5  Pivoting and Joining

5.1 Introduction

This document demonstrates the use of the pandas library in Python to do pivoting and joining of datasets.

Note

If you do not have the pandas library installed then you will need to run

pip install pandas

in the Jupyter terminal to install. Remember: you only need to install once per machine (or Colab session).

import pandas as pd
# Population data from GapMinder
population = pd.read_csv("/content/pop.csv")

5.2 Pivoting Data in Python

Data come in all shapes and forms! Rare is the day when we can open a dataset for the first time and it’s ready for every type of visualization or analysis that we could want to do with it.

In addition to the wrangling we discussed in the previous chapter, there may be a need to reshape the dataset entirely. For example, the column names might be values themselves that we want to make use of.

Recall our introduction of tidy data in the previous chapter…

5.2.1 Tidy Data is Special Tabular Data

For most people, the image that comes to mind when thinking about data is indeed something tabular or spreadsheet-like in nature. Which is great!

Tabular data is a form preferred by MANY different data operations and work. However, we will want to take this one step further. In almost all data science work we want our data to be tidy

Note

A dataset is tidy if it adheres to following three characteristics:

  • Every column is a variable

  • Every row is an observation

  • Every cell is a single value

In the previous chapter you were asked to open up a GapMinder dataset here and to comment on whether this dataset was tidy or not. The answer was no, this dataset is not tidy. These datasets come with a row representing a country, each column representing a year, and each cell representing the value of the global indicator selected. To be tidy these three variables (country, year, global indicator) should each have their own column, instead of the year variable taking values as the column headers.

5.2.2 Wide to Long Format

The GapMinder dataset is an example of what’s commonly referred to as data in a wide format. To make this dataset tidy we aim for a dataset with columns for country, year, and global indicator (e.g. population). Three columns is many fewer than the current number of columns, and so we will convert this dataset from wide to long format.

Warning

It often helps to physically draw/map out what our current dataset looks like and what the look of our target dataset is, before actually trying to write any code to do this. Writing the code can be extremely easier after this exercise, and only makes future pivot operations easier.

In order to convert our dataset from wide to long format we will use .melt() (or .wide_to_long()) in pandas.

long_population = population.melt(id_vars=["country"], var_name="year", value_name="population")
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With 2-3 people around you navigate to GapMinder, download the population dataset, and convert it from wide to long format. Does the result look how you expect? Is any other wrangling necessary?

5.2.3 Long to Wide Format

Even though certain data shapes are not considered tidy, they may be more conducive to performing certain operations than other shapes. For example, what if we were interested in the change in country population between 1950 and 2010? In the original wide shape of the GapMinder data this operation would have been a simple difference of columns like below.

population["pop_diff"] = population["2010"] - population["1950"]
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Why doesn’t the above code work without further wrangling? What in the dataset needs to change for this operation to work?

In the long format of our Gapminder dataset (long_population), this operation is less straightforward. Sometimes datasets come to us in long format and to do things like the operation above we need to convert that dataset from long to wide format. We can go the reverse direction (i.e. long to wide format) with .pivot() in pandas.

wide_population = long_population.pivot(index = "country", columns = "year", values = "population")
wide_population = wide_population.reset_index()
Learn More

We haven’t spent much time discussing the index of a pandas DataFrame, but you can think of it like an address for data, or slices of data in a DataFrame. You can also think of an index (or indices) as row names, or axis labels, for your dataset. This can be useful for a number of functions in Python, and can enhance the look of results or visualizations.

However, understanding them is not critical for what we will do in Python. Furthermore, variables that are indices for a DataFrame cannot be accessed or referenced in the same way as other variables in the DataFrame. So, we will avoid their use if possible.

5.3 Joining Datasets in Python

The information you need is often spread across multiple data sets, so you will need to combine multiple data sets into one. In this chapter, we discuss strategies for combining information from multiple (tabular) data sets.

