In [1]:
from dsc80_utils import *
In [2]:
# Pandas Tutor setup
%reload_ext pandas_tutor
%set_pandas_tutor_options {"maxDisplayCols": 8, "nohover": True, "projectorMode": True}

Lecture 3 – Grouping and Pivoting¶

DSC 80, Winter 2024¶

There was a (very short) Pre-Lecture Reading for this lecture – we'll assume you've done it.

Announcements 📣¶

  • Lab 1 is due tomorrow at 5PM. You cannot use slip days on it!
    • Please fill out the Welcome Survey if you haven't already!
  • Project 1 is released.
    • The checkpoint (Questions 1-7) is due on Saturday, January 20th.
    • The full project is due on Saturday, January 27th.
  • Lab 2 will be released by tomorrow.

Agenda¶

  • Data granularity and the groupby method.
  • DataFrameGroupBy objects and aggregation.
  • Other DataFrameGroupBy methods.
  • Pivot tables using the pivot_table method.

You will need to code a lot today – make sure to pull the course repository

I will code a lot too, and will post my filled-in slides after class.

Question 🤔 (Answer at q.dsc80.com)

Remember, you can always ask questions at q.dsc80.com!

A question for you now: did you look at the pre-lecture reading diagram? Have you set up your development environment?

  • A. Yes, I looked at the pre-lecture reading. Yes, I have set up my development environment.
  • B. Yes, I looked at the pre-lecture reading. No, I have not set up my development environment.
  • C. No, I did not look at the pre-lecture reading. Yes, I have set up my development environment.
  • D. No, I did not look at the pre-lecture reading. No, I have not set up my development environment.

Data granularity and the groupby method¶

Example: Palmer Penguins¶

No description has been provided for this image Artwork by @allison_horst

The dataset we'll work with for the rest of the lecture involves various measurements taken of three species of penguins in Antarctica.

In [3]:
IFrame('https://www.youtube-nocookie.com/embed/CCrNAHXUstU?si=-DntSyUNp5Kwitjm&start=11',
       width=560, height=315)
Out[3]:
In [4]:
import seaborn as sns
penguins = sns.load_dataset('penguins').dropna()
penguins
Out[4]:
species island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g sex
0 Adelie Torgersen 39.1 18.7 181.0 3750.0 Male
1 Adelie Torgersen 39.5 17.4 186.0 3800.0 Female
2 Adelie Torgersen 40.3 18.0 195.0 3250.0 Female
... ... ... ... ... ... ... ...
341 Gentoo Biscoe 50.4 15.7 222.0 5750.0 Male
342 Gentoo Biscoe 45.2 14.8 212.0 5200.0 Female
343 Gentoo Biscoe 49.9 16.1 213.0 5400.0 Male

333 rows × 7 columns

Here, each row corresponds to a single penguin, and each column corresponds to a different attribute (or feature) we have for each penguin. Data formatted in this way is called tidy data.

Granularity¶

  • Granularity refers to what each observation in a dataset represents.
    • Fine: small details.
    • Coarse: bigger picture.
  • If you can control how your dataset is created, you should opt for finer granularity, i.e. for more detail.
    • You can always remove details, but it's difficult to add detail that isn't already there.
    • But obtaining fine-grained data can take more time/money.
  • Today, we'll focus on how to remove details from fine-grained data, in order to help us understand bigger-picture trends in our data.

Initial exploration¶

Given our penguins dataset, we may wonder:

  • What is the distribution of 'species' in this dataset?
In [5]:
penguins['species'].value_counts()
Out[5]:
Adelie       146
Gentoo       119
Chinstrap     68
Name: species, dtype: int64
In [6]:
penguins['species'].value_counts(normalize=True)
Out[6]:
Adelie       0.44
Gentoo       0.36
Chinstrap    0.20
Name: species, dtype: float64
  • What is the distribution of 'islands'?
In [7]:
penguins['island'].value_counts()
Out[7]:
Biscoe       163
Dream        123
Torgersen     47
Name: island, dtype: int64

Aggregating¶

Aggregating is the act of combining many values into a single value.

  • What is the mean 'body_mass_g' for all penguins?
In [8]:
penguins['body_mass_g'].mean()
Out[8]:
4207.057057057057
  • What is the mean 'body_mass_g' for each species?
In [9]:
# ???

