• Perform advanced aggregation using .groupby()
• Use the pd.pivot_table method to contruct a pivot table
• Perform simple merges between DataFrames using pd.merge()

## 4.1 More on agg() Function

Last time, we introduced the concept of aggregating data – we familiarized ourselves with GroupBy objects and used them as tools to consolidate and summarize a DataFrame. In this lecture, we will explore some advanced .groupby methods to show just how powerful of a resource they can be for understanding our data. We will also introduce other techniques for data aggregation to provide flexibility in how we manipulate our tables.

## 4.2GroupBy(), Continued

As we learned last lecture, a groupby operation involves some combination of splitting a DataFrame into grouped subframes, applying a function, and combining the results.

For some arbitrary DataFrame df below, the code df.groupby("year").agg(sum) does the following:

• Organizes all rows with the same year into a subframe for that year.
• Creates a new DataFrame with one row representing each subframe year.
• Combines all integer rows in each subframe using the sum function.

### 4.2.1 Aggregation with lambda Functions

Throughout this note, we’ll work with the elections DataFrame.

Code
import pandas as pd

elections.head(5)
Year Candidate Party Popular vote Result %
0 1824 Andrew Jackson Democratic-Republican 151271 loss 57.210122
1 1824 John Quincy Adams Democratic-Republican 113142 win 42.789878
2 1828 Andrew Jackson Democratic 642806 win 56.203927
3 1828 John Quincy Adams National Republican 500897 loss 43.796073
4 1832 Andrew Jackson Democratic 702735 win 54.574789

What if we wish to aggregate our DataFrame using a non-standard function – for example, a function of our own design? We can do so by combining .agg with lambda expressions.

Let’s first consider a puzzle to jog our memory. We will attempt to find the Candidate from each Party with the highest % of votes.

A naive approach may be to group by the Party column and aggregate by the maximum.

elections.groupby("Party").agg(max).head(10)
Year Candidate Popular vote Result %
Party
American 1976 Thomas J. Anderson 873053 loss 21.554001
American Independent 1976 Lester Maddox 9901118 loss 13.571218
Anti-Masonic 1832 William Wirt 100715 loss 7.821583
Anti-Monopoly 1884 Benjamin Butler 134294 loss 1.335838
Citizens 1980 Barry Commoner 233052 loss 0.270182
Communist 1932 William Z. Foster 103307 loss 0.261069
Constitution 2016 Michael Peroutka 203091 loss 0.152398
Constitutional Union 1860 John Bell 590901 loss 12.639283
Democratic 2020 Woodrow Wilson 81268924 win 61.344703
Democratic-Republican 1824 John Quincy Adams 151271 win 57.210122

This approach is clearly wrong – the DataFrame claims that Woodrow Wilson won the presidency in 2020.

Why is this happening? Here, the max aggregation function is taken over every column independently. Among Democrats, max is computing:

• The most recent Year a Democratic candidate ran for president (2020)
• The Candidate with the alphabetically “largest” name (“Woodrow Wilson”)
• The Result with the alphabetically “largest” outcome (“win”)

Instead, let’s try a different approach. We will:

1. Sort the DataFrame so that rows are in descending order of %
2. Group by Party and select the first row of each groupby object

While it may seem unintuitive, sorting elections by descending order of % is extremely helpful. If we then group by Party, the first row of each groupby object will contain information about the Candidate with the highest voter %.

elections_sorted_by_percent = elections.sort_values("%", ascending=False)
elections_sorted_by_percent.head(5)
Year Candidate Party Popular vote Result %
114 1964 Lyndon Johnson Democratic 43127041 win 61.344703
91 1936 Franklin Roosevelt Democratic 27752648 win 60.978107
120 1972 Richard Nixon Republican 47168710 win 60.907806
79 1920 Warren Harding Republican 16144093 win 60.574501
133 1984 Ronald Reagan Republican 54455472 win 59.023326
elections_sorted_by_percent.groupby("Party").agg(lambda x : x.iloc[0]).head(10)