As a working example, we will use a data set of baby names collected by the Social Security Administration. Each data set in this collection contains the names of all babies born in the United States in a particular year. This data is publicly available, and a copy has been made available at https://dlsun.github.io/pods/data/names/.

5.3.1 Concatenating and Merging Data

5.3.1.1 Concatenation

Sometimes, the rows of data are spread across multiple files, and we want to combine the rows into a single data set. The process of combining rows from different data sets is known as concatenation.

Visually, to concatenate two DataFrames, we simply stack them on top of one another.

For example, suppose we want to understand how the popularity of different names evolved between 1995 and 2015. The 1995 names and the 2015 names are stored in two different files: yob1995.txt and yob2015.txt, respectively. To carry out this analysis, we will need to combine these two data sets into one.

data_dir = "http://dlsun.github.io/pods/data/names/"
names1995 = pd.read_csv(data_dir + "yob1995.txt",
                        header=None,
                        names=["Name", "Sex", "Count"])
names1995
Name Sex Count
0 Jessica F 27935
1 Ashley F 26603
2 Emily F 24378
3 Samantha F 21646
4 Sarah F 21369
... ... ... ...
26075 Zerek M 5
26076 Zhen M 5
26077 Ziggy M 5
26078 Zuberi M 5
26079 Zyon M 5

26080 rows × 3 columns

names2015 = pd.read_csv(data_dir + "yob2015.txt",
                        header=None,
                        names=["Name", "Sex", "Count"])
names2015
Name Sex Count
0 Emma F 20455
1 Olivia F 19691
2 Sophia F 17417
3 Ava F 16378
4 Isabella F 15617
... ... ... ...
33116 Zykell M 5
33117 Zyking M 5
33118 Zykir M 5
33119 Zyrus M 5
33120 Zyus M 5

33121 rows × 3 columns

To concatenate the two, we use the pd.concat() function, which accepts a list of pandas objects (DataFrames or Series) and concatenates them.

pd.concat([names1995, names2015])
Name Sex Count
0 Jessica F 27935
1 Ashley F 26603
2 Emily F 24378
3 Samantha F 21646
4 Sarah F 21369
... ... ... ...
33116 Zykell M 5
33117 Zyking M 5
33118 Zykir M 5
33119 Zyrus M 5
33120 Zyus M 5

59201 rows × 3 columns

  1. There is no longer any way to distinguish the 1995 data from the 2015 data. To fix this, we can add a Year column to each DataFrame before we concatenate.

  2. The indexes from the original DataFrames are preserved in the concatenated DataFrame. (To see this, observe that the last index in the DataFrame is about 33000, which corresponds to the number of rows in names2015, even though there are 59000 rows in the DataFrame.) That means that there are two rows with an index of 0, two rows with an index of 1, and so on. To force pandas to generate a completely new index for this DataFrame, ignoring the indices from the original DataFrames, we specify ignore_index=True.

names1995["Year"] = 1995
names2015["Year"] = 2015
names = pd.concat([names1995, names2015], ignore_index=True)
names
Name Sex Count Year
0 Jessica F 27935 1995
1 Ashley F 26603 1995
2 Emily F 24378 1995
3 Samantha F 21646 1995
4 Sarah F 21369 1995
... ... ... ... ...
59196 Zykell M 5 2015
59197 Zyking M 5 2015
59198 Zykir M 5 2015
59199 Zyrus M 5 2015
59200 Zyus M 5 2015

59201 rows × 4 columns

Now this is a DataFrame we can use!

5.3.1.2 Merging (a.k.a Joining)

More commonly, the data sets that we want to combine actually contain different information about the same observations. In other words, instead of stacking the DataFrames on top of each other, as in concatenation, we want to stack them next to each other. The process of combining columns or variables from different data sets is known as merging or joining.

The observations may be in a different order in the two data sets, so merging is not as simple as placing the two DataFrames side-by-side.

Merging is an operation on two DataFrames that returns a third DataFrame. By convention, the first DataFrame is referred to as the one on the “left”, while the second DataFrame is the one on the “right”.