Naive approach: looping through unique values¶

In [10]:
species_map = pd.Series([], dtype=float)

for species in penguins['species'].unique():
    species_only = penguins.loc[penguins['species'] == species]
    species_map.loc[species] = species_only['body_mass_g'].mean()
    
species_map
Out[10]:
Adelie       3706.16
Chinstrap    3733.09
Gentoo       5092.44
dtype: float64
  • For each unique 'species', we make a pass through the entire dataset.
    • The asymptotic runtime of this procedure is $\Theta(ns)$, where $n$ is the number of rows and $s$ is the number of unique species.
  • While there are other loop-based solutions that only involve a single pass over the DataFrame, we'd like to avoid Python loops entirely, as they're slow.

Grouping¶

A better solution, as we know from DSC 10, is to use the groupby method.

In [11]:
# Before:
penguins['body_mass_g'].mean()
Out[11]:
4207.057057057057
In [12]:
# After:
penguins.groupby('species').mean()['body_mass_g']
Out[12]:
species
Adelie       3706.16
Chinstrap    3733.09
Gentoo       5092.44
Name: body_mass_g, dtype: float64

Somehow, the groupby method computes what we're looking for in just one line. How?

In [13]:
%%pt

penguins.groupby('species')['body_mass_g'].mean()

"Split-apply-combine" paradigm¶

The groupby method involves three steps: split, apply, and combine. This is the same terminology that the pandas documentation uses.

No description has been provided for this image

  • Split breaks up and "groups" the rows of a DataFrame according to the specified key. There is one "group" for every unique value of the key.

  • Apply uses a function (e.g. aggregation, transformation, filtration) within the individual groups.

  • Combine stitches the results of these operations into an output DataFrame.

  • The split-apply-combine pattern can be parallelized to work on multiple computers or threads, by sending computations for each group to different processors.

More examples¶

Before we dive into the internals, let's look at a few more examples.

In [14]:
penguins
Out[14]:
species island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g sex
0 Adelie Torgersen 39.1 18.7 181.0 3750.0 Male
1 Adelie Torgersen 39.5 17.4 186.0 3800.0 Female
2 Adelie Torgersen 40.3 18.0 195.0 3250.0 Female
... ... ... ... ... ... ... ...
341 Gentoo Biscoe 50.4 15.7 222.0 5750.0 Male
342 Gentoo Biscoe 45.2 14.8 212.0 5200.0 Female
343 Gentoo Biscoe 49.9 16.1 213.0 5400.0 Male

333 rows × 7 columns

Exercise

Which 'species' has the highest median 'bill_length_mm'?
In [15]:
# Your code goes here.

What proportion of penguins of each 'species' live on 'Dream' island?

In [16]:
(penguins
 .assign(on_dream=penguins['island'] == 'Dream')
 .groupby('species')
 .mean()
 ['on_dream']
)
Out[16]:
species
Adelie       0.38
Chinstrap    1.00
Gentoo       0.00
Name: on_dream, dtype: float64

DataFrameGroupBy objects and aggregation¶

DataFrameGroupBy objects¶

We've just evaluated a few expressions of the following form.

In [17]:
penguins.groupby('species').mean()
Out[17]:
bill_length_mm bill_depth_mm flipper_length_mm body_mass_g
species
Adelie 38.82 18.35 190.10 3706.16
Chinstrap 48.83 18.42 195.82 3733.09
Gentoo 47.57 15.00 217.24 5092.44

There are two method calls in the expression above: .groupby('species') and .mean(). What happens if we remove the latter?

In [18]:
penguins.groupby('species')
Out[18]:
<pandas.core.groupby.generic.DataFrameGroupBy object at 0x1558fca00>

Peeking under the hood¶

If df is a DataFrame, then df.groupby(key) returns a DataFrameGroupBy object.

This object represents the "split" in "split-apply-combine".

In [19]:
# Simplified DataFrame for demonstration:
penguins_small = penguins.iloc[[0, 150, 300, 1, 251, 151, 301], [0, 5, 6]]
penguins_small
Out[19]:
species body_mass_g sex
0 Adelie 3750.0 Male
156 Chinstrap 3725.0 Male
308 Gentoo 4875.0 Female
1 Adelie 3800.0 Female
258 Gentoo 4350.0 Female
157 Chinstrap 3950.0 Female
309 Gentoo 5550.0 Male
In [20]:
# Creates one group for each unique value in the species column.
penguin_groups = penguins_small.groupby('species')
penguin_groups
Out[20]:
<pandas.core.groupby.generic.DataFrameGroupBy object at 0x1558afeb0>
In [21]:
%%pt
penguin_groups

DataFrameGroupBy objects have a groups attribute, which is a dictionary in which the keys are group names and the values are lists of row labels.

