# Gain Statistical Insights into Your Data¶

Woodwork provides methods on your DataFrames to allow you to use the typing information stored by Woodwork to better understand your data.

Follow along to learn how to use Woodwork’s statistical methods on a DataFrame of retail data while demonstrating the full capabilities of the functions.

[1]:

import pandas as pd
import numpy as np

df.ww

[1]:

Physical Type Logical Type Semantic Tag(s)
Column
order_product_id category Categorical ['index']
order_id category Categorical ['category']
product_id category Categorical ['category']
description string NaturalLanguage []
quantity int64 Integer ['numeric']
order_date datetime64[ns] Datetime ['time_index']
unit_price float64 Double ['numeric']
customer_name category Categorical ['category']
country category Categorical ['category']
total float64 Double ['numeric']
cancelled bool Boolean []

## DataFrame.ww.describe¶

Use df.ww.describe() to calculate statistics for the columns in a DataFrame, returning the results in the format of a pandas DataFrame with the relevant calculations done for each column. Note, that both nan and (nan, nan) values contribute to nan_count for LatLong logical types

[2]:

df.ww.describe()

[2]:

order_id product_id description quantity order_date unit_price customer_name country total cancelled
physical_type category category string int64 datetime64[ns] float64 category category float64 bool
logical_type Categorical Categorical NaturalLanguage Integer Datetime Double Categorical Categorical Double Boolean
semantic_tags {category} {category} {} {numeric} {time_index} {numeric} {category} {category} {numeric} {}
count 401604 401604 401604 401604.0 401604 401604.0 401604 401604 401604.0 401604
nunique 22190 3684 NaN 436.0 20460 620.0 4372 37 3946.0 NaN
nan_count 0 0 0 0 0 0 0 0 0 0
mean NaN NaN NaN 12.183273 2011-07-10 12:08:23.848567552 5.732205 NaN NaN 34.012502 NaN
mode 576339 85123A WHITE HANGING HEART T-LIGHT HOLDER 1 2011-11-14 15:27:00 2.0625 Mary Dalton United Kingdom 24.75 False
std NaN NaN NaN 250.283037 NaN 115.110658 NaN NaN 710.081161 NaN
min NaN NaN NaN -80995.0 2010-12-01 08:26:00 0.0 NaN NaN -277974.84 NaN
first_quartile NaN NaN NaN 2.0 NaN 2.0625 NaN NaN 7.0125 NaN
second_quartile NaN NaN NaN 5.0 NaN 3.2175 NaN NaN 19.305 NaN
third_quartile NaN NaN NaN 12.0 NaN 6.1875 NaN NaN 32.67 NaN
max NaN NaN NaN 80995.0 2011-12-09 12:50:00 64300.5 NaN NaN 277974.84 NaN
num_true NaN NaN NaN NaN NaN NaN NaN NaN NaN 8872
num_false NaN NaN NaN NaN NaN NaN NaN NaN NaN 392732

There are a couple things to note in the above dataframe:

• The Woodwork index, order_product_id, is not included

• We provide each column’s typing information according to Woodwork’s typing system

• Any statistics that can’t be calculated for a column, such as num_false on a Datetime are filled with NaN.

• Null values do not get counted in any of the calculations other than nunique

## DataFrame.ww.value_counts¶

Use df.ww.value_counts() to calculate the most frequent values for each column that has category as a standard tag. This returns a dictionary where each column is associated with a sorted list of dictionaries. Each dictionary contains value and count.

[3]:

df.ww.value_counts()

[3]:

{'order_product_id': [{'value': 0, 'count': 1},
{'value': 267744, 'count': 1},
{'value': 267742, 'count': 1},
{'value': 267741, 'count': 1},
{'value': 267740, 'count': 1},
{'value': 267739, 'count': 1},
{'value': 267738, 'count': 1},
{'value': 267737, 'count': 1},
{'value': 267736, 'count': 1},
{'value': 267735, 'count': 1}],
'order_id': [{'value': '576339', 'count': 542},
{'value': '579196', 'count': 533},
{'value': '580727', 'count': 529},
{'value': '578270', 'count': 442},
{'value': '573576', 'count': 435},
{'value': '567656', 'count': 421},
{'value': '567183', 'count': 392},
{'value': '575607', 'count': 377},
{'value': '571441', 'count': 364},
{'value': '570488', 'count': 353}],
'product_id': [{'value': '85123A', 'count': 2065},
{'value': '22423', 'count': 1894},
{'value': '85099B', 'count': 1659},
{'value': '47566', 'count': 1409},
{'value': '84879', 'count': 1405},
{'value': '20725', 'count': 1346},
{'value': '22720', 'count': 1224},
{'value': 'POST', 'count': 1196},
{'value': '22197', 'count': 1110},
{'value': '23203', 'count': 1108}],
'customer_name': [{'value': 'Mary Dalton', 'count': 7812},
{'value': 'Dalton Grant', 'count': 5898},
{'value': 'Jeremy Woods', 'count': 5128},
{'value': 'Jasmine Salazar', 'count': 4459},
{'value': 'James Robinson', 'count': 2759},
{'value': 'Bryce Stewart', 'count': 2478},
{'value': 'Vanessa Sanchez', 'count': 2085},
{'value': 'Laura Church', 'count': 1853},
{'value': 'Ashley Meyer', 'count': 1640}],
'country': [{'value': 'United Kingdom', 'count': 356728},
{'value': 'Germany', 'count': 9480},
{'value': 'France', 'count': 8475},
{'value': 'EIRE', 'count': 7475},
{'value': 'Spain', 'count': 2528},
{'value': 'Netherlands', 'count': 2371},
{'value': 'Belgium', 'count': 2069},
{'value': 'Switzerland', 'count': 1877},
{'value': 'Portugal', 'count': 1471},
{'value': 'Australia', 'count': 1258}]}


## DataFrame.ww.mutual_information¶

df.ww.mutual_information calculates the mutual information between all pairs of relevant columns. Certain types, like strings, can’t have mutual information calculated.

The mutual information between columns A and B can be understood as the amount of knowledge you can have about column A if you have the values of column B. The more mutual information there is between A and B, the less uncertainty there is in A knowing B, and vice versa.

[4]:

df.ww.mutual_information()

[4]:

column_1 column_2 mutual_info
0 order_id customer_name 0.886411
1 order_id product_id 0.475745
2 product_id unit_price 0.426383
3 order_id order_date 0.391906
4 product_id customer_name 0.361855
5 order_date customer_name 0.187982
6 quantity total 0.184497
7 customer_name country 0.155593
8 product_id total 0.152183
9 order_id total 0.129882
10 order_id country 0.126048
11 order_id quantity 0.114714
12 unit_price total 0.103210
13 customer_name total 0.099530
14 product_id quantity 0.088663
15 quantity customer_name 0.085515
16 quantity unit_price 0.082515
17 order_id unit_price 0.077681
18 product_id order_date 0.057175
19 total cancelled 0.044032
20 unit_price customer_name 0.041308
21 quantity cancelled 0.035528
22 product_id country 0.028569
23 country total 0.025071
24 order_id cancelled 0.022204
25 quantity country 0.021515
26 order_date country 0.010361
27 customer_name cancelled 0.006456
28 product_id cancelled 0.003769
29 country cancelled 0.003607
30 order_date unit_price 0.003180
31 order_date total 0.002625
32 unit_price country 0.002603
33 quantity order_date 0.002146
34 unit_price cancelled 0.001677
35 order_date cancelled 0.000199

### Available Parameters¶

df.ww.mutual_information provides various parameters for tuning the mutual information calculation.

• num_bins - In order to calculate mutual information on continuous data, Woodwork bins numeric data into categories. This parameter allows you to choose the number of bins with which to categorize data.

• Defaults to using 10 bins

• The more bins there are, the more variety a column will have. The number of bins used should accurately portray the spread of the data.

• nrows - If nrows is set at a value below the number of rows in the DataFrame, that number of rows is randomly sampled from the underlying data

• Defaults to using all the available rows.

• Decreasing the number of rows can speed up the mutual information calculation on a DataFrame with many rows, but you should be careful that the number being sampled is large enough to accurately portray the data.

• include_index - If set to True and an index is defined with a logical type that is valid for mutual information, the index column will be included in the mutual information output.

• Defaults to False

Now that you understand the parameters, you can explore changing the number of bins. Note—this only affects numeric columns quantity and unit_price. Increase the number of bins from 10 to 50, only showing the impacted columns.