This naming convention is reflected in the syntax of the .merge() function in pandas. In the code below, the “left” DataFrame, names1995, is quite literally on the left in the code, while the “right” DataFrame, names2015, is to the right. We also specify the variables to match across the two DataFrames.

names1995.merge(names2015, on=["Name", "Sex"])
Name Sex Count_x Year_x Count_y Year_y
0 Jessica F 27935 1995 1587 2015
1 Ashley F 26603 1995 3424 2015
2 Emily F 24378 1995 11786 2015
3 Samantha F 21646 1995 5340 2015
4 Sarah F 21369 1995 4521 2015
... ... ... ... ... ... ...
15675 Zephan M 5 1995 23 2015
15676 Zeppelin M 5 1995 70 2015
15677 Zerek M 5 1995 5 2015
15678 Ziggy M 5 1995 44 2015
15679 Zyon M 5 1995 148 2015

15680 rows × 6 columns

The most important component of merging two datasets is the presence of at least one key variable that both datasets share. This variable is sometimes referred to as an ID variable. It’s this variable that we will want to merge on, i.e. use to combine the two datasets intelligently.

The variables that we joined on (Name and Sex) appear once in the final DataFrame. The variable Count, which we did not join on, appears twice—since there was a column called Count in both of the original DataFrames. Notice that pandas automatically appended the suffix _x to the name of the variable from the left DataFrame and _y to the one from the right DataFrame. We can customize the suffixes by specifying the suffixes= parameter.

names1995.merge(names2015, on=["Name", "Sex"], suffixes=("1995", "2015"))
Name Sex Count1995 Year1995 Count2015 Year2015
0 Jessica F 27935 1995 1587 2015
1 Ashley F 26603 1995 3424 2015
2 Emily F 24378 1995 11786 2015
3 Samantha F 21646 1995 5340 2015
4 Sarah F 21369 1995 4521 2015
... ... ... ... ... ... ...
15675 Zephan M 5 1995 23 2015
15676 Zeppelin M 5 1995 70 2015
15677 Zerek M 5 1995 5 2015
15678 Ziggy M 5 1995 44 2015
15679 Zyon M 5 1995 148 2015

15680 rows × 6 columns

In the code above, we assumed that the columns that we joined on had the same names in the two data sets. What if they had different names? For example, suppose the variable had been called Sex in one data set and Gender in the other. We can specify which variables to use from the left and right data sets using the left_on= and right_on= parameters.

# Create new DataFrames where the column names are different
names2015_ = names2015.rename({"Sex": "Gender"}, axis=1)

# This is how you merge them.
names1995.merge(
    names2015_,
    left_on=("Name", "Sex"),
    right_on=("Name", "Gender")
)
Name Sex Count_x Year_x Gender Count_y Year_y
0 Jessica F 27935 1995 F 1587 2015
1 Ashley F 26603 1995 F 3424 2015
2 Emily F 24378 1995 F 11786 2015
3 Samantha F 21646 1995 F 5340 2015
4 Sarah F 21369 1995 F 4521 2015
... ... ... ... ... ... ... ...
15675 Zephan M 5 1995 M 23 2015
15676 Zeppelin M 5 1995 M 70 2015
15677 Zerek M 5 1995 M 5 2015
15678 Ziggy M 5 1995 M 44 2015
15679 Zyon M 5 1995 M 148 2015

15680 rows × 7 columns

5.3.1.3 One-to-One and Many-to-One Relationships

In the example above, there was at most one combination of Name and Sex in the 2015 data set for each combination of Name and Sex in the 1995 data set. These two data sets are thus said to have a one-to-one relationship. The same would be true of combining two GapMinder datasets.

However, two data sets need not have a one-to-one relationship! Two datasets could have a many-to-one relationship. In general, it’s extremely important to think carefully about what variables each of your two datasets have to begin with, and what variables you want your merged dataset to have…and what that merged dataset will represent with respect to your data.