In [22]:
penguin_groups.groups
Out[22]:
{'Adelie': [0, 1], 'Chinstrap': [156, 157], 'Gentoo': [308, 258, 309]}

DataFrameGroupBy objects also have a get_group(key) method, which returns a DataFrame with only the values for the given key.

In [23]:
penguin_groups.get_group('Chinstrap')
Out[23]:
species body_mass_g sex
156 Chinstrap 3725.0 Male
157 Chinstrap 3950.0 Female
In [24]:
# Same as the above!
penguins_small.query('species == "Chinstrap"')
Out[24]:
species body_mass_g sex
156 Chinstrap 3725.0 Male
157 Chinstrap 3950.0 Female

We usually don't use these attributes and methods, but they're useful in understanding how groupby works under the hood.

Aggregation¶

  • Once we create a DataFrameGroupBy object, we need to apply some function to each group, and combine the results.

  • The most common operation we apply to each group is an aggregation.

    • Remember, aggregation is the act of combining many values into a single value.

  • To perform an aggregation, use an aggregation method on the DataFrameGroupBy object, e.g. .mean(), .max(), or .median().

Let's look at some examples.

In [25]:
penguins_small
Out[25]:
species body_mass_g sex
0 Adelie 3750.0 Male
156 Chinstrap 3725.0 Male
308 Gentoo 4875.0 Female
1 Adelie 3800.0 Female
258 Gentoo 4350.0 Female
157 Chinstrap 3950.0 Female
309 Gentoo 5550.0 Male
In [26]:
penguins_small.groupby('species').mean()
Out[26]:
body_mass_g
species
Adelie 3775.0
Chinstrap 3837.5
Gentoo 4925.0
In [27]:
penguins_small.groupby('species').sum()
Out[27]:
body_mass_g
species
Adelie 7550.0
Chinstrap 7675.0
Gentoo 14775.0
In [28]:
penguins_small.groupby('species').last()
Out[28]:
body_mass_g sex
species
Adelie 3800.0 Female
Chinstrap 3950.0 Female
Gentoo 5550.0 Male
In [29]:
penguins_small.groupby('species').max()
Out[29]:
body_mass_g sex
species
Adelie 3800.0 Male
Chinstrap 3950.0 Male
Gentoo 5550.0 Male

Column independence¶

Within each group, the aggregation method is applied to each column independently.

In [30]:
penguins_small.groupby('species').max()
Out[30]:
body_mass_g sex
species
Adelie 3800.0 Male
Chinstrap 3950.0 Male
Gentoo 5550.0 Male

It is not telling us that there is a 'Male' 'Adelie' penguin with a 'body_mass_g' of 3800.0!

In [31]:
# This penguin is Female!
penguins_small.loc[(penguins['species'] == 'Adelie') & (penguins['body_mass_g'] == 3800.0)]
Out[31]:
species body_mass_g sex
1 Adelie 3800.0 Female

Exercise

Find the 'species' and 'body_mass_g' of the heaviest 'Male' and 'Female' penguins in penguins (not penguins_small).
In [32]:
# Your code goes here.

Column selection and performance implications¶

  • By default, the aggregator will be applied to all columns that it can be applied to.
    • max and min are defined on strings, while median and mean are not.
  • If we only care about one column, we can select that column before aggregating to save time.
    • DataFrameGroupBy objects support [] notation, just like DataFrames.
In [33]:
# Back to the big penguins dataset!
penguins.groupby('species').mean()
Out[33]:
bill_length_mm bill_depth_mm flipper_length_mm body_mass_g
species
Adelie 38.82 18.35 190.10 3706.16
Chinstrap 48.83 18.42 195.82 3733.09
Gentoo 47.57 15.00 217.24 5092.44
In [34]:
# Works, but involves wasted effort since the other columns had to be aggregated for no reason.
penguins.groupby('species').mean()['bill_length_mm']
Out[34]:
species
Adelie       38.82
Chinstrap    48.83
Gentoo       47.57
Name: bill_length_mm, dtype: float64
In [35]:
# This is a SeriesGroupBy object!
penguins.groupby('species')['bill_length_mm']
Out[35]:
<pandas.core.groupby.generic.SeriesGroupBy object at 0x15598dbb0>
In [36]:
# Saves time!
penguins.groupby('species')['bill_length_mm'].mean()
Out[36]:
species
Adelie       38.82
Chinstrap    48.83
Gentoo       47.57
Name: bill_length_mm, dtype: float64

To demonstrate that the former is slower than the latter, we can use %%timeit. For reference, we'll also include our earlier for-loop-based solution.