# Equivalent to the below code
# elections_sorted_by_percent.groupby("Party").agg('first').head(10)
Year Candidate Popular vote Result %
Party
American 1856 Millard Fillmore 873053 loss 21.554001
American Independent 1968 George Wallace 9901118 loss 13.571218
Anti-Masonic 1832 William Wirt 100715 loss 7.821583
Anti-Monopoly 1884 Benjamin Butler 134294 loss 1.335838
Citizens 1980 Barry Commoner 233052 loss 0.270182
Communist 1932 William Z. Foster 103307 loss 0.261069
Constitution 2008 Chuck Baldwin 199750 loss 0.152398
Constitutional Union 1860 John Bell 590901 loss 12.639283
Democratic 1964 Lyndon Johnson 43127041 win 61.344703
Democratic-Republican 1824 Andrew Jackson 151271 loss 57.210122

Notice how our code correctly determines that Lyndon Johnson from the Democratic Party has the highest voter %.

More generally, lambda functions are used to design custom aggregation functions that aren’t pre-defined by Python. The input parameter x to the lambda function is a GroupBy object. Therefore, it should make sense why lambda x : x.iloc[0] selects the first row in each groupby object.

In fact, there’s a few different ways to approach this problem. Each approach has different tradeoffs in terms of readability, performance, memory consumption, complexity, etc. We’ve given a few examples below.

Note: Understanding these alternative solutions is not required. They are given to demonstrate the vast number of problem-solving approaches in pandas.

# Using the idxmax function
best_per_party = elections.loc[elections.groupby('Party')['%'].idxmax()]
best_per_party.head(5)
Year Candidate Party Popular vote Result %
22 1856 Millard Fillmore American 873053 loss 21.554001
115 1968 George Wallace American Independent 9901118 loss 13.571218
6 1832 William Wirt Anti-Masonic 100715 loss 7.821583
38 1884 Benjamin Butler Anti-Monopoly 134294 loss 1.335838
127 1980 Barry Commoner Citizens 233052 loss 0.270182
# Using the .drop_duplicates function
best_per_party2 = elections.sort_values('%').drop_duplicates(['Party'], keep='last')
best_per_party2.head(5)
Year Candidate Party Popular vote Result %
148 1996 John Hagelin Natural Law 113670 loss 0.118219
164 2008 Chuck Baldwin Constitution 199750 loss 0.152398
110 1956 T. Coleman Andrews States' Rights 107929 loss 0.174883
147 1996 Howard Phillips Taxpayers 184656 loss 0.192045
136 1988 Lenora Fulani New Alliance 217221 loss 0.237804

### 4.2.2 Other GroupBy Features

There are many aggregation methods we can use with .agg. Some useful options are:

In fact, these (and other) aggregation functions are so common that pandas allows for writing shorthand. Instead of explicitly stating the use of .agg, we can call the function directly on the GroupBy object.

For example, the following are equivalent:

• elections.groupby("Candidate").agg(mean)
• elections.groupby("Candidate").mean()

### 4.2.3 The groupby.filter() function

Another common use for GroupBy objects is to filter data by group.

groupby.filter takes an argument $$\text{f}$$, where $$\text{f}$$ is a function that:

• Takes a GroupBy object as input
• Returns a single True or False for the entire subframe

GroupBy objects that correspond to True are returned in the final result, whereas those with a False value are not. Importantly, groupby.filter is different from groupby.agg in that the entire subframe is returned in the final DataFrame, not just a single row.

To illustrate how this happens, consider the following .filter function applied on some arbitrary data. Say we want to identify “tight” election years – that is, we want to find all rows that correspond to elections years where all candidates in that year won a similar portion of the total vote. Specifically, let’s find all rows corresponding to a year where no candidate won more than 45% of the total vote.

