What is the difference between pandas agg and apply function?

Question

I can't figure out the difference between Pandas .aggregate and .apply functions.
Take the following as an example: I load a dataset, do a groupby, define a simple function, and either user .agg or .apply.

As you may see, the printing statement within my function results in the same output after using .agg and .apply. The result, on the other hand is different. Why is that?

import pandas
import pandas as pd
iris = pd.read_csv('iris.csv')
by_species = iris.groupby('Species')
def f(x):
    ...:     print type(x)
    ...:     print x.head(3)
    ...:     return 1

Using apply:

by_species.apply(f)
#<class 'pandas.core.frame.DataFrame'>
#   Sepal.Length  Sepal.Width  Petal.Length  Petal.Width Species
#0           5.1          3.5           1.4          0.2  setosa
#1           4.9          3.0           1.4          0.2  setosa
#2           4.7          3.2           1.3          0.2  setosa
#<class 'pandas.core.frame.DataFrame'>
#   Sepal.Length  Sepal.Width  Petal.Length  Petal.Width Species
#0           5.1          3.5           1.4          0.2  setosa
#1           4.9          3.0           1.4          0.2  setosa
#2           4.7          3.2           1.3          0.2  setosa
#<class 'pandas.core.frame.DataFrame'>
#    Sepal.Length  Sepal.Width  Petal.Length  Petal.Width     Species
#50           7.0          3.2           4.7          1.4  versicolor
#51           6.4          3.2           4.5          1.5  versicolor
#52           6.9          3.1           4.9          1.5  versicolor
#<class 'pandas.core.frame.DataFrame'>
#     Sepal.Length  Sepal.Width  Petal.Length  Petal.Width    Species
#100           6.3          3.3           6.0          2.5  virginica
#101           5.8          2.7           5.1          1.9  virginica
#102           7.1          3.0           5.9          2.1  virginica
#Out[33]: 
#Species
#setosa        1
#versicolor    1
#virginica     1
#dtype: int64

Using agg

by_species.agg(f)
#<class 'pandas.core.frame.DataFrame'>
#   Sepal.Length  Sepal.Width  Petal.Length  Petal.Width Species
#0           5.1          3.5           1.4          0.2  setosa
#1           4.9          3.0           1.4          0.2  setosa
#2           4.7          3.2           1.3          0.2  setosa
#<class 'pandas.core.frame.DataFrame'>
#    Sepal.Length  Sepal.Width  Petal.Length  Petal.Width     Species
#50           7.0          3.2           4.7          1.4  versicolor
#51           6.4          3.2           4.5          1.5  versicolor
#52           6.9          3.1           4.9          1.5  versicolor
#<class 'pandas.core.frame.DataFrame'>
#     Sepal.Length  Sepal.Width  Petal.Length  Petal.Width    Species
#100           6.3          3.3           6.0          2.5  virginica
#101           5.8          2.7           5.1          1.9  virginica
#102           7.1          3.0           5.9          2.1  virginica
#Out[34]: 
#           Sepal.Length  Sepal.Width  Petal.Length  Petal.Width
#Species                                                         
#setosa                 1            1             1            1
#versicolor             1            1             1            1
#virginica              1            1             1            1

Answer 1

apply applies the function to each group (your Species). Your function returns 1, so you end up with 1 value for each of 3 groups.

agg aggregates each column (feature) for each group, so you end up with one value per column per group.

Do read the groupby docs, they're quite helpful. There are also a bunch of tutorials floating around the web.