In [37]:
%%timeit
penguins.groupby('species').mean()['bill_length_mm']

312 µs ± 8.43 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)
In [38]:
%%timeit
penguins.groupby('species')['bill_length_mm'].mean()

115 µs ± 667 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)
In [39]:
%%timeit
species_map = pd.Series([], dtype=float)

for species in penguins['species'].unique():
    species_only = penguins.loc[penguins['species'] == species]
    species_map.loc[species] = species_only['body_mass_g'].mean()
    
species_map

885 µs ± 8.49 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)

Takeaways¶

  • It's important to understand what each piece of your code evaluates to – in the first two timed examples, the code is almost identical, but the performance is quite different.

    # Slower
penguins.groupby('species').mean()['bill_length_mm']

# Faster
penguins.groupby('species')['bill_length_mm'].mean()

  • The groupby method is much quicker than for-looping over the DataFrame in Python. It can often produce results using just a single, fast pass over the data, updating the sum, mean, count, min, or other aggregate for each group along the way.

Beyond default aggregation methods¶

  • There are many built-in aggregation methods.
  • What if you want to apply different aggregation methods to different columns?
  • What if the aggregation method you want to use doesn't already exist in pandas?

The aggregate method¶

  • The DataFrameGroupBy object has a general aggregate method, which aggregates using one or more operations.
    • Remember, aggregation is the act of combining many values into a single value.
  • There are many ways of using aggregate; refer to the documentation for a comprehensive list.
  • Example arguments:
    • A single function.
    • A list of functions.
    • A dictionary mapping column names to functions.
  • Per the documentation, agg is an alias for aggregate.

Example¶

How many penguins are there of each 'species', and what is the mean 'body_mass_g' of each 'species'?

In [40]:
(penguins
 .groupby('species')
 ['body_mass_g']
 .aggregate(['count', 'mean'])
)
Out[40]:
count mean
species
Adelie 146 3706.16
Chinstrap 68 3733.09
Gentoo 119 5092.44

Note what happens when we don't select a column before aggregating.

In [41]:
(penguins
 .groupby('species')
 .aggregate(['count', 'mean'])
)
Out[41]:
bill_length_mm bill_depth_mm flipper_length_mm body_mass_g
count mean count mean count mean count mean
species
Adelie 146 38.82 146 18.35 146 190.10 146 3706.16
Chinstrap 68 48.83 68 18.42 68 195.82 68 3733.09
Gentoo 119 47.57 119 15.00 119 217.24 119 5092.44

Example¶

What is the maximum 'bill_length_mm' of each 'species', and which 'island's is each 'species' found on?

In [42]:
(penguins
 .groupby('species')
 .aggregate({'bill_length_mm': 'max', 'island': 'unique'})
)
Out[42]:
bill_length_mm island
species
Adelie 46.0 [Torgersen, Biscoe, Dream]
Chinstrap 58.0 [Dream]
Gentoo 59.6 [Biscoe]

Example¶

What is the interquartile range of the 'body_mass_g' of each 'species'?

In [43]:
# Here, the argument to agg is a function,
# which takes in a pd.Series and returns a scalar.

def iqr(s):
    return np.percentile(s, 75) - np.percentile(s, 25)

(penguins
 .groupby('species')
 ['body_mass_g']
 .agg(iqr)
)
Out[43]:
species
Adelie       637.5
Chinstrap    462.5
Gentoo       800.0
Name: body_mass_g, dtype: float64

Question 🤔 (Answer at q.dsc80.com)

What questions do you have?

Other DataFrameGroupBy methods¶

Split-apply-combine, revisited¶

When we introduced the split-apply-combine pattern, the "apply" step involved aggregation – our final DataFrame had one row for each group.

No description has been provided for this image

Instead of aggregating during the apply step, we could instead perform a:

  • Transformation, in which we perform operations to every value within each group.

  • Filtration, in which we keep only the groups that satisfy some condition.

