• Recognize common file formats
• Categorize data by its variable type
• Build awareness of issues with data faithfulness and develop targeted solutions

In the past few lectures, we’ve learned that pandas is a toolkit to restructure, modify, and explore a dataset. What we haven’t yet touched on is how to make these data transformation decisions. When we receive a new set of data from the “real world,” how do we know what processing we should do to convert this data into a usable form?

Data cleaning, also called data wrangling, is the process of transforming raw data to facilitate subsequent analysis. It is often used to address issues like:

• Unclear structure or formatting
• Missing or corrupted values
• Unit conversions
• …and so on

Exploratory Data Analysis (EDA) is the process of understanding a new dataset. It is an open-ended, informal analysis that involves familiarizing ourselves with the variables present in the data, discovering potential hypotheses, and identifying potential issues with the data. This last point can often motivate further data cleaning to address any problems with the dataset’s format; because of this, EDA and data cleaning are often thought of as an “infinite loop,” with each process driving the other.

In this lecture, we will consider the key properties of data to consider when performing data cleaning and EDA. In doing so, we’ll develop a “checklist” of sorts for you to consider when approaching a new dataset. Throughout this process, we’ll build a deeper understanding of this early (but very important!) stage of the data science lifecycle.

## 5.1 Structure

### 5.1.1 File Format

In the past two pandas lectures, we briefly touched on the idea of file format: the way data is encoded in a file for storage. Specifically, our elections and babynames datasets were stored and loaded as CSVs:

import pandas as pd
pd.read_csv("data/elections.csv").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

CSVs, which stand for Comma-Separated Values, are a common tabular data format. To better understand the properties of a CSV, let’s take a look at the first few rows of the raw data file to see what it looks like before being loaded into a DataFrame.

Year,Candidate,Party,Popular vote,Result,%

1824,Andrew Jackson,Democratic-Republican,151271,loss,57.21012204

1828,Andrew Jackson,Democratic,642806,win,56.20392707


Each row, or record, in the data is delimited by a newline. Each column, or field, in the data is delimited by a comma (hence, comma-separated!).

Another common file type is the TSV (Tab-Separated Values). In a TSV, records are still delimited by a newline, while fields are delimited by \t tab character. A TSV can be loaded into pandas using pd.read_csv() with the delimiter parameter: pd.read_csv("file_name.tsv", delimiter="\t"). A raw TSV file is shown below.

ï»¿Year Candidate   Party   Popular vote    Result  %

1824    Andrew Jackson  Democratic-Republican   151271  loss    57.21012204

1824    John Quincy Adams   Democratic-Republican   113142  win 42.78987796

1828    Andrew Jackson  Democratic  642806  win 56.20392707


JSON (JavaScript Object Notation) files behave similarly to Python dictionaries. They can be loaded into pandas using pd.read_json. A raw JSON is shown below.

[

{

"Year": 1824,

"Candidate": "Andrew Jackson",

"Party": "Democratic-Republican",

"Popular vote": 151271,

"Result": "loss",

"%": 57.21012204

},


### 5.1.2 Variable Types

After loading data into a file, it’s a good idea to take the time to understand what pieces of information are encoded in the dataset. In particular, we want to identify what variable types are present in our data. Broadly speaking, we can categorize variables into one of two overarching types.

Quantitative variables describe some numeric quantity or amount. We can sub-divide quantitative data into:

• Continuous quantitative variables: numeric data that can be measured on a continuous scale to arbitrary precision. Continuous variables do not have a strict set of possible values – they can be recorded to any number of decimal places. For example, weights, GPA, or CO2 concentrations
• Discrete quantitative variables: numeric data that can only take on a finite set of possible values. For example, someone’s age or number of siblings.

Qualitative variables, also known as categorical variables, describe data that isn’t measuring some quantity or amount. The sub-categories of categorical data are:

• Ordinal qualitative variables: categories with ordered levels. Specifically, ordinal variables are those where the difference between levels has no consistent, quantifiable meaning. For example, a Yelp rating or set of income brackets.
• Nominal qualitative variables: categories with no specific order. For example, someone’s political affiliation or Cal ID number.

### 5.1.3 Primary and Foreign Keys

Last time, we introduced .merge as the pandas method for joining multiple DataFrames together. In our discussion of joins, we touched on the idea of using a “key” to determine what rows should be merged from each table. Let’s take a moment to examine this idea more closely.