An equivalent way of framing this goal is to say:

• Find the years where the maximum % in that year is less than 45%
• Return all DataFrame rows that correspond to these years

For each year, we need to find the maximum % among all rows for that year. If this maximum % is lower than 45%, we will tell pandas to keep all rows corresponding to that year.

elections.groupby("Year").filter(lambda sf: sf["%"].max() < 45).head(9)
Year Candidate Party Popular vote Result %
23 1860 Abraham Lincoln Republican 1855993 win 39.699408
24 1860 John Bell Constitutional Union 590901 loss 12.639283
25 1860 John C. Breckinridge Southern Democratic 848019 loss 18.138998
26 1860 Stephen A. Douglas Northern Democratic 1380202 loss 29.522311
66 1912 Eugene V. Debs Socialist 901551 loss 6.004354
67 1912 Eugene W. Chafin Prohibition 208156 loss 1.386325
68 1912 Theodore Roosevelt Progressive 4122721 loss 27.457433
69 1912 William Taft Republican 3486242 loss 23.218466
70 1912 Woodrow Wilson Democratic 6296284 win 41.933422

What’s going on here? In this example, we’ve defined our filtering function, $$\text{f}$$, to be lambda sf: sf["%"].max() < 45. This filtering function will find the maximum "%" value among all entries in the grouped subframe, which we call sf. If the maximum value is less than 45, then the filter function will return True and all rows in that grouped subframe will appear in the final output DataFrame.

Examine the DataFrame above. Notice how, in this preview of the first 9 rows, all entries from the years 1860 and 1912 appear. This means that in 1860 and 1912, no candidate in that year won more than 45% of the total vote.

You may ask: how is the groupby.filter procedure different to the boolean filtering we’ve seen previously? Boolean filtering considers individual rows when applying a boolean condition. For example, the code elections[elections["%"] < 45] will check the "%" value of every single row in elections; if it is less than 45, then that row will be kept in the output. groupby.filter, in contrast, applies a boolean condition across all rows in a group. If not all rows in that group satisfy the condition specified by the filter, the entire group will be discarded in the output.

## 4.3 Aggregating Data with Pivot Tables

We know now that .groupby gives us the ability to group and aggregate data across our DataFrame. The examples above formed groups using just one column in the DataFrame. It’s possible to group by multiple columns at once by passing in a list of columns names to .groupby.

Let’s consider the babynames dataset from last lecture. In this problem, we will find the total number of baby names associated with each sex for each year. To do this, we’ll group by both the "Year" and "Sex" columns.

Code
import urllib.request
import os.path

data_url = "https://www.ssa.gov/oact/babynames/names.zip"
local_filename = "data/babynames.zip"
with urllib.request.urlopen(data_url) as resp, open(local_filename, 'wb') as f:

# Load data without unzipping the file
import zipfile
babynames = []
with zipfile.ZipFile(local_filename, "r") as zf:
data_files = [f for f in zf.filelist if f.filename[-3:] == "txt"]
def extract_year_from_filename(fn):
return int(fn[3:7])
for f in data_files:
year = extract_year_from_filename(f.filename)
with zf.open(f) as fp:
df = pd.read_csv(fp, names=["Name", "Sex", "Count"])
df["Year"] = year
babynames.append(df)
babynames = pd.concat(babynames)
babynames.head()
Name Sex Count Year
0 Mary F 7065 1880
1 Anna F 2604 1880
2 Emma F 2003 1880
3 Elizabeth F 1939 1880
4 Minnie F 1746 1880
# Find the total number of baby names associated with each sex for each year in the data
babynames.groupby(["Year", "Sex"])[["Count"]].agg(sum).head(6)
Count
Year Sex
1880 F 90994
M 110490
1881 F 91953
M 100737
1882 F 107847
M 113686

Notice that both "Year" and "Sex" serve as the index of the DataFrame (they are both rendered in bold). We’ve created a multindex where two different index values, the year and sex, are used to uniquely identify each row.

This isn’t the most intuitive way of representing this data – and, because multindexes have multiple dimensions in their index, they can often be difficult to use.

Another strategy to aggregate across two columns is to create a pivot table. You saw these back in Data 8. One set of values is used to create the index of the table; another set is used to define the column names. The values contained in each cell of the table correspond to the aggregated data for each index-column pair.

The best way to understand pivot tables is to see one in action. Let’s return to our original goal of summing the total number of names associated with each combination of year and sex. We’ll call the pandas .pivot_table method to create a new table.

