Dataframes and Series

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This chapter introduces Pandas, which is a powerful library for working with data. Pandas provides functions for reading and writing data files, exploring and analyzing data, and generating visualizations. And it provides two new types for working with data, DataFrame and Series.

We will use these tools to answer a data question: what is the average birth weight of babies in the United States? This example will demonstrate important steps in almost any data science project:

  1. Identifying data that can answer a question.

  2. Obtaining the data and loading it in Python.

  3. Checking the data and dealing with errors.

  4. Selecting relevant subsets from the data.

  5. Using histograms to visualize a distribution of values.

  6. Using summary statistics to describe the data in a way that best answers the question.

  7. Considering possible sources of error and limitations in our conclusions.

Let’s start by getting the data.

Reading the data

We’ll use data from the National Survey of Family Growth (NSFG), which is available from the National Center for Health Statistics.

To download the data, you have to agree to the Data User’s Agreement. You should read those terms carefully, but let me draw your attention to what I think is the most important one:

Make no attempt to learn the identity of any person or establishment included in these data.

NSFG respondents provide honest answers to questions of the most personal nature with the expectation that their identities will not be revealed. As ethical data scientists, we should respect their privacy and adhere to the terms of use.

Respondents to the NSFG provide general information about themselves, which is stored in the respondent file, and information about each time they have been pregnant, which is stored in the pregnancy file.

We will work with the pregnancy file, which contains one row for each pregnancy and 248 variables. Each variable represents responses to a question on the NSFG questionnaire.

The data is stored in a fixed-width format, which means that every row is the same length and each variable spans a fixed range of columns.

In addition to the data file, we also need the data dictionary, which includes the names of the variables and specifies the range of columns where each variable appears.

dict_file = '2015_2017_FemPregSetup.dct'
data_file = '2015_2017_FemPregData.dat'

Pandas can read data in most common formats, including CSV, Excel, and fixed-width format, but it cannot read the data dictionary, which is in Stata format. For that, we’ll use a Python library called parse_stata_dict.

From parse_stata_dict, we’ll import parse_stata_dict, which reads the data dictionary.

from statadict import parse_stata_dict

stata_dict = parse_stata_dict(dict_file)
stata_dict
<statadict.base.StataDict at 0x7ff25831bdd0>

The result is an object that contains

  • names, which is a list of variable names, and

  • colspecs, which is a list of tuples.

Each tuple in colspecs specifies the first and last column where a variable appears.

These values are exactly the arguments we need to use read_fwf, which is the Pandas function that reads a file in fixed-width format.

import pandas as pd

nsfg = pd.read_fwf(data_file, 
                   names=stata_dict.names, 
                   colspecs=stata_dict.colspecs)
type(nsfg)
pandas.core.frame.DataFrame

The result from read_hdf() is a DataFrame, which is the primary type Pandas uses to store data. DataFrame has a method called head() that shows the first 5 rows:

nsfg.head()
CASEID PREGORDR HOWPREG_N HOWPREG_P MOSCURRP NOWPRGDK PREGEND1 PREGEND2 HOWENDDK NBRNALIV ... SECU SEST CMINTVW CMLSTYR CMJAN3YR CMJAN4YR CMJAN5YR QUARTER PHASE INTVWYEAR
0 70627 1 NaN NaN NaN NaN 6.0 NaN NaN 1.0 ... 3 322 1394 1382 1357 1345 1333 18 1 2016
1 70627 2 NaN NaN NaN NaN 1.0 NaN NaN NaN ... 3 322 1394 1382 1357 1345 1333 18 1 2016
2 70627 3 NaN NaN NaN NaN 6.0 NaN NaN 1.0 ... 3 322 1394 1382 1357 1345 1333 18 1 2016
3 70628 1 NaN NaN NaN NaN 6.0 NaN NaN 1.0 ... 2 366 1409 1397 1369 1357 1345 23 1 2017
4 70628 2 NaN NaN NaN NaN 6.0 NaN NaN 1.0 ... 2 366 1409 1397 1369 1357 1345 23 1 2017

5 rows × 248 columns

The first column is CASEID, which is a unique identifier for each respondent. The first three rows have the same CASEID, so this respondent reported information about three pregnancies.