The primary key is the column or set of columns in a table that determine the values of the remaining columns. It can be thought of as the unique identifier for each individual row in the table. For example, a table of Data 100 students might use each student’s Cal ID as the primary key.

Cal ID Name Major
0 3034619471 Oski Data Science
1 3035619472 Ollie Computer Science
2 3025619473 Orrie Data Science
3 3046789372 Ollie Economics

The foreign key is the column or set of columns in a table that reference primary keys in other tables. Knowing a dataset’s foreign keys can be useful when assigning the left_on and right_on parameters of .merge. In the table of office hour tickets below, "Cal ID" is a foreign key referencing the previous table.

OH Request Cal ID Question
0 1 3034619471 HW 2 Q1
1 2 3035619472 HW 2 Q3
2 3 3025619473 Lab 3 Q4
3 4 3035619472 HW 2 Q7

## 5.2 Granularity, Scope, and Temporality

After understanding the structure of the dataset, the next task is to determine what exactly the data represents. We’ll do so by considering the data’s granularity, scope, and temporality.

The granularity of a dataset is what a single row represents. You can also think of it as the level of detail included in the data. To determine the data’s granularity, ask: what does each row in the dataset represent? Fine-grained data contains a high level of detail, with a single row representing a small individual unit. For example, each record may represent one person. Coarse-grained data is encoded such that a single row represents a large individual unit – for example, each record may represent a group of people.

The scope of a dataset is the subset of the population covered by the data. If we were investigating student performance in Data Science courses, a dataset with narrow scope might encompass all students enrolled in Data 100; a dataset with expansive scope might encompass all students in California.

The temporality of a dataset describes the time period over which the data was collected. To fully understand the temporality of the data, it may be necessary to standardize timezones or inspect recurring time-based trends in the data (Do patterns recur in 24-hour patterns? Over the course of a month? Seasonally?).

## 5.3 Faithfulness

At this stage in our data cleaning and EDA workflow, we’ve achieved quite a lot: we’ve identified how our data is structured, come to terms with what information it encodes, and gained insight as to how it was generated. Throughout this process, we should always recall the original intent of our work in Data Science – to use data to better understand and model the real world. To achieve this goal, we need to ensure that the data we use is faithful to reality; that is, that our data accurately captures the “real world.”

Data used in research or industry is often “messy” – there may be errors or inaccuracies that impact the faithfulness of the dataset. Signs that data may not be faithful include:

• Unrealistic or “incorrect” values, such as negative counts, locations that don’t exist, or dates set in the future
• Violations of obvious dependencies, like an age that does not match a birthday
• Clear signs that data was entered by hand, which can lead to spelling errors or fields that are incorrectly shifted
• Signs of data falsification, such as fake email addresses or repeated use of the same names
• Duplicated records or fields containing the same information

A common issue encountered with real-world datasets is that of missing data. One strategy to resolve this is to simply drop any records with missing values from the dataset. This does, however, introduce the risk of inducing biases – it is possible that the missing or corrupt records may be systemically related to some feature of interest in the data.

Another method to address missing data is to perform imputation: infer the missing values using other data available in the dataset. There is a wide variety of imputation techniques that can be implemented; some of the most common are listed below.

• Average imputation: replace missing values with the average value for that field
• Hot deck imputation: replace missing values with some random value
• Regression imputation: develop a model to predict missing values
• Multiple imputation: replace missing values with multiple random values

Regardless of the strategy used to deal with missing data, we should think carefully about why particular records or fields may be missing – this can help inform whether or not the absence of these values is signficant in some meaningful way.

# 6 EDA Demo: Tuberculosis in the United States

Now, let’s follow this data-cleaning and EDA workflow to see what can we say about the presence of Tuberculosis in the United States!

We will examine the data included in the original CDC article published in 2021.

## 6.1 CSVs and Field Names

Suppose Table 1 was saved as a CSV file located in data/cdc_tuberculosis.csv.

We can then explore the CSV (which is a text file, and does not contain binary-encoded data) in many ways: 1. Using a text editor like emacs, vim, VSCode, etc. 2. Opening the CSV directly in DataHub (read-only), Excel, Google Sheets, etc. 3. The Python file object 4. pandas, using pd.read_csv()

1, 2. Let’s start with the first two so we really solidify the idea of a CSV as rectangular data (i.e., tabular data) stored as comma-separated values.