5.3.1.4 Many-to-Many Relationships: A Cautionary Tale

It is also possible for multiple rows in the left DataFrame to match multiple rows in the right DataFrame. In this case, the two data sets are said to have a many-to-many relationship. Many-to-many joins can lead to misleading analyses, so it is important to exercise caution when working with many-to-many relationships.

For example, in the baby names data set, the Name variable is not uniquely identifying. For example, there are both males and females with the name “Jessie”.

jessie1995 = names1995[names1995["Name"] == "Jessie"]
jessie1995
Name Sex Count Year
248 Jessie F 1138 1995
16047 Jessie M 903 1995 
jessie2015 = names2015[names2015["Name"] == "Jessie"]
jessie2015
Name Sex Count Year
615 Jessie F 469 2015
20009 Jessie M 233 2015

If we join these two DataFrames on Name, then we will end up with a many-to-many join, since each “Jessie” row in the 1995 data will be paired with each “Jessie” row in the 2015 data.

jessie1995.merge(jessie2015, on=["Name"])
Name Sex_x Count_x Year_x Sex_y Count_y Year_y
0 Jessie F 1138 1995 F 469 2015
1 Jessie F 1138 1995 M 233 2015
2 Jessie M 903 1995 F 469 2015
3 Jessie M 903 1995 M 233 2015

Notice that Jessie ends up appearing four times:

  • Female Jessies from 1995 are matched with female Jessies from 2015. (Good!)
  • Male Jessies from 1995 are matched with male Jessies from 2015. (Good!)
  • Female Jessies from 1995 are matched with male Jessies from 2015. (This is perhaps undesirable.)
  • Male Jessies from 1995 are matched with female Jessies from 2015. (Also unexpected and undesirable.)

If we had used a data set like this to determine the number of Jessies in 1995, then we would end up with the wrong answer, since we would have double-counted both female and male Jessies as a result of the many-to-many join. This is why it is important to exercise caution when working with (potential) many-to-many relationships.

5.3.2 Types of Joins

Above, we saw how to merge (or join) two data sets by matching on certain variables. But what happens when a row in one DataFrame has no match in the other?

First, let’s investigate how pandas handles this situation by default. The name “Nevaeh”, which is “heaven” spelled backwards, took after Sonny Sandoval of the band P.O.D. gave his daughter the name in 2000. Let’s look at how common this name was five years earlier and five years after.

data_dir = "http://dlsun.github.io/pods/data/names/"

names1995 = pd.read_csv(data_dir + "yob1995.txt",
                        header=None, names=["Name", "Sex", "Count"])
names2005 = pd.read_csv(data_dir + "yob2005.txt",
                        header=None, names=["Name", "Sex", "Count"])
names1995[names1995.Name == "Nevaeh"]
Name Sex Count 
names2005[names2005.Name == "Nevaeh"]
Name Sex Count
68 Nevaeh F 4552
21353 Nevaeh M 56

In 1995, there were no girls (at least fewer than 5) named Nevaeh; just eight years later, there were over 4500 girls (and even 56 boys) with the name. It seems like Sonny Sandoval had a huge effect.

What happens to the name “Nevaeh” when we merge the two data sets?

names = names1995.merge(names2005, on=["Name", "Sex"])
names[names.Name == "Nevaeh"]
Name Sex Count_x Count_y

By default, pandas only includes combinations that are present in both DataFrames. If it cannot find a match for a row in one DataFrame, then the combination is simply dropped.

But in this context, the fact that a name does not appear in one data set is informative. It means that no babies were born in that year with that name. We might want to include names that appeared in only one of the two DataFrames, rather than just the names that appeared in both.

There are four types of joins, distinguished by whether they include the rows from the left DataFrame, the right DataFrame, both, or neither:

  1. inner join (default): only values that are present in both DataFrames are included in the result
  2. outer join: any value that appears in either DataFrame is included in the result
  3. left join: any value that appears in the left DataFrame is included in the result, whether or not it appears in the right DataFrame
  4. right join: any value that appears in the right DataFrame is included in the result, whether or not it appears in the left DataFrame.

