Lab 8
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Western University *
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1000A
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Statistics
Date
Jan 9, 2024
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11/2/22, 5:35 PM
Lab 8
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Lab 8
In this lab we discuss simple random sampling, systematic sampling, and stratified random sampling.
Simple Random Sampling
random.sample:
https://www.w3schools.com/python/ref_random_sample.asp
(https://www.w3schools.com/python/ref_random_sample.asp)
In [1]:
import
numpy
as
np
import
pandas
as
pd
import
random
In [2]:
# Random sampling using random.sample()
# random.sample returns unique random elements from a sequence or set. This is sampling without replacement.
random
.
seed(
52
)
## setting the seed so that we all get the same sample
names
=
[
"Roger"
,
"Jack"
,
"John"
,
"Jason"
,
"Laura"
,
"Mariya"
,
"Martina"
,
"Lauren"
]
sampled_list1
=
random
.
sample(names,
3
)
print
(sampled_list1)
In [3]:
# if we change the seed another sample is obtained
random
.
seed(
17
)
sampled_list2
=
random
.
sample(names,
3
)
print
(sampled_list2)
In [4]:
# an alternative way to sample is to assign a number to each name (or ID) in the list and then sample the numbers
# generating 8 consecutive numbers corresponding to the positions of each name in the list:
sequence_numbers
=
list
(
range
(
8
))
print
(sequence_numbers)
# Python starts with zero
random
.
seed(
17
)
# same seed as before to obtain the same sample of names as in the code cell above
sample_list3
=
random
.
sample(sequence_numbers,
3
)
# randomly sampling 3 number positions
print
(sample_list3)
In [5]:
[names[i]
for
i
in
sample_list3 ]
# getting the names corresponding to the sampled number positions
In [6]:
# Getting a sample array from a multidimensional array
array
=
np
.
array([[
2
,
5
,
7
], [
5
,
11
,
16
], [
6
,
13
,
19
], [
7
,
15
,
22
], [
8
,
17
,
25
]])
print
(
"2D array
\n
"
, array)
In [7]:
random
.
seed(
48
)
random_rows
=
random
.
sample(
range
(
5
),
2
)
# randomly selecting two row indices, without replacement
print
(random_rows)
In [8]:
array[random_rows, :]
Systematic Sampling
Systematic sampling is a type of sampling where we obtain a sample by going through a list of the population at fixed intervals from a randomly chosen starting point.
['Laura', 'Roger', 'Mariya']
['Martina', 'Lauren', 'John']
[0, 1, 2, 3, 4, 5, 6, 7]
[6, 7, 2]
Out[5]:
['Martina', 'Lauren', 'John']
2D array
[[ 2
5
7]
[ 5 11 16]
[ 6 13 19]
[ 7 15 22]
[ 8 17 25]]
[4, 2]
Out[8]:
array([[ 8, 17, 25],
[ 6, 13, 19]])
11/2/22, 5:35 PM
Lab 8
localhost:8888/nbconvert/html/Documents/Python_examples/Lab_8/Lab 8.ipynb?download=false
2/4
np.arange:
https://numpy.org/doc/stable/reference/generated/numpy.arange.html
(https://numpy.org/doc/stable/reference/generated/numpy.arange.html)
In [9]:
# Let's assume we are interested in sampling from a population of 15 students with the following ID list:
df_students
=
pd
.
DataFrame({
'ID'
:np
.
arange(
1
,
16
)
.
tolist()})
df_students
In [10]:
# Defining the function for systematic sampling
def
systematic_sampling
(df, starting_index, step):
indices
=
np
.
arange(starting_index,
len
(df), step
=
step)
systematic_sample
=
df
.
iloc[indices]
return
systematic_sample
In [11]:
# Obtaining a systematic sample of size 5
# Because 15/3=5, choose one of the first 3 IDs on the list at random and then every 3rd ID after that.
random
.
seed(
68
)
random_start
=
random
.
randint(
0
,
2
)
print
(random_start)
# another way
# random.seed(68)
# random_start = random.sample(range(3),1)
# print(random_start)
In [12]:
systematic_sample
=
systematic_sampling(df
=
df_students, starting_index
=
random_start, step
=3
)
systematic_sample
# recall that Python starts at position 0, so position 2 corresponds to ID = 3
Stratified Random Sampling
Another type of sampling is stratified random sampling, in which a population is split into groups and a certain number of members from each group are randomly
selected to be included in the sample.