1. Next, let’s try using the Python file object. Let’s check out the first three lines:
Code
with open("data/cdc_tuberculosis.csv", "r") as f:
i = 0
for row in f:
print(row)
i += 1
if i > 3:
break
,No. of TB cases,,,TB incidence,,

U.S. jurisdiction,2019,2020,2021,2019,2020,2021

Total,"8,900","7,173","7,860",2.71,2.16,2.37

Alabama,87,72,92,1.77,1.43,1.83


Whoa, why are there blank lines interspaced between the lines of the CSV?

You may recall that all line breaks in text files are encoded as the special newline character \n. Python’s print() prints each string (including the newline), and an additional newline on top of that.

If you’re curious, we can use the repr() function to return the raw string with all special characters:

Code
with open("data/cdc_tuberculosis.csv", "r") as f:
i = 0
for row in f:
print(repr(row)) # print raw strings
i += 1
if i > 3:
break
',No. of TB cases,,,TB incidence,,\n'
'U.S. jurisdiction,2019,2020,2021,2019,2020,2021\n'
'Total,"8,900","7,173","7,860",2.71,2.16,2.37\n'
'Alabama,87,72,92,1.77,1.43,1.83\n'
1. Finally, let’s see the tried-and-true Data 100 approach: pandas.
Code
tb_df = pd.read_csv("data/cdc_tuberculosis.csv")
tb_df.head()
Unnamed: 0 No. of TB cases Unnamed: 2 Unnamed: 3 TB incidence Unnamed: 5 Unnamed: 6
0 U.S. jurisdiction 2019 2020 2021 2019.00 2020.00 2021.00
1 Total 8,900 7,173 7,860 2.71 2.16 2.37
2 Alabama 87 72 92 1.77 1.43 1.83
3 Alaska 58 58 58 7.91 7.92 7.92
4 Arizona 183 136 129 2.51 1.89 1.77

Wait, what’s up with the “Unnamed” column names? And the first row, for that matter?

Congratulations – you’re ready to wrangle your data. Because of how things are stored, we’ll need to clean the data a bit to name our columns better.

A reasonable first step is to identify the row with the right header. The pd.read_csv() function (documentation) has the convenient header parameter:

Code
tb_df = pd.read_csv("data/cdc_tuberculosis.csv", header=1) # row index
tb_df.head(5)
U.S. jurisdiction 2019 2020 2021 2019.1 2020.1 2021.1
0 Total 8,900 7,173 7,860 2.71 2.16 2.37
1 Alabama 87 72 92 1.77 1.43 1.83
2 Alaska 58 58 58 7.91 7.92 7.92
3 Arizona 183 136 129 2.51 1.89 1.77
4 Arkansas 64 59 69 2.12 1.96 2.28

Wait…but now we can’t differentiate betwen the “Number of TB cases” and “TB incidence” year columns. pandas has tried to make our lives easier by automatically adding “.1” to the latter columns, but this doesn’t help us as humans understand the data.

We can do this manually with df.rename() (documentation):

Code
rename_dict = {'2019': 'TB cases 2019',
'2020': 'TB cases 2020',
'2021': 'TB cases 2021',
'2019.1': 'TB incidence 2019',
'2020.1': 'TB incidence 2020',
'2021.1': 'TB incidence 2021'}
tb_df = tb_df.rename(columns=rename_dict)
tb_df.head(5)
U.S. jurisdiction TB cases 2019 TB cases 2020 TB cases 2021 TB incidence 2019 TB incidence 2020 TB incidence 2021
0 Total 8,900 7,173 7,860 2.71 2.16 2.37
1 Alabama 87 72 92 1.77 1.43 1.83
2 Alaska 58 58 58 7.91 7.92 7.92
3 Arizona 183 136 129 2.51 1.89 1.77
4 Arkansas 64 59 69 2.12 1.96 2.28

## 6.2 Record Granularity

You might already be wondering: What’s up with that first record?

Row 0 is what we call a rollup record, or summary record. It’s often useful when displaying tables to humans. The granularity of record 0 (Totals) vs the rest of the records (States) is different.