[5]:

mi = df.ww. mutual_information()
mi[mi['column_1'].isin(['unit_price', 'quantity']) | mi['column_2'].isin(['unit_price', 'quantity'])]

[5]:

column_1 column_2 mutual_info
2 product_id unit_price 0.426383
6 quantity total 0.184497
11 order_id quantity 0.114714
12 unit_price total 0.103210
14 product_id quantity 0.088663
15 quantity customer_name 0.085515
16 quantity unit_price 0.082515
17 order_id unit_price 0.077681
20 unit_price customer_name 0.041308
21 quantity cancelled 0.035528
25 quantity country 0.021515
30 order_date unit_price 0.003180
32 unit_price country 0.002603
33 quantity order_date 0.002146
34 unit_price cancelled 0.001677
[6]:

mi = df.ww.mutual_information(num_bins = 50)
mi[mi['column_1'].isin(['unit_price', 'quantity']) | mi['column_2'].isin(['unit_price', 'quantity'])]

[6]:

column_1 column_2 mutual_info
2 product_id unit_price 0.528865
4 unit_price total 0.405555
7 quantity total 0.349243
10 order_id quantity 0.157188
13 product_id quantity 0.143938
14 order_id unit_price 0.140257
16 quantity customer_name 0.113431
17 quantity unit_price 0.105052
18 quantity cancelled 0.081334
19 unit_price customer_name 0.078942
24 quantity country 0.023758
27 order_date unit_price 0.011905
30 unit_price country 0.006311
31 quantity order_date 0.004170
34 unit_price cancelled 0.001671

In order to include the index column in the mutual information output, run the calculation with include_index=True.

[7]:

mi = df.ww.mutual_information(include_index=True)
mi[mi['column_1'].isin(['order_product_id']) | mi['column_2'].isin(['order_product_id'])]

[7]:

column_1 column_2 mutual_info
1 order_product_id order_id 0.845419
2 order_product_id customer_name 0.736457
3 order_product_id product_id 0.732680
8 order_product_id order_date 0.302856
9 order_product_id total 0.302435
10 order_product_id unit_price 0.299486
11 order_product_id quantity 0.266489
21 order_product_id country 0.093880
34 order_product_id cancelled 0.016307

## Outlier Detection with Series.ww.box_plot_dict¶

Woodwork allows for univariate outlier detection using the IQR, or interquartile range, method. This can be done on a by-column basis using the series.ww.box_plot_dict method that identifies outliers and includes the statistical data necessary for building a box and whisker plot.

[8]:

total = df.ww['total']
box_plot_dict = total.ww.box_plot_dict()

print('high bound: ', box_plot_dict['high_bound'])
print('low_bound: ', box_plot_dict['low_bound'])
print('quantiles: ', box_plot_dict['quantiles'])
print('number of low outliers: ', len(box_plot_dict['low_values']))
print('number of high outliers: ', len(box_plot_dict['high_values']))

high bound:  71.15625
low_bound:  -31.473750000000003
quantiles:  {0.0: -277974.84, 0.25: 7.0124999999999975, 0.5: 19.305, 0.75: 32.669999999999995, 1.0: 277974.84}
number of low outliers:  1922
number of high outliers:  31016


We can see that the total column in the retail dataset has many outliers, and they are skewed more towards the top of the dataset. There are around 400K rows in the dataframe, so about 8% of all values are outliers. Let’s also look at a normally distributed column of data of the same length and see what the statistics generated for it look like.

[9]:

rnd = np.random.RandomState(33)
s = pd.Series(rnd.normal(50, 10, 401604))
s.ww.init()
box_plot_dict = s.ww.box_plot_dict()
print('high bound: ', box_plot_dict['high_bound'])
print('low_bound: ', box_plot_dict['low_bound'])
print('quantiles: ', box_plot_dict['quantiles'])
print('number of low outliers: ', len(box_plot_dict['low_values']))
print('number of high outliers: ', len(box_plot_dict['high_values']))

high bound:  77.04098129791424
low_bound:  22.897953681834856
quantiles:  {0.0: 4.519658918840335, 0.25: 43.20158903786463, 0.5: 49.988236390934304, 0.75: 56.73734594188448, 1.0: 95.28094989391388}
number of low outliers:  1460
number of high outliers:  1381


With the normally distributed set of data, the likelyhood of outliers is closer to what we’d expect, around .7%.