga
	74 2505 20878 3519 19737 16513
	75 60303 40065 7062 19422 61808
	76 6311 6756 3561 15910 23349
	77 13345 38902 2583 11096 68663
	78 2623 18264 3745 16787 16900

view raw pygets2.py hosted with ❤ by GitHub

To R programmers, above is the equivalent of print(head(df)) which prints the first six rows of the data, and print(tail(df)) -- the last six rows of the data, respectively. In Python, however, the number of rows for head of the data by default is 5 unlike in R, which is 6. So that the equivalent of the R code head(df, n = 10) in Python, is df.head(n = 10). Same goes for the tail of the data.

Column and row names of the data are extracted using the colnames and rownames functions in R, respectively. In Python, we extract it using the columns and index attributes. That is,

	# Extracting column names
	print df.columns
	# OUTPUT
	Index([u'Abra', u'Apayao', u'Benguet', u'Ifugao', u'Kalinga'], dtype='object')
	# Extracting row names or the index
	print df.index
	# OUTPUT
	Int64Index([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78], dtype='int64')

view raw pygets3.py hosted with ❤ by GitHub

Transposing the data is obtain using the T method,

	# Transpose data
	print df.T
	# OUTPUT
	0 1 2 3 4 5 6 7 8 9 \
	Abra 1243 4158 1787 17152 1266 5576 927 21540 1039 5424
	Apayao 2934 9235 1922 14501 2385 7452 1099 17038 1382 10588
	Benguet 148 4287 1955 3536 2530 771 2796 2463 2592 1064
	Ifugao 3300 8063 1074 19607 3315 13134 5134 14226 6842 13828
	Kalinga 10553 35257 4544 31687 8520 28252 3106 36238 4973 40140
	... 69 70 71 72 73 74 75 76 77 \
	Abra ... 12763 2470 59094 6209 13316 2505 60303 6311 13345
	Apayao ... 37625 19532 35126 6335 38613 20878 40065 6756 38902
	Benguet ... 2354 4045 5987 3530 2585 3519 7062 3561 2583
	Ifugao ... 9838 17125 18940 15560 7746 19737 19422 15910 11096
	Kalinga ... 65782 15279 52437 24385 66148 16513 61808 23349 68663
	78
	Abra 2623
	Apayao 18264
	Benguet 3745
	Ifugao 16787
	Kalinga 16900

view raw pygets4.py hosted with ❤ by GitHub

Other transformations such as sort can be done using sort attribute. Now let's extract a specific column. In Python, we do it using either iloc or ix attributes, but ix is more robust and thus I prefer it. Assuming we want the head of the first column of the data, we have

	print df.ix[:, 0].head()
	# OUTPUT
	0 1243
	1 4158
	2 1787
	3 17152
	4 1266
	Name: Abra, dtype: int64

view raw pygets5.py hosted with ❤ by GitHub

By the way, the indexing in Python starts with 0 and not 1. To slice the index and first three columns of the 11th to 21st rows, run the following

	print df.ix[10:20, 0:3]
	# OUTPUT
	Abra Apayao Benguet
	10 981 1311 2560
	11 27366 15093 3039
	12 1100 1701 2382
	13 7212 11001 1088
	14 1048 1427 2847
	15 25679 15661 2942
	16 1055 2191 2119
	17 5437 6461 734
	18 1029 1183 2302
	19 23710 12222 2598
	20 1091 2343 2654

view raw pygets6.py hosted with ❤ by GitHub

Which is equivalent to print df.ix[10:20, ['Abra', 'Apayao', 'Benguet']]

To drop a column in the data, say columns 1 (Apayao) and 2 (Benguet), use the drop attribute. That is,

	print df.drop(df.columns[[1, 2]], axis = 1).head()
	# OUTPUT
	Abra Ifugao Kalinga
	0 1243 3300 10553
	1 4158 8063 35257
	2 1787 1074 4544
	3 17152 19607 31687
	4 1266 3315 8520

view raw pygets7.py hosted with ❤ by GitHub

axis argument above tells the function to drop with respect to columns, if axis = 0, then the function drops with respect to rows.

Descriptive Statistics

Next step is to do descriptive statistics for preliminary analysis of our data using the describe attribute:

	print df.describe()
	# OUTPUT
	Abra Apayao Benguet Ifugao Kalinga
	count 79.000000 79.000000 79.000000 79.000000 79.000000
	mean 12874.379747 16860.645570 3237.392405 12414.620253 30446.417722
	std 16746.466945 15448.153794 1588.536429 5034.282019 22245.707692
	min 927.000000 401.000000 148.000000 1074.000000 2346.000000
	25% 1524.000000 3435.500000 2328.000000 8205.000000 8601.500000
	50% 5790.000000 10588.000000 3202.000000 13044.000000 24494.000000
	75% 13330.500000 33289.000000 3918.500000 16099.500000 52510.500000
	max 60303.000000 54625.000000 8813.000000 21031.000000 68663.000000

view raw pygets8.py hosted with ❤ by GitHub

Hypothesis Testing

Python has a great package for statistical inference. And that's the stats library of scipy. The one sample t-test is implemented in ttest_1samp function. So that, if we want to test the mean of the Abra's volume of palay production against the null hypothesis with 15000 assumed population mean of the volume of palay production, we have

	from scipy import stats as ss
	# Perform one sample t-test using 1500 as the true mean
	print ss.ttest_1samp(a = df.ix[:, 'Abra'], popmean = 15000)
	# OUTPUT
	(-1.1281738488299586, 0.26270472069109496)

view raw pygets9.py hosted with ❤ by GitHub

The values returned are tuple of the following values:

• t : float or array
      t-statistic
• prob : float or array
      two-tailed p-value

From the above numerical output, we see that the p-value = 0.2627 is greater than $\alpha=0.05$, hence there is no sufficient evidence to conclude that the average volume of palay production is not equal to 15000. Applying this test for all variables against the population mean 15000 volume of production, we have

	print ss.ttest_1samp(a = df, popmean = 15000)
	# OUTPUT
	(array([ -1.12817385, 1.07053437, -65.81425599, -4.564575 , 6.17156198]),
	array([ 2.62704721e-01, 2.87680340e-01, 4.15643528e-70,
	1.83764399e-05, 2.82461897e-08]))

view raw pygets10.py hosted with ❤ by GitHub

The first array returned is the t-statistic of the data, and the second array is the corresponding p-values.