Okay, EDA step two. How was the rollup record aggregated?

Let’s check if Total TB cases is the sum of all state TB cases. If we sum over all rows, we should get 2x the total cases in each of our TB cases by year (why?).

Code
tb_df.sum(axis=0)
U.S. jurisdiction    TotalAlabamaAlaskaArizonaArkansasCaliforniaCol...
TB cases 2019        8,9008758183642,111666718245583029973261085237...
TB cases 2020        7,1737258136591,706525417194122219282169239376...
TB cases 2021        7,8609258129691,750585443194992281064255127494...
TB incidence 2019                                               109.94
TB incidence 2020                                                93.09
TB incidence 2021                                               102.94
dtype: object

Whoa, what’s going on? Check out the column types:

Code
tb_df.dtypes
U.S. jurisdiction     object
TB cases 2019         object
TB cases 2020         object
TB cases 2021         object
TB incidence 2019    float64
TB incidence 2020    float64
TB incidence 2021    float64
dtype: object

Looks like those commas are causing all TB cases to be read as the object datatype, or storage type (close to the Python string datatype), so pandas is concatenating strings instead of adding integers.

Fortunately read_csv also has a thousands parameter (https://pandas.pydata.org/docs/reference/api/pandas.read_csv.html):

Code
# improve readability: chaining method calls with outer parentheses/line breaks
tb_df = (
.rename(columns=rename_dict)
)
tb_df.head(5)
U.S. jurisdiction TB cases 2019 TB cases 2020 TB cases 2021 TB incidence 2019 TB incidence 2020 TB incidence 2021
0 Total 8900 7173 7860 2.71 2.16 2.37
1 Alabama 87 72 92 1.77 1.43 1.83
2 Alaska 58 58 58 7.91 7.92 7.92
3 Arizona 183 136 129 2.51 1.89 1.77
4 Arkansas 64 59 69 2.12 1.96 2.28
Code
tb_df.sum()
U.S. jurisdiction    TotalAlabamaAlaskaArizonaArkansasCaliforniaCol...
TB cases 2019                                                    17800
TB cases 2020                                                    14346
TB cases 2021                                                    15720
TB incidence 2019                                               109.94
TB incidence 2020                                                93.09
TB incidence 2021                                               102.94
dtype: object

The Total TB cases look right. Phew!

Let’s just look at the records with state-level granularity:

Code
state_tb_df = tb_df[1:]
state_tb_df.head(5)
U.S. jurisdiction TB cases 2019 TB cases 2020 TB cases 2021 TB incidence 2019 TB incidence 2020 TB incidence 2021
1 Alabama 87 72 92 1.77 1.43 1.83
2 Alaska 58 58 58 7.91 7.92 7.92
3 Arizona 183 136 129 2.51 1.89 1.77
4 Arkansas 64 59 69 2.12 1.96 2.28
5 California 2111 1706 1750 5.35 4.32 4.46

## 6.3 Gather More Data: Census

U.S. Census population estimates source (2019), source (2020-2021).

Running the below cells cleans the data. There are a few new methods here: * df.convert_dtypes() (documentation) conveniently converts all float dtypes into ints and is out of scope for the class. * df.drop_na() (documentation) will be explained in more detail next time.

Code
# 2010s census data
census_2010s_df = (
census_2010s_df
.reset_index()
.drop(columns=["index", "Census", "Estimates Base"])
.rename(columns={"Unnamed: 0": "Geographic Area"})
.convert_dtypes()                 # "smart" converting of columns, use at your own risk
.dropna()                         # we'll introduce this next time
)
census_2010s_df['Geographic Area'] = census_2010s_df['Geographic Area'].str.strip('.')

# with pd.option_context('display.min_rows', 30): # shows more rows
#     display(census_2010s_df)

census_2010s_df.head(5)
Geographic Area 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019
0 United States 309321666 311556874 313830990 315993715 318301008 320635163 322941311 324985539 326687501 328239523
1 Northeast 55380134 55604223 55775216 55901806 56006011 56034684 56042330 56059240 56046620 55982803
2 Midwest 66974416 67157800 67336743 67560379 67745167 67860583 67987540 68126781 68236628 68329004
3 South 114866680 116006522 117241208 118364400 119624037 120997341 122351760 123542189 124569433 125580448
4 West 72100436 72788329 73477823 74167130 74925793 75742555 76559681 77257329 77834820 78347268