Transformations¶

Suppose we want to convert the 'body_mass_g' column to to z-scores (i.e. standard units):

$$z(x_i) = \frac{x_i - \text{mean of } x}{\text{SD of } x}$$
In [44]:
def z_score(x):
    return (x - x.mean()) / x.std(ddof=0)
In [45]:
z_score(penguins['body_mass_g'])
Out[45]:
0     -0.57
1     -0.51
2     -1.19
       ... 
341    1.92
342    1.23
343    1.48
Name: body_mass_g, Length: 333, dtype: float64

Transformations within groups¶

  • Now, what if we wanted the z-score within each group?

  • To do so, we can use the transform method on a DataFrameGroupBy object. The transform method takes in a function, which itself takes in a Series and returns a new Series.

  • A transformation produces a DataFrame or Series of the same size – it is not an aggregation!

In [46]:
z_mass = (penguins
          .groupby('species')
          ['body_mass_g']
          .transform(z_score))
z_mass
Out[46]:
0      0.10
1      0.21
2     -1.00
       ... 
341    1.32
342    0.22
343    0.62
Name: body_mass_g, Length: 333, dtype: float64
In [47]:
penguins.assign(z_mass=z_mass)
Out[47]:
species island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g sex z_mass
0 Adelie Torgersen 39.1 18.7 181.0 3750.0 Male 0.10
1 Adelie Torgersen 39.5 17.4 186.0 3800.0 Female 0.21
2 Adelie Torgersen 40.3 18.0 195.0 3250.0 Female -1.00
... ... ... ... ... ... ... ... ...
341 Gentoo Biscoe 50.4 15.7 222.0 5750.0 Male 1.32
342 Gentoo Biscoe 45.2 14.8 212.0 5200.0 Female 0.22
343 Gentoo Biscoe 49.9 16.1 213.0 5400.0 Male 0.62

333 rows × 8 columns

In [48]:
display_df(penguins.assign(z_mass=z_mass), rows=8)
species island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g sex z_mass
0 Adelie Torgersen 39.1 18.7 181.0 3750.0 Male 0.10
1 Adelie Torgersen 39.5 17.4 186.0 3800.0 Female 0.21
2 Adelie Torgersen 40.3 18.0 195.0 3250.0 Female -1.00
4 Adelie Torgersen 36.7 19.3 193.0 3450.0 Female -0.56
... ... ... ... ... ... ... ... ...
340 Gentoo Biscoe 46.8 14.3 215.0 4850.0 Female -0.49
341 Gentoo Biscoe 50.4 15.7 222.0 5750.0 Male 1.32
342 Gentoo Biscoe 45.2 14.8 212.0 5200.0 Female 0.22
343 Gentoo Biscoe 49.9 16.1 213.0 5400.0 Male 0.62

333 rows × 8 columns

Note that above, penguin 340 has a larger 'body_mass_g' than penguin 0, but a lower 'z_mass'.

  • Penguin 0 has an above average 'body_mass_g' among 'Adelie' penguins.
  • Penguin 340 has a below average 'body_mass_g' among 'Gentoo' penguins. Remember from earlier that the average 'body_mass_g' of 'Gentoo' penguins is much higher than for other species.
In [49]:
penguins.groupby('species')['body_mass_g'].mean()
Out[49]:
species
Adelie       3706.16
Chinstrap    3733.09
Gentoo       5092.44
Name: body_mass_g, dtype: float64

Filtering groups¶

  • To keep only the groups that satisfy a particular condition, use the filter method on a DataFrameGroupBy object.

  • The filter method takes in a function, which itself takes in a DataFrame/Series and return a single Boolean. The result is a new DataFrame/Series with only the groups for which the filter function returned True.

For example, suppose we want only the 'species' whose average 'bill_length_mm' is above 39.

In [50]:
(penguins
 .groupby('species')
 .filter(lambda df: df['bill_length_mm'].mean() > 39)
)
Out[50]:
species island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g sex
152 Chinstrap Dream 46.5 17.9 192.0 3500.0 Female
153 Chinstrap Dream 50.0 19.5 196.0 3900.0 Male
154 Chinstrap Dream 51.3 19.2 193.0 3650.0 Male
... ... ... ... ... ... ... ...
341 Gentoo Biscoe 50.4 15.7 222.0 5750.0 Male
342 Gentoo Biscoe 45.2 14.8 212.0 5200.0 Female
343 Gentoo Biscoe 49.9 16.1 213.0 5400.0 Male

187 rows × 7 columns

No more 'Adelie's!