The second column is PREGORDR, which indicates the order of the pregnancies for each respondent, starting from 1.

We will learn more about the other variables as we go along.

In addition to methods like head, nsfg has several attributes, which are variables associated with a particular type. For example, nsfg has an attribute called shape, which is the number of rows and columns:

nsfg.shape
(9553, 248)

There are 9553 rows in this dataset, one for each pregnancy, and 248 columns, one for each variable.

nsfg also has an attribute called columns, which contains the column names:

nsfg.columns
Index(['CASEID', 'PREGORDR', 'HOWPREG_N', 'HOWPREG_P', 'MOSCURRP', 'NOWPRGDK',
       'PREGEND1', 'PREGEND2', 'HOWENDDK', 'NBRNALIV',
       ...
       'SECU', 'SEST', 'CMINTVW', 'CMLSTYR', 'CMJAN3YR', 'CMJAN4YR',
       'CMJAN5YR', 'QUARTER', 'PHASE', 'INTVWYEAR'],
      dtype='object', length=248)

The column names are stored in an Index, which is another Pandas type, similar to a list.

Based on the column names, you might be able to guess what some of the variables are, but in general you have to read the documentation.

When you work with datasets like the NSFG, it is important to read the documentation carefully. If you interpret a variable incorrectly, you can generate nonsense results and never realize it. So, before we start looking at data, let’s get familiar with the NSFG codebook, which describes every variable.

Until recently, the NSFG codebook was available in an interactive online format. Unfortunately, it is no longer available, so we have to make due with this PDF file, which contains a short description of each variable.

If you search that document for “weigh at birth” you should find these variables related to birth weight.

  • BIRTHWGT_LB1: Birthweight in Pounds - 1st baby from this pregnancy

  • BIRTHWGT_OZ1: Birthweight in Ounces - 1st baby from this pregnancy

There are similar variables for a 2nd or 3rd baby, in the case of twins or triplets. For now we will focus on the first baby from each pregnancy, and we will come back to the issue of multiple births.

Series

In many ways a DataFrame is like a Python dictionary, where the column names are the keys and the columns are the values. You can select a column from a DataFrame using the bracket operator, with a string as the key.

pounds = nsfg['BIRTHWGT_LB1']
type(pounds)
pandas.core.series.Series

The result is a Series, which is another Pandas type. In this case the Series contains the birth weight, in pounds, for each live birth.

head shows the first five values in the series, the name of the series, and the data type:

pounds.head()
0    7.0
1    NaN
2    9.0
3    6.0
4    7.0
Name: BIRTHWGT_LB1, dtype: float64

One of the values is NaN, which stands for “Not a Number”. NaN is a special value used to indicate invalid or missing data. In this example, the pregnancy did not end in live birth, so birth weight is inapplicable.

Exercise: The variable BIRTHWGT_OZ1 contains the ounces part of birth weight.

Select the column 'BIRTHWGT_OZ1' from the nsfg DataFrame and assign it to a new variable called ounces. Then display the first 5 elements of ounces.

Exercise: The Pandas types we have seen so far are DataFrame, Index, and Series. You can find the documentation of these types at:

This documentation can be overwhelming; I don’t recommend trying to read it all now. But you might want to skim it so you know where to look later.

Validation

At this point we have identified the columns we need to answer the question and assigned them to variables named pounds and ounces.

pounds = nsfg['BIRTHWGT_LB1']
ounces = nsfg['BIRTHWGT_OZ1']

Before we do anything with this data, we have to validate it. One part of validation is confirming that we are interpreting the data correctly.

We can use the value_counts method to see what values appear in pounds and how many times each value appears.

pounds.value_counts()

By default, the results are sorted with the most frequent value first, but we can use sort_index to sort them by value instead, with the lightest babies first and heaviest babies last.

pounds.value_counts().sort_index()
0.0        2
1.0       28
2.0       46
3.0       76
4.0      179
5.0      570
6.0     1644
7.0     2268
8.0     1287
9.0      396
10.0      82
11.0      17
12.0       2
13.0       1
14.0       1
98.0       2
99.0      89
Name: BIRTHWGT_LB1, dtype: int64

As we’d expect, the most frequent values are 6-8 pounds, but there are some very light babies, a few very heavy babies, and two special values, 98, and 99. According to the codebook, these values indicate that the respondent declined to answer the question (98) or did not know (99).