Occasionally, you will want to modify code that you have imported. To reimport those modifications you can either use the python importlib library:

from importlib import reload
reload(utils)

or use iPython magic which will intelligently import code when files change:

%load_ext autoreload
%autoreload 2
Code
# census 2020s data
census_2020s_df = (
census_2020s_df
.reset_index()
.drop(columns=["index", "Unnamed: 1"])
.rename(columns={"Unnamed: 0": "Geographic Area"})
.convert_dtypes()                 # "smart" converting of columns, use at your own risk
.dropna()                         # we'll introduce this next time
)
census_2020s_df['Geographic Area'] = census_2020s_df['Geographic Area'].str.strip('.')

census_2020s_df.head(5)
Geographic Area 2020 2021 2022
0 United States 331511512 332031554 333287557
1 Northeast 57448898 57259257 57040406
2 Midwest 68961043 68836505 68787595
3 South 126450613 127346029 128716192
4 West 78650958 78589763 78743364

## 6.4 Joining Data on Primary Keys

Time to merge! Here we use the DataFrame method df1.merge(right=df2, ...) on DataFrame df1 (documentation). Contrast this with the function pd.merge(left=df1, right=df2, ...) (documentation). Feel free to use either.

Code
# merge TB dataframe with two US census dataframes
tb_census_df = (
tb_df
.merge(right=census_2010s_df,
left_on="U.S. jurisdiction", right_on="Geographic Area")
.merge(right=census_2020s_df,
left_on="U.S. jurisdiction", right_on="Geographic Area")
)
tb_census_df.head(5)
U.S. jurisdiction TB cases 2019 TB cases 2020 TB cases 2021 TB incidence 2019 TB incidence 2020 TB incidence 2021 Geographic Area_x 2010 2011 ... 2014 2015 2016 2017 2018 2019 Geographic Area_y 2020 2021 2022
0 Alabama 87 72 92 1.77 1.43 1.83 Alabama 4785437 4799069 ... 4841799 4852347 4863525 4874486 4887681 4903185 Alabama 5031362 5049846 5074296
1 Alaska 58 58 58 7.91 7.92 7.92 Alaska 713910 722128 ... 736283 737498 741456 739700 735139 731545 Alaska 732923 734182 733583
2 Arizona 183 136 129 2.51 1.89 1.77 Arizona 6407172 6472643 ... 6730413 6829676 6941072 7044008 7158024 7278717 Arizona 7179943 7264877 7359197
3 Arkansas 64 59 69 2.12 1.96 2.28 Arkansas 2921964 2940667 ... 2967392 2978048 2989918 3001345 3009733 3017804 Arkansas 3014195 3028122 3045637
4 California 2111 1706 1750 5.35 4.32 4.46 California 37319502 37638369 ... 38596972 38918045 39167117 39358497 39461588 39512223 California 39501653 39142991 39029342

5 rows × 22 columns

This is a little unwieldy. We could either drop the unneeded columns now, or just merge on smaller census DataFrames. Let’s do the latter.

Code
# try merging again, but cleaner this time
tb_census_df = (
tb_df
.merge(right=census_2010s_df[["Geographic Area", "2019"]],
left_on="U.S. jurisdiction", right_on="Geographic Area")
.drop(columns="Geographic Area")
.merge(right=census_2020s_df[["Geographic Area", "2020", "2021"]],
left_on="U.S. jurisdiction", right_on="Geographic Area")
.drop(columns="Geographic Area")
)
tb_census_df.head(5)
U.S. jurisdiction TB cases 2019 TB cases 2020 TB cases 2021 TB incidence 2019 TB incidence 2020 TB incidence 2021 2019 2020 2021
0 Alabama 87 72 92 1.77 1.43 1.83 4903185 5031362 5049846
1 Alaska 58 58 58 7.91 7.92 7.92 731545 732923 734182
2 Arizona 183 136 129 2.51 1.89 1.77 7278717 7179943 7264877
3 Arkansas 64 59 69 2.12 1.96 2.28 3017804 3014195 3028122
4 California 2111 1706 1750 5.35 4.32 4.46 39512223 39501653 39142991

## 6.5 Reproducing Data: Compute Incidence

Let’s recompute incidence to make sure we know where the original CDC numbers came from.