Or, as another example, suppose we only want 'species' with at least 100 penguins:

In [51]:
(penguins
 .groupby('species')
 .filter(lambda df: df.shape[0] > 100)
)
Out[51]:
species island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g sex
0 Adelie Torgersen 39.1 18.7 181.0 3750.0 Male
1 Adelie Torgersen 39.5 17.4 186.0 3800.0 Female
2 Adelie Torgersen 40.3 18.0 195.0 3250.0 Female
... ... ... ... ... ... ... ...
341 Gentoo Biscoe 50.4 15.7 222.0 5750.0 Male
342 Gentoo Biscoe 45.2 14.8 212.0 5200.0 Female
343 Gentoo Biscoe 49.9 16.1 213.0 5400.0 Male

265 rows × 7 columns

No more 'Chinstrap's!

Grouping with multiple columns¶

When we group with multiple columns, one group is created for every unique combination of elements in the specified columns.

In [52]:
species_and_island = penguins.groupby(['species', 'island']).mean()
species_and_island
Out[52]:
bill_length_mm bill_depth_mm flipper_length_mm body_mass_g
species island
Adelie Biscoe 38.98 18.37 188.80 3709.66
Dream 38.52 18.24 189.93 3701.36
Torgersen 39.04 18.45 191.53 3708.51
Chinstrap Dream 48.83 18.42 195.82 3733.09
Gentoo Biscoe 47.57 15.00 217.24 5092.44

Grouping and indexes¶

  • The groupby method creates an index based on the specified columns.
  • When grouping by multiple columns, the resulting DataFrame has a MultiIndex.
  • Advice: When working with a MultiIndex, use reset_index or set as_index=False in groupby.
In [53]:
species_and_island
Out[53]:
bill_length_mm bill_depth_mm flipper_length_mm body_mass_g
species island
Adelie Biscoe 38.98 18.37 188.80 3709.66
Dream 38.52 18.24 189.93 3701.36
Torgersen 39.04 18.45 191.53 3708.51
Chinstrap Dream 48.83 18.42 195.82 3733.09
Gentoo Biscoe 47.57 15.00 217.24 5092.44
In [54]:
species_and_island['body_mass_g']
Out[54]:
species    island   
Adelie     Biscoe       3709.66
           Dream        3701.36
           Torgersen    3708.51
Chinstrap  Dream        3733.09
Gentoo     Biscoe       5092.44
Name: body_mass_g, dtype: float64
In [55]:
species_and_island.loc['Adelie']
Out[55]:
bill_length_mm bill_depth_mm flipper_length_mm body_mass_g
island
Biscoe 38.98 18.37 188.80 3709.66
Dream 38.52 18.24 189.93 3701.36
Torgersen 39.04 18.45 191.53 3708.51
In [56]:
species_and_island.loc[('Adelie', 'Torgersen')]
Out[56]:
bill_length_mm         39.04
bill_depth_mm          18.45
flipper_length_mm     191.53
body_mass_g          3708.51
Name: (Adelie, Torgersen), dtype: float64
In [57]:
species_and_island.reset_index()
Out[57]:
species island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g
0 Adelie Biscoe 38.98 18.37 188.80 3709.66
1 Adelie Dream 38.52 18.24 189.93 3701.36
2 Adelie Torgersen 39.04 18.45 191.53 3708.51
3 Chinstrap Dream 48.83 18.42 195.82 3733.09
4 Gentoo Biscoe 47.57 15.00 217.24 5092.44
In [58]:
penguins.groupby(['species', 'island'], as_index=False).mean()
Out[58]:
species island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g
0 Adelie Biscoe 38.98 18.37 188.80 3709.66
1 Adelie Dream 38.52 18.24 189.93 3701.36
2 Adelie Torgersen 39.04 18.45 191.53 3708.51
3 Chinstrap Dream 48.83 18.42 195.82 3733.09
4 Gentoo Biscoe 47.57 15.00 217.24 5092.44

Exercise

Find the most popular 'Male' and 'Female' baby 'Name' for each 'Year' in baby. Exclude 'Year's where there were fewer than 1 million births recorded.
In [59]:
baby_path = Path('data') / 'baby.csv'
baby = pd.read_csv(baby_path)
baby
Out[59]:
Name Sex Count Year
0 Liam M 20456 2022
1 Noah M 18621 2022
2 Olivia F 16573 2022
... ... ... ... ...
2085155 Wright M 5 1880
2085156 York M 5 1880
2085157 Zachariah M 5 1880

2085158 rows × 4 columns

In [60]:
# Your code goes here.