One way to visualize the different types of joins is using Venn diagrams. The shaded region indicates which rows that are included in the output. For example, only rows that appear in both the left and right DataFrames are included in the output of an inner join.

In pandas, the join type is specified using the how= argument.

Now let’s look at the examples of each of these types of joins.

# inner join
names_inner = names1995.merge(names2005, on=["Name", "Sex"], how="inner")
names_inner
Name Sex Count_x Count_y
0 Jessica F 27935 8108
1 Ashley F 26603 13270
2 Emily F 24378 23930
3 Samantha F 21646 13633
4 Sarah F 21369 11527
... ... ... ... ...
19119 Zeppelin M 5 7
19120 Zerek M 5 8
19121 Zhen M 5 7
19122 Ziggy M 5 6
19123 Zyon M 5 102

19124 rows × 4 columns

# outer join
names_outer = names1995.merge(names2005, on=["Name", "Sex"], how="outer")
names_outer
Name Sex Count_x Count_y
0 Jessica F 27935.0 8108.0
1 Ashley F 26603.0 13270.0
2 Emily F 24378.0 23930.0
3 Samantha F 21646.0 13633.0
4 Sarah F 21369.0 11527.0
... ... ... ... ...
39490 Zymiere M NaN 5.0
39491 Zyrell M NaN 5.0
39492 Zyrian M NaN 5.0
39493 Zyshon M NaN 5.0
39494 Zytavious M NaN 5.0

39495 rows × 4 columns

Names like “Zyrell” and “Zyron” appeared in the 2005 data but not the 1995 data. For this reason, their count in 1995 is NaN. In general, there will be missing values in DataFrames that result from an outer join. Any time a value appears in one DataFrame but not the other, there will be NaNs in the columns from the DataFrame missing that value.

names_inner.isnull().sum()
Name       0
Sex        0
Count_x    0
Count_y    0
dtype: int64

Left and right joins preserve data from one DataFrame but not the other. For example, if we were trying to calculate the percentage change for each name from 1995 to 2005, we would want to include all of the names that appeared in the 1995 data. If the name did not appear in the 2005 data, then that is informative.

# left join
names_left = names1995.merge(names2005, on=["Name", "Sex"], how="left")
names_left
Name Sex Count_x Count_y
0 Jessica F 27935 8108.0
1 Ashley F 26603 13270.0
2 Emily F 24378 23930.0
3 Samantha F 21646 13633.0
4 Sarah F 21369 11527.0
... ... ... ... ...
26075 Zerek M 5 8.0
26076 Zhen M 5 7.0
26077 Ziggy M 5 6.0
26078 Zuberi M 5 NaN
26079 Zyon M 5 102.0

26080 rows × 4 columns

The result of the left join has NaNs in the columns from the right DataFrame.

names_left.isnull().sum()
Name          0
Sex           0
Count_x       0
Count_y    6956
dtype: int64

The result of the right join, on the other hand, has NaNs in the column from the left DataFrame.

# right join
names_right = names1995.merge(names2005, on=["Name", "Sex"], how="right")
names_right
Name Sex Count_x Count_y
0 Emily F 24378.0 23930
1 Emma F 5041.0 20335
2 Madison F 9775.0 19562
3 Abigail F 7821.0 15747
4 Olivia F 7624.0 15691
... ... ... ... ...
32534 Zymiere M NaN 5
32535 Zyrell M NaN 5
32536 Zyrian M NaN 5
32537 Zyshon M NaN 5
32538 Zytavious M NaN 5

32539 rows × 4 columns

names_right.isnull().sum()
Name           0
Sex            0
Count_x    13415
Count_y        0
dtype: int64
Check In

Download a second GapMinder dataset and merge it with the population dataset from above. Did you have to pivot first? Which order of operations makes the most sense? Is your resulting dataset tidy?

Practice Activity

Click here to solve a riddle using data manipulation.