From the CDC report: TB incidence is computed as “Cases per 100,000 persons using mid-year population estimates from the U.S. Census Bureau.”

If we define a group as 100,000 people, then we can compute the TB incidence for a given state population as

$\text{TB incidence} = \frac{\text{TB cases in population}}{\text{groups in population}} = \frac{\text{TB cases in population}}{\text{population}/100000}$

$= \frac{\text{TB cases in population}}{\text{population}} \times 100000$

Let’s try this for 2019:

Code
tb_census_df["recompute incidence 2019"] = tb_census_df["TB cases 2019"]/tb_census_df["2019"]*100000
tb_census_df.head(5)
U.S. jurisdiction TB cases 2019 TB cases 2020 TB cases 2021 TB incidence 2019 TB incidence 2020 TB incidence 2021 2019 2020 2021 recompute incidence 2019
0 Alabama 87 72 92 1.77 1.43 1.83 4903185 5031362 5049846 1.774357
1 Alaska 58 58 58 7.91 7.92 7.92 731545 732923 734182 7.928425
2 Arizona 183 136 129 2.51 1.89 1.77 7278717 7179943 7264877 2.514179
3 Arkansas 64 59 69 2.12 1.96 2.28 3017804 3014195 3028122 2.120747
4 California 2111 1706 1750 5.35 4.32 4.46 39512223 39501653 39142991 5.342651

Awesome!!!

Let’s use a for-loop and Python format strings to compute TB incidence for all years. Python f-strings are just used for the purposes of this demo, but they’re handy to know when you explore data beyond this course (Python documentation).

Code
# recompute incidence for all years
for year in [2019, 2020, 2021]:
tb_census_df[f"recompute incidence {year}"] = tb_census_df[f"TB cases {year}"]/tb_census_df[f"{year}"]*100000
tb_census_df.head(5)
U.S. jurisdiction TB cases 2019 TB cases 2020 TB cases 2021 TB incidence 2019 TB incidence 2020 TB incidence 2021 2019 2020 2021 recompute incidence 2019 recompute incidence 2020 recompute incidence 2021
0 Alabama 87 72 92 1.77 1.43 1.83 4903185 5031362 5049846 1.774357 1.431024 1.821838
1 Alaska 58 58 58 7.91 7.92 7.92 731545 732923 734182 7.928425 7.913519 7.899949
2 Arizona 183 136 129 2.51 1.89 1.77 7278717 7179943 7264877 2.514179 1.894165 1.775667
3 Arkansas 64 59 69 2.12 1.96 2.28 3017804 3014195 3028122 2.120747 1.957405 2.27864
4 California 2111 1706 1750 5.35 4.32 4.46 39512223 39501653 39142991 5.342651 4.318807 4.470788

These numbers look pretty close!!! There are a few errors in the hundredths place, particularly in 2021. It may be useful to further explore reasons behind this discrepancy.

Code
tb_census_df.describe()
TB cases 2019 TB cases 2020 TB cases 2021 TB incidence 2019 TB incidence 2020 TB incidence 2021 2019 2020 2021 recompute incidence 2019 recompute incidence 2020 recompute incidence 2021
count 51.000000 51.000000 51.000000 51.000000 51.000000 51.000000 5.100000e+01 5.100000e+01 5.100000e+01 51.000000 51.000000 51.000000
mean 174.509804 140.647059 154.117647 2.102549 1.782941 1.971961 6.436069e+06 6.500226e+06 6.510423e+06 2.104969 1.784655 1.969928
std 341.738752 271.055775 286.781007 1.498745 1.337414 1.478468 7.360660e+06 7.408168e+06 7.394300e+06 1.500236 1.338263 1.474929
min 1.000000 0.000000 2.000000 0.170000 0.000000 0.210000 5.787590e+05 5.776050e+05 5.794830e+05 0.172783 0.000000 0.210049
25% 25.500000 29.000000 23.000000 1.295000 1.210000 1.235000 1.789606e+06 1.820311e+06 1.844920e+06 1.297485 1.211433 1.233905
50% 70.000000 67.000000 69.000000 1.800000 1.520000 1.700000 4.467673e+06 4.507445e+06 4.506589e+06 1.808606 1.521612 1.694502
75% 180.500000 139.000000 150.000000 2.575000 1.990000 2.220000 7.446805e+06 7.451987e+06 7.502811e+06 2.577577 1.993607 2.219482
max 2111.000000 1706.000000 1750.000000 7.910000 7.920000 7.920000 3.951222e+07 3.950165e+07 3.914299e+07 7.928425 7.913519 7.899949

## 6.6 Bonus EDA: Reproducing the reported statistic

How do we reproduce that reported statistic in the original CDC report?