Pivot tables using the pivot_table method¶

Pivot tables: an extension of grouping¶

Pivot tables are a compact way to display tables for humans to read:

Sex F M
Year
2018 1698373 1813377
2019 1675139 1790682
2020 1612393 1721588
2021 1635800 1743913
2022 1628730 1733166
  • Notice that each value in the table is a sum over the counts, split by year and sex.
  • You can think of pivot tables as grouping using two columns, then "pivoting" one of the group labels into columns.

pivot_table¶

The pivot_table DataFrame method aggregates a DataFrame using two columns. To use it:

df.pivot_table(index=index_col,
               columns=columns_col,
               values=values_col,
               aggfunc=func)

The resulting DataFrame will have:

  • One row for every unique value in index_col.
  • One column for every unique value in columns_col.
  • Values determined by applying func on values in values_col.
In [61]:
last_5_years = baby.query('Year >= 2018')
last_5_years
Out[61]:
Name Sex Count Year
0 Liam M 20456 2022
1 Noah M 18621 2022
2 Olivia F 16573 2022
... ... ... ... ...
159444 Zyrie M 5 2018
159445 Zyron M 5 2018
159446 Zzyzx M 5 2018

159447 rows × 4 columns

In [62]:
last_5_years.pivot_table(
    index='Year',
    columns='Sex',
    values='Count',
    aggfunc='sum',
)
Out[62]:
Sex F M
Year
2018 1698373 1813377
2019 1675139 1790682
2020 1612393 1721588
2021 1635800 1743913
2022 1628730 1733166
In [63]:
# Look at the similarity to the snippet above!
(last_5_years
 .groupby(['Year', 'Sex'])
 [['Count']]
 .sum()
)
Out[63]:
Count
Year Sex
2018 F 1698373
M 1813377
2019 F 1675139
... ... ...
2021 M 1743913
2022 F 1628730
M 1733166

10 rows × 1 columns

Example¶

Find the number of penguins per 'island' and 'species'.

In [64]:
penguins
Out[64]:
species island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g sex
0 Adelie Torgersen 39.1 18.7 181.0 3750.0 Male
1 Adelie Torgersen 39.5 17.4 186.0 3800.0 Female
2 Adelie Torgersen 40.3 18.0 195.0 3250.0 Female
... ... ... ... ... ... ... ...
341 Gentoo Biscoe 50.4 15.7 222.0 5750.0 Male
342 Gentoo Biscoe 45.2 14.8 212.0 5200.0 Female
343 Gentoo Biscoe 49.9 16.1 213.0 5400.0 Male

333 rows × 7 columns

In [65]:
penguins.pivot_table(
    index='species', 
    columns='island', 
    values='bill_length_mm', # Choice of column here doesn't actually matter!
    aggfunc='count',
)
Out[65]:
island Biscoe Dream Torgersen
species
Adelie 44.0 55.0 47.0
Chinstrap NaN 68.0 NaN
Gentoo 119.0 NaN NaN

Note that there is a NaN at the intersection of 'Biscoe' and 'Chinstrap', because there were no Chinstrap penguins on Biscoe Island.

We can either use the fillna method afterwards or the fill_value argument to fill in NaNs.

In [66]:
penguins.pivot_table(
    index='species', 
    columns='island', 
    values='bill_length_mm', 
    aggfunc='count',
    fill_value=0,
)
Out[66]:
island Biscoe Dream Torgersen
species
Adelie 44 55 47
Chinstrap 0 68 0
Gentoo 119 0 0

Granularity, revisited¶

Take another look at the pivot table from the previous slide. Each row of the original penguins DataFrame represented a single penguin, and each column represented features of the penguins.

What is the granularity of the DataFrame below?

In [67]:
penguins.pivot_table(
    index='species', 
    columns='island', 
    values='bill_length_mm', 
    aggfunc='count',
    fill_value=0,
)
Out[67]:
island Biscoe Dream Torgersen
species
Adelie 44 55 47
Chinstrap 0 68 0
Gentoo 119 0 0

Reshaping¶

  • pivot_table reshapes DataFrames from "long" to "wide".
  • Other DataFrame reshaping methods:
    • melt: Un-pivots a DataFrame. Very useful in data cleaning.
    • pivot: Like pivot_table, but doesn't do aggregation.
    • stack: Pivots multi-level columns to multi-indices.
    • unstack: Pivots multi-indices to columns.
    • Google and the documentation are your friends!