We can validate the results by comparing them to the codebook, which lists the values and their frequencies.

value

label

Total

.

INAPPLICABLE

2863

0-5

UNDER 6 POUNDS

901

6

6 POUNDS

1644

7

7 POUNDS

2268

8

8 POUNDS

1287

9-95

9 POUNDS OR MORE

499

98

Refused

2

99

Don’t know

89

Total

9553

The results from value_counts agree with the codebook, so we have some confidence that we are reading and interpreting the data correctly.

Exercise: In the nsfg DataFrame, the column 'OUTCOME' encodes the outcome of each pregnancy as shown below:

Value

Meaning

1

Live birth

2

Induced abortion

3

Stillbirth

4

Miscarriage

5

Ectopic pregnancy

6

Current pregnancy

Use value_counts to display the values in this column and how many times each value appears. Are the results consistent with the codebook?

Summary statistics

Another way to validate the data is with describe, which computes summary statistics like the mean, standard deviation, minimum, and maximum.

Here are the results for pounds.

pounds.describe()
count    6690.000000
mean        8.008819
std        10.771360
min         0.000000
25%         6.000000
50%         7.000000
75%         8.000000
max        99.000000
Name: BIRTHWGT_LB1, dtype: float64

count is the number of values, not including NaN. For this variable, there are 6690 value that are not NaN.

mean and std are the mean and standard deviation. min and max are the minimum and maximum values, and in between are the 25th, 50th, and 75th percentiles. The 50th percentile is the median.

The mean is about 8.05, but that doesn’t mean much because it includes the special values 98 and 99. Before we can really compute the mean, we have to replace those values with NaN to identify them as missing data.

The replace() method does what we want:

import numpy as np

pounds_clean = pounds.replace([98, 99], np.nan)

replace takes a list of the values we want to replace and the value we want to replace them with. np.nan means we are getting the special value NaN from the NumPy library, which is imported as np.

The result from replace() is a new Series, which I assign to pounds_clean. If we run describe again, we see that count includes only the valid values.

pounds_clean.describe()
count    6599.000000
mean        6.754357
std         1.383268
min         0.000000
25%         6.000000
50%         7.000000
75%         8.000000
max        14.000000
Name: BIRTHWGT_LB1, dtype: float64

The mean of the new series is about 6.7 pounds. Remember that the mean of the original series was more than 8 pounds. It makes a big difference when you remove a few 99-pound babies!

Exercise: Use describe to summarize ounces.
Then use replace to replace the special values 98 and 99 with NaN, and assign the result to ounces_clean. Run describe again. How much does this cleaning affect the results?

Series arithmetic

Now we want to combine pounds and ounces into a single Series that contains total birth weight. Arithmetic operators work with Series objects; so, for example, to convert pounds to ounces, we could write

pounds * 16

Then we could add in ounces like this

pounds * 16 + ounces

Exercise: Use pounds_clean and ounces_clean to compute the total birth weight expressed in kilograms (there are roughly 2.2 pounds per kilogram). What is the mean birth weight in kilograms?

Exercise: For each pregnancy in the NSFG dataset, the variable 'AGECON' encodes the respondent’s age at conception, and 'AGEPREG' the respondent’s age at the end of the pregnancy.

Both variables are recorded as integers with two implicit decimal places, so the value 2575 means that the respondent’s age was 25.75.

  • Read the documentation of these variables. Are there any special values we have to deal with?

  • Select 'AGECON' and 'AGEPREG', divide them by 100, and assign them to variables named agecon and agepreg.

  • Compute the difference, which is an estimate of the duration of the pregnancy.

  • Use .describe() to compute the mean duration and other summary statistics.

If the mean length of pregnancy seems short, remember that this dataset includes all pregnancies, not just the ones that ended in live birth.