Reported TB incidence (cases per 100,000 persons) increased 9.4%, from 2.2 during 2020 to 2.4 during 2021 but was lower than incidence during 2019 (2.7). Increases occurred among both U.S.-born and non–U.S.-born persons.

This is TB incidence computed across the entire U.S. population! How do we reproduce this * We need to reproduce the “Total” TB incidences in our rolled record. * But our current tb_census_df only has 51 entries (50 states plus Washington, D.C.). There is no rolled record. * What happened…?

Let’s get exploring!

Before we keep exploring, we’ll set all indexes to more meaningful values, instead of just numbers that pertained to some row at some point. This will make our cleaning slightly easier.

Code
tb_df = tb_df.set_index("U.S. jurisdiction")
tb_df.head(5)
TB cases 2019 TB cases 2020 TB cases 2021 TB incidence 2019 TB incidence 2020 TB incidence 2021
U.S. jurisdiction
Total 8900 7173 7860 2.71 2.16 2.37
Alabama 87 72 92 1.77 1.43 1.83
Alaska 58 58 58 7.91 7.92 7.92
Arizona 183 136 129 2.51 1.89 1.77
Arkansas 64 59 69 2.12 1.96 2.28
Code
census_2010s_df = census_2010s_df.set_index("Geographic Area")
census_2010s_df.head(5)
2010 2011 2012 2013 2014 2015 2016 2017 2018 2019
Geographic Area
United States 309321666 311556874 313830990 315993715 318301008 320635163 322941311 324985539 326687501 328239523
Northeast 55380134 55604223 55775216 55901806 56006011 56034684 56042330 56059240 56046620 55982803
Midwest 66974416 67157800 67336743 67560379 67745167 67860583 67987540 68126781 68236628 68329004
South 114866680 116006522 117241208 118364400 119624037 120997341 122351760 123542189 124569433 125580448
West 72100436 72788329 73477823 74167130 74925793 75742555 76559681 77257329 77834820 78347268
Code
census_2020s_df = census_2020s_df.set_index("Geographic Area")
census_2020s_df.head(5)
2020 2021 2022
Geographic Area
United States 331511512 332031554 333287557
Northeast 57448898 57259257 57040406
Midwest 68961043 68836505 68787595
South 126450613 127346029 128716192
West 78650958 78589763 78743364

It turns out that our merge above only kept state records, even though our original tb_df had the “Total” rolled record:

Code
tb_df.head()
TB cases 2019 TB cases 2020 TB cases 2021 TB incidence 2019 TB incidence 2020 TB incidence 2021
U.S. jurisdiction
Total 8900 7173 7860 2.71 2.16 2.37
Alabama 87 72 92 1.77 1.43 1.83
Alaska 58 58 58 7.91 7.92 7.92
Arizona 183 136 129 2.51 1.89 1.77
Arkansas 64 59 69 2.12 1.96 2.28

Recall that merge by default does an inner merge by default, meaning that it only preserves keys that are present in both DataFrames.

The rolled records in our census dataframes have different Geographic Area fields, which was the key we merged on:

Code
census_2010s_df.head(5)
2010 2011 2012 2013 2014 2015 2016 2017 2018 2019
Geographic Area
United States 309321666 311556874 313830990 315993715 318301008 320635163 322941311 324985539 326687501 328239523
Northeast 55380134 55604223 55775216 55901806 56006011 56034684 56042330 56059240 56046620 55982803
Midwest 66974416 67157800 67336743 67560379 67745167 67860583 67987540 68126781 68236628 68329004
South 114866680 116006522 117241208 118364400 119624037 120997341 122351760 123542189 124569433 125580448
West 72100436 72788329 73477823 74167130 74925793 75742555 76559681 77257329 77834820 78347268

The Census DataFrame has several rolled records. The aggregate record we are looking for actually has the Geographic Area named “United States”.