Question 🤔 (Answer at q.dsc80.com)

What questions do you have?

Distributions¶

Joint distribution¶

When using aggfunc='count', a pivot table describes the joint distribution of two categorical variables. This is also called a contingency table.

In [68]:
counts = penguins.pivot_table(
    index='species', 
    columns='sex', 
    values='body_mass_g', 
    aggfunc='count', 
    fill_value=0
)
counts
Out[68]:
sex Female Male
species
Adelie 73 73
Chinstrap 34 34
Gentoo 58 61

We can normalize the DataFrame by dividing by the total number of penguins. The resulting numbers can be interpreted as probabilities that a randomly selected penguin from the dataset belongs to a given combination of species and sex.

In [69]:
joint = counts / counts.sum().sum()
joint
Out[69]:
sex Female Male
species
Adelie 0.22 0.22
Chinstrap 0.10 0.10
Gentoo 0.17 0.18

Marginal probabilities¶

If we sum over one of the axes, we can compute marginal probabilities, i.e. unconditional probabilities.

In [70]:
joint
Out[70]:
sex Female Male
species
Adelie 0.22 0.22
Chinstrap 0.10 0.10
Gentoo 0.17 0.18
In [71]:
# Recall, joint.sum(axis=0) sums across the rows, 
# which computes the sum of the **columns**.
joint.sum(axis=0)
Out[71]:
sex
Female    0.5
Male      0.5
dtype: float64
In [72]:
joint.sum(axis=1)
Out[72]:
species
Adelie       0.44
Chinstrap    0.20
Gentoo       0.36
dtype: float64

For instance, the second Series tells us that a randomly selected penguin has a 0.36 chance of being of species 'Gentoo'.

Conditional probabilities¶

Using counts, how might we compute conditional probabilities like $$P(\text{species } = \text{"Adelie"} \mid \text{sex } = \text{"Female"})?$$

In [73]:
counts
Out[73]:
sex Female Male
species
Adelie 73 73
Chinstrap 34 34
Gentoo 58 61
$$\begin{align*} P(\text{species} = c \mid \text{sex} = x) &= \frac{\# \: (\text{species} = c \text{ and } \text{sex} = x)}{\# \: (\text{sex} = x)} \end{align*}$$
➡️ Click here to see more of a derivation. $$\begin{align*} P(\text{species} = c \mid \text{sex} = x) &= \frac{P(\text{species} = c \text{ and } \text{sex} = x)}{P(\text{sex = }x)} \\ &= \frac{\frac{\# \: (\text{species } = \: c \text{ and } \text{sex } = \: x)}{N}}{\frac{\# \: (\text{sex } = \: x)}{N}} \\ &= \frac{\# \: (\text{species} = c \text{ and } \text{sex} = x)}{\# \: (\text{sex} = x)} \end{align*}$$

Answer: To find conditional probabilities of 'species' given 'sex', divide by column sums. To find conditional probabilities of 'sex' given 'species', divide by row sums.

Conditional probabilities¶

To find conditional probabilities of 'species' given 'sex', divide by column sums. To find conditional probabilities of 'sex' given 'species', divide by row sums.

In [74]:
counts
Out[74]:
sex Female Male
species
Adelie 73 73
Chinstrap 34 34
Gentoo 58 61
In [75]:
counts.sum(axis=0)
Out[75]:
sex
Female    165
Male      168
dtype: int64

The conditional distribution of 'species' given 'sex' is below. Note that in this new DataFrame, the 'Female' and 'Male' columns each sum to 1.

In [76]:
counts / counts.sum(axis=0)
Out[76]:
sex Female Male
species
Adelie 0.44 0.43
Chinstrap 0.21 0.20
Gentoo 0.35 0.36

For instance, the above DataFrame tells us that the probability that a randomly selected penguin is of 'species' 'Adelie' given that they are of 'sex' 'Female' is 0.442424.

Exercise

Find the conditional distribution of 'sex' given 'species'.
Hint: Use .T.
In [77]:
# Your code goes here.

Summary, next time¶

Summary¶

  • Grouping allows us to change the level of granularity in a DataFrame.
  • Grouping involves three steps – split, apply, and combine.
    • Usually, what is applied is an aggregation, but it could be a transformation or filtration.
  • pivot_table aggregates data based on two categorical columns, and reshapes the result to be "wide" instead of "long".

Next time¶

  • Simpson's paradox.
  • Merging.
    • Review this diagram from DSC 10!
  • The pitfalls of the apply method.