Histograms

Let’s get back to the original queston: what is the average birth weight for babies in the U.S.?
As an answer we could take the results from the previous section and compute the mean:

pounds_clean = pounds.replace([98, 99], np.nan)
ounces_clean = ounces.replace([98, 99], np.nan)

birth_weight = pounds_clean + ounces_clean / 16
birth_weight.mean()
7.180217889908257

But it is risky to compute a summary statistic, like the mean, before we look at the whole distribution of values.

A distribution is a set of possible values and their frequencies. One way to visualize a distribution is a histogram, which shows values on the x axis and their frequencies on the y axis.

Series provides a hist method that makes histograms. And we can use Matplotlib to label the axes.

import matplotlib.pyplot as plt

birth_weight.hist(bins=30)
plt.xlabel('Birth weight in pounds')
plt.ylabel('Number of live births')
plt.title('Distribution of U.S. birth weight');
_images/07_dataframes_66_0.png

The keyword argument, bins, tells hist to divide the range of weights into 30 intervals, called bins, and count how many values fall in each bin. The x axis is birth weight in pounds; the y axis is the number of births in each bin.

The distribution looks a little like a bell curve, but the tail is longer on the left than on the right; that is, there are more light babies than heavy babies. That makes sense, because the distribution includes some babies that were born preterm.

Exercise: hist takes keyword arguments that specify the type and appearance of the histogram. Find the documentation of hist and see if you can figure out how to plot the histogram as an unfilled line.

Exercise: As we saw in a previous exercise, the NSFG dataset includes a column called AGECON that records age at conception for each pregnancy.

  • Select this column from the DataFrame and divide by 100 to convert it to years.

  • Plot the histogram of these values with 20 bins.

  • Label the x and y axes appropriately.

Boolean series

We have seen that the distribution of birth weights is skewed to the left; that is, there are more light babies than heavy ones and they are farther from the mean. That’s because preterm babies tend to be lighter. The most common duration for pregnancy is 39 weeks, which is “full term”; “preterm” is usually defined to be less than 37 weeks.

To see which babies are preterm, we can use PRGLNGTH, which records pregnancy length in weeks and compute it to 37.

preterm = (nsfg['PRGLNGTH'] < 37)
preterm.dtype
dtype('bool')

When you compare a Series to a value, the result is a Boolean Series; that is, each element is a Boolean value, True or False. In this case, it’s True for each preterm baby and False otherwise. We can use head to see the first 5 elements.

preterm.head()
0    False
1     True
2    False
3    False
4    False
Name: PRGLNGTH, dtype: bool

If you compute the sum of a Boolean Series, it treats True as 1 and False as 0, so the sum is the number of True values, which is the number of preterm babies, about 3700.

preterm.sum()
3675

If you compute the mean of a Boolean Series, you get the fraction of True values. In this case, it’s about 0.38; that is, about 38% of the pregnancies are less than 37 weeks.

preterm.mean()
0.38469590704490736

However, this result might be misleading because it includes all pregnancy outcomes, not just live births. We can create another Boolean Series to indicate which pregnancies ended in live birth:

live = (nsfg['OUTCOME'] == 1)
live.mean()
0.7006176070344394

Now we can use the logical operator & to identify pregnancies where the outcome is a preterm live birth:

live_preterm = (live & preterm)
live_preterm.mean()
0.08929132209777034

Exercise: Of all live births, what fraction are preterm?

The other common logical operators are:

  • |, which is the OR operator; for example live | preterm is true if either live is true, or preterm is true, or both.

  • ~, which is the NOT operator; for example ~live is true if live is false or NaN.

The logical operators treat NaN the same as False. So you should be careful about using the NOT operator with a Series that contains NaN values. For example, ~preterm would include not just full term pregnancies, but also pregnancies with unknown length.

Exercise: Of all pregnancies, what fraction are full term, that is, 37 weeks or more? Of all live births, what fraction are full term?