# The pivot_table method is used to generate a Pandas pivot table
import numpy as np
babynames.pivot_table(index = "Year", columns = "Sex", values = "Count", aggfunc = np.sum).head(5)
Sex F M
Year
1880 90994 110490
1881 91953 100737
1882 107847 113686
1883 112319 104625
1884 129019 114442

Looks a lot better! Now, our DataFrame is structured with clear index-column combinations. Each entry in the pivot table represents the summed count of names for a given combination of "Year" and "Sex".

Let’s take a closer look at the code implemented above.

• index = "Year" specifies the column name in the original DataFrame that should be used as the index of the pivot table
• columns = "Sex" specifies the column name in the original DataFrame that should be used to generate the columns of the pivot table
• values = "Count" indicates what values from the original DataFrame should be used to populate the entry for each index-column combination
• aggfunc = np.sum tells pandas what function to use when aggregating the data specified by values. Here, we are summing the name counts for each pair of "Year" and "Sex"

We can even include multiple values in the index or columns of our pivot tables.

babynames_pivot = babynames.pivot_table(
index="Year",     # the rows (turned into index)
columns="Sex",    # the column values
values=["Count", "Name"],
aggfunc=max,   # group operation
)
babynames_pivot.head(6)
Count Name
Sex F M F M
Year
1880 7065 9655 Zula Zeke
1881 6919 8769 Zula Zeb
1882 8148 9557 Zula Zed
1883 8012 8894 Zula Zeno
1884 9217 9388 Zula Zollie
1885 9128 8756 Zula Zollie

## 4.4 Joining Tables

When working on data science projects, we’re unlikely to have absolutely all the data we want contained in a single DataFrame – a real-world data scientist needs to grapple with data coming from multiple sources. If we have access to multiple datasets with related information, we can join two or more tables into a single DataFrame.

To put this into practice, we’ll revisit the elections dataset.

elections.head(5)
Year Candidate Party Popular vote Result %
0 1824 Andrew Jackson Democratic-Republican 151271 loss 57.210122
1 1824 John Quincy Adams Democratic-Republican 113142 win 42.789878
2 1828 Andrew Jackson Democratic 642806 win 56.203927
3 1828 John Quincy Adams National Republican 500897 loss 43.796073
4 1832 Andrew Jackson Democratic 702735 win 54.574789

Say we want to understand the 2020 popularity of the names of each presidential candidate. To do this, we’ll need the combined data of babynames and elections.

We’ll start by creating a new column containing the first name of each presidential candidate. This will help us join each name in elections to the corresponding name data in babynames.

# This str operation splits each candidate's full name at each
# blank space, then takes just the candidiate's first name
elections["First Name"] = elections["Candidate"].str.split().str[0]
elections.head(5)
Year Candidate Party Popular vote Result % First Name
0 1824 Andrew Jackson Democratic-Republican 151271 loss 57.210122 Andrew
1 1824 John Quincy Adams Democratic-Republican 113142 win 42.789878 John
2 1828 Andrew Jackson Democratic 642806 win 56.203927 Andrew
3 1828 John Quincy Adams National Republican 500897 loss 43.796073 John
4 1832 Andrew Jackson Democratic 702735 win 54.574789 Andrew
# Here, we'll only consider babynames data from 2020
babynames_2020 = babynames[babynames["Year"]==2020]
babynames_2020.head()
Name Sex Count Year
0 Olivia F 17641 2020
1 Emma F 15656 2020
2 Ava F 13160 2020
3 Charlotte F 13065 2020
4 Sophia F 13036 2020

Now, we’re ready to join the two tables. pd.merge is the pandas method used to join DataFrames together. The left and right parameters are used to specify the DataFrames to be joined. The left_on and right_on parameters are assigned to the string names of the columns to be used when performing the join. These two on parameters tell pandas what values should act as pairing keys to determine which rows to merge across the DataFrames. We’ll talk more about this idea of a pairing key next lecture.

merged = pd.merge(left = elections, right = babynames_2020, \
left_on = "First Name", right_on = "Name")
# Notice that pandas automatically specifies Year_x and Year_y
# when both merged DataFrames have the same column name to avoid confusion