One straightforward way to get the right merge is to rename the value itself. Because we now have the Geographic Area index, we’ll use df.rename() (documentation):

Code
# rename rolled record for 2010s
census_2010s_df.rename(index={'United States':'Total'}, inplace=True)
census_2010s_df.head(5)
2010 2011 2012 2013 2014 2015 2016 2017 2018 2019
Geographic Area
Total 309321666 311556874 313830990 315993715 318301008 320635163 322941311 324985539 326687501 328239523
Northeast 55380134 55604223 55775216 55901806 56006011 56034684 56042330 56059240 56046620 55982803
Midwest 66974416 67157800 67336743 67560379 67745167 67860583 67987540 68126781 68236628 68329004
South 114866680 116006522 117241208 118364400 119624037 120997341 122351760 123542189 124569433 125580448
West 72100436 72788329 73477823 74167130 74925793 75742555 76559681 77257329 77834820 78347268
Code
# same, but for 2020s rename rolled record
census_2020s_df.rename(index={'United States':'Total'}, inplace=True)
census_2020s_df.head(5)
2020 2021 2022
Geographic Area
Total 331511512 332031554 333287557
Northeast 57448898 57259257 57040406
Midwest 68961043 68836505 68787595
South 126450613 127346029 128716192
West 78650958 78589763 78743364

Next let’s rerun our merge. Note the different chaining, because we are now merging on indexes (df.merge() documentation).

Code
tb_census_df = (
tb_df
.merge(right=census_2010s_df[["2019"]],
left_index=True, right_index=True)
.merge(right=census_2020s_df[["2020", "2021"]],
left_index=True, right_index=True)
)
tb_census_df.head(5)
TB cases 2019 TB cases 2020 TB cases 2021 TB incidence 2019 TB incidence 2020 TB incidence 2021 2019 2020 2021
Total 8900 7173 7860 2.71 2.16 2.37 328239523 331511512 332031554
Alabama 87 72 92 1.77 1.43 1.83 4903185 5031362 5049846
Alaska 58 58 58 7.91 7.92 7.92 731545 732923 734182
Arizona 183 136 129 2.51 1.89 1.77 7278717 7179943 7264877
Arkansas 64 59 69 2.12 1.96 2.28 3017804 3014195 3028122

Finally, let’s recompute our incidences:

Code
# recompute incidence for all years
for year in [2019, 2020, 2021]:
tb_census_df[f"recompute incidence {year}"] = tb_census_df[f"TB cases {year}"]/tb_census_df[f"{year}"]*100000
tb_census_df.head(5)
TB cases 2019 TB cases 2020 TB cases 2021 TB incidence 2019 TB incidence 2020 TB incidence 2021 2019 2020 2021 recompute incidence 2019 recompute incidence 2020 recompute incidence 2021
Total 8900 7173 7860 2.71 2.16 2.37 328239523 331511512 332031554 2.711435 2.163726 2.367245
Alabama 87 72 92 1.77 1.43 1.83 4903185 5031362 5049846 1.774357 1.431024 1.821838
Alaska 58 58 58 7.91 7.92 7.92 731545 732923 734182 7.928425 7.913519 7.899949
Arizona 183 136 129 2.51 1.89 1.77 7278717 7179943 7264877 2.514179 1.894165 1.775667
Arkansas 64 59 69 2.12 1.96 2.28 3017804 3014195 3028122 2.120747 1.957405 2.27864

We reproduced the total U.S. incidences correctly!

We’re almost there. Let’s revisit the quote:

Reported TB incidence (cases per 100,000 persons) increased 9.4%, from 2.2 during 2020 to 2.4 during 2021 but was lower than incidence during 2019 (2.7). Increases occurred among both U.S.-born and non–U.S.-born persons.

Recall that percent change from $$A$$ to $$B$$ is computed as $$\text{percent change} = \frac{B - A}{A} \times 100$$.

Code
incidence_2020 = tb_census_df.loc['Total', 'recompute incidence 2020']
incidence_2020
2.1637257652759883
Code
incidence_2021 = tb_census_df.loc['Total', 'recompute incidence 2021']
incidence_2021
2.3672448914298068
Code
difference = (incidence_2021 - incidence_2020)/incidence_2020 * 100
difference
9.405957511804143