Filtering

We can use a Boolean Series as a filter; that is, we can select only rows that satisfy a condition or meet some criterion. For example, we can use preterm and the bracket operator to select values from birth_weight, so preterm_weight gets birth weights for preterm babies.

preterm_weight = birth_weight[preterm]
preterm_weight.mean()
5.480958781362007

To select full-term babies, we can create a Boolean Series like this:

fullterm = (nsfg['PRGLNGTH'] >= 37)

And use it to select birth weights for full term babies:

full_term_weight = birth_weight[fullterm]
full_term_weight.mean()
7.429609416096791

As expected, full term babies are heavier, on average, than preterm babies. To be more explicit, we could also limit the results to live births, like this:

full_term_weight = birth_weight[live & fullterm]
full_term_weight.mean()
7.429609416096791

But in this case we get the same result because birth_weight is only valid for live births.

Exercise: Let’s see if there is a difference in weight between single births and multiple births (twins, triplets, etc.). The variable NBRNALIV represents the number of babies born alive from a single pregnancy.

nbrnaliv = nsfg['NBRNALIV']
nbrnaliv.value_counts()
1.0    6573
2.0     111
3.0       6
Name: NBRNALIV, dtype: int64

Use nbrnaliv and live to create a Boolean series called multiple that is true for multiple live births. Of all live births, what fraction are multiple births?

Exercise: Make a Boolean series called single that is true for single live births. Of all single births, what fraction are preterm? Of all multiple births, what fraction are preterm?

Exercise: What is the average birth weight for live, single, full-term births?

Weighted mean

We are almost ready to compute the average birth weight, but there’s one more problem we have to solve: oversampling.

The NSFG is not exactly representative of the U.S. population. By design, some groups are more likely to appear in the sample than others; that is, they are oversampled. Oversampling helps to ensure that you have enough people in every subgroup to get reliable statistics, but it makes data analysis a little more complicated.

Each pregnancy in the dataset has a sampling weight that indicates how many pregnancies it represents. In nsfg, the sampling weight is stored in a column named wgt2015_2017. Here’s what it looks like.

sampling_weight = nsfg['WGT2015_2017']
sampling_weight.describe()
count      9553.000000
mean      13337.425944
std       16138.878271
min        1924.916000
25%        4575.221221
50%        7292.490835
75%       15724.902673
max      106774.400000
Name: WGT2015_2017, dtype: float64

The median value (50th percentile) in this column is about 7292, which means that a pregnancy with that weight represents 7292 total pregnancies in the population. But the range of values is wide, so some rows represent many more pregnancies than others.

To take these weights into account, we can compute a weighted mean. Here are the steps:

  1. Multiply the birth weights for each pregnancy by the sampling weights and add up the products.

  2. Add up the sampling weights.

  3. Divide the first sum by the second.

To do this correctly, we have to be careful with missing data. To help with that, we’ll use two Series methods, isna and notna.

isna returns a Boolean Series that is True where the corresponding value is NaN.

missing = birth_weight.isna()
missing.sum()
3013

In birth_weight there are 3013 missing values (mostly for pregnancies that did not end in live birth).

notna returns a Boolean Series that is True where the corresponding value is not NaN.

valid = birth_weight.notna()
valid.sum()
6540

We can combine valid with the other Boolean Series we have computed to identify single, full term, live births with valid birth weights.

single = (nbrnaliv == 1)
selected = valid & live & single & fullterm
selected.sum()
5648

Exercise: Use selected, birth_weight, and sampling_weight to compute the weighted mean of birth weight for live, single, full term births.

You should find that the weighted mean is a little higher than the unweighted mean we computed in the previous section. That’s because the groups that are oversampled in the NSFG tend to have lighter babies, on average.

Summary

This chapter poses what seems like a simple question: what is the average birth weight of babies in the United States?

To answer it, we found an appropriate dataset and read the files. Then we validated the data and dealt with special values, missing data, and errors. To explore the data, we used value_counts, hist, describe, and other Pandas methods. And to select relevant data, we used Boolean Series.

Along the way, we had to think more about the question. What do we mean by “average”, and which babies should we include? Should we include all live births or exclude preterm babies or multiple births?

And we had to think about the sampling process. By design, the NSFG respondents are not representative of the U.S. population, but we can use sampling weights to correct for this effect.

Even a simple question can be a challenging data science project.