Stratified Random Sampling Using Counts
Out[9]:
ID
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
11
11
12
12
13
13
14
14
15
2
Out[12]:
ID
2
3
5
6
8
9
11
12
14
15
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In [13]:
# Suppose we have the following dataframe containing the ID of 8 students from 2 different undergrad programs.
# This is our population list.
df
=
pd
.
DataFrame({
'ID'
:np
.
arange(
1
,
9
)
.
tolist(),
'program'
:[
'Stats'
]
*4 +
[
'Math'
]
*4
})
# 4 students in Stats, 4 students in Math
df
In [14]:
# random sample of 2 Stats students
df_Stats
=
df[df[
'program'
]
==
'Stats'
]
df_Stats
random_rows
=
random
.
sample(
range
(
4
),
2
)
#randomly selecting 2 students from the 4 Stats students in the populatio
n
print
(df_Stats
.
iloc[random_rows])
In [15]:
# random sample of 2 Math students
df_Math
=
df[df[
'program'
]
==
'Math'
]
df_Math
random_rows
=
random
.
sample(
range
(
4
),
2
)
#randomly selecting 2 students from the 4 Math students in the population
print
(df_Math
.
iloc[random_rows])
In [16]:
# Alternative way using one line of code and additional Python functions
DataFrame.groupby:
https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.groupby.html
(https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.groupby.html)
DataFrame.apply:
https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.apply.html
(https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.apply.html)
DataFrame.sample:
https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.sample.html
(https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.sample.html)
In [17]:
# Stratified random sampling by randomly selecting 2 students from each program to be included in the sample
df
.
groupby(
'program'
, group_keys
=
False
)
.
apply(
lambda
x:x
.
sample(
2
))
Stratified Random Sampling Using Proportions
Out[13]:
ID
program
0
1
Stats
1
2
Stats
2
3
Stats
3
4
Stats
4
5
Math
5
6
Math
6
7
Math
7
8
Math
ID program
3
4
Stats
2
3
Stats
ID program
4
5
Math
6
7
Math
Out[17]:
ID
program
4
5
Math
6
7
Math
0
1
Stats
1
2
Stats
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In [18]:
# Now suppose we have the following population dataframe with 25% Stats and 75% Math students.
df
=
pd
.
DataFrame({
'ID'
:np
.
arange(
1
,
9
)
.
tolist(),
'program'
:[
'Stats'
]
*2 +
[
'Math'
]
*6
})
# 2 students in Stats, 6 students in Math
df
np.rint:
https://numpy.org/doc/stable/reference/generated/numpy.rint.html
(https://numpy.org/doc/stable/reference/generated/numpy.rint.html)
In [19]:
# Stratified random sampling such that the proportion of students in each program sample
# matches the proportion of students from each program in the population dataframe
N
= 4
# sample size
# So, the sample must contain 1 random student from Stats and 3 from Math to maintain the population proportions
In [20]:
# random sample of Stats students
df_Stats
=
df[df[
'program'
]
==
'Stats'
]
df_Stats
random_rows
=
random
.
sample(
range
(
2
),
1
)
#sampling 1 student from the 2 Stats students in the population
print
(df_Stats
.
iloc[random_rows])
In [21]:
# random sample of Math students
df_Math
=
df[df[
'program'
]
==
'Math'
]
df_Math
random_rows
=
random
.
sample(
range
(
6
),
3
)
#sampling 3 students from the 6 Math students in the population
print
(df_Math
.
iloc[random_rows])
Alternative way:
np.rint:
https://numpy.org/doc/stable/reference/generated/numpy.rint.html
(https://numpy.org/doc/stable/reference/generated/numpy.rint.html)
In [22]:
df
.
groupby(
'program'
, group_keys
=
False
)
.
apply(
lambda
x:x
.
sample(
int
(np
.
rint(N
*
len
(x)
/
len
(df)))))
In [ ]:
Out[18]:
ID
program
0
1
Stats
1
2
Stats
2
3
Math
3
4
Math
4
5
Math
5
6
Math
6
7
Math
7
8
Math
ID program
0
1
Stats
ID program
5
6
Math
7
8
Math
4
5
Math
Out[22]:
ID
program
4
5
Math
2
3
Math
3
4
Math
0
1
Stats
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