Visualization

There are several module for visualization in Python, and the most popular one is the matplotlib library. To mention few, we have bokeh and seaborn modules as well to choose from. In my previous post, I've demonstrated the matplotlib package which has the following graphic for box-whisker plot,

	# Import the module for plotting
	import matplotlib.pyplot as plt
	plt.show(df.plot(kind = 'box'))

view raw pygets11.py hosted with ❤ by GitHub

Now plotting using pandas module can beautify the above plot into the theme of the popular R plotting package, the ggplot. To use the ggplot theme just add one more line to the above code,

	import matplotlib.pyplot as plt
	pd.options.display.mpl_style = 'default' # Sets the plotting display theme to ggplot2
	df.plot(kind = 'box')

view raw pygets12.py hosted with ❤ by GitHub

And you'll have the following,

Even neater than the default matplotlib.pyplot theme. But in this post, I would like to introduce the seaborn module which is a statistical data visualization library. So that, we have the following

	# Import the seaborn library
	import seaborn as sns
	# Do the boxplot
	plt.show(sns.boxplot(df, widths = 0.5, color = "pastel"))

view raw pygets13.py hosted with ❤ by GitHub

Sexy boxplot, scroll down for more.

plt.show(sns.violinplot(df, widths = 0.5, color = "pastel"))

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plt.show(sns.distplot(df.ix[:,2], rug = True, bins = 15))

view raw pygets15.py hosted with ❤ by GitHub

	with sns.axes_style("white"):
	plt.show(sns.jointplot(df.ix[:,1], df.ix[:,2], kind = "kde"))

view raw pygets16.py hosted with ❤ by GitHub

plt.show(sns.lmplot("Benguet", "Ifugao", df))

view raw pygets17.py hosted with ❤ by GitHub

Creating custom function

To define a custom function in Python, we use the def function. For example, say we define a function that will add two numbers, we do it as follows,

	def add_2int(x, y):
	return x + y
	print add_2int(2, 2)
	# OUTPUT
	4

view raw pygets18.py hosted with ❤ by GitHub

By the way, in Python indentation is important. Use indentation for scope of the function, which in R we do it with braces {...}. Now here's an algorithm from my previous post,

1. Generate samples of size 10 from Normal distribution with $\mu$ = 3 and $\sigma^2$ = 5;
2. Compute the $\bar{x}$ and $\bar{x}\mp z_{\alpha/2}\displaystyle\frac{\sigma}{\sqrt{n}}$ using the 95% confidence level;
3. Repeat the process 100 times; then
4. Compute the percentage of the confidence intervals containing the true mean.

Coding this in Python we have,

	import numpy as np
	import scipy.stats as ss
	def case(n = 10, mu = 3, sigma = np.sqrt(5), p = 0.025, rep = 100):
	m = np.zeros((rep, 4))
	for i in range(rep):
	norm = np.random.normal(loc = mu, scale = sigma, size = n)
	xbar = np.mean(norm)
	low = xbar - ss.norm.ppf(q = 1 - p) * (sigma / np.sqrt(n))
	up = xbar + ss.norm.ppf(q = 1 - p) * (sigma / np.sqrt(n))
	if (mu > low) & (mu < up):
	rem = 1
	else:
	rem = 0
	m[i, :] = [xbar, low, up, rem]
	inside = np.sum(m[:, 3])
	per = inside / rep
	desc = "There are " + str(inside) + " confidence intervals that contain " \
	"the true mean (" + str(mu) + "), that is " + str(per) + " percent of the total CIs"
	return {"Matrix": m, "Decision": desc}

view raw pyvsr3.py hosted with ❤ by GitHub

Above code might be easy to read, but it's slow in replication. Below is the improvement of the above code, thanks to Python gurus, see 16 Comments on my previous post.

	import numpy as np
	import scipy.stats as ss
	def case2(n = 10, mu = 3, sigma = np.sqrt(5), p = 0.025, rep = 100):
	scaled_crit = ss.norm.ppf(q = 1 - p) * (sigma / np.sqrt(n))
	norm = np.random.normal(loc = mu, scale = sigma, size = (rep, n))
	xbar = norm.mean(1)
	low = xbar - scaled_crit
	up = xbar + scaled_crit
	rem = (mu > low) & (mu < up)
	m = np.c_[xbar, low, up, rem]
	inside = np.sum(m[:, 3])
	per = inside / rep
	desc = "There are " + str(inside) + " confidence intervals that contain " \
	"the true mean (" + str(mu) + "), that is " + str(per) + " percent of the total CIs"
	return {"Matrix": m, "Decision": desc}

view raw pyvsr8.py hosted with ❤ by GitHub

Update

For those who are interested in the ipython notebook of this article, please click here. This article was converted to ipython notebook by of Nuttens Claude.

Data Source

• Philippine Bureau of Agricultural Statistics

Reference

1. Pandas, Scipy, and Seaborn Documentations.
2. Wes McKinney & PyData Development Team (2014). pandas: powerful Python data analysis toolkit.