Python: Descriptives and Indexing

1.7. Python: Descriptives and Indexing#

In this notebook we cover some key Pandas syntax and functions:

Syntax for getting various descriptive statistics from a Pandas dataframe
Syntax for indexing a dataframe - finding the rows and columns that you need
- this allows you to get descriptives for specific rows and columns

Here we meet indexing in the context of descriptive statistics, but indexing is something you will do every single time you write code for data analysis. Incorrect syntax in indexing is the number one biggest source of bugs for student on this course, so it is well worth spending the time to get to grips with it.

You absolutely should work through all the exercises in this notebook in advance of the tutorial.

1.7.1. Set up Python Libraries#

As usual you will need to run this code block to import the relevant Python libraries

# Set-up Python libraries - you need to run this but you don't need to change it
import numpy as np
import matplotlib.pyplot as plt
import scipy.stats as stats
import pandas as pd
import seaborn as sns
sns.set_theme(style='white')
import statsmodels.api as sm
import statsmodels.formula.api as smf

1.7.2. Import a dataset to work with#

We will work with weather data from the Oxford weather station. This code block will read it automatically from the internet.

weather = pd.read_csv("https://raw.githubusercontent.com/jillxoreilly/StatsCourseBook_2024/main/data/OxfordWeather.csv")
display(weather)

	YYYY	Month	MM	DD	DD365	Tmax	Tmin	Tmean	Trange	Rainfall_mm
0	1827	Jan	1	1	1	8.3	5.6	7.0	2.7	0.0
1	1827	Jan	1	2	2	2.2	0.0	1.1	2.2	0.0
2	1827	Jan	1	3	3	-2.2	-8.3	-5.3	6.1	9.7
3	1827	Jan	1	4	4	-1.7	-7.8	-4.8	6.1	0.0
4	1827	Jan	1	5	5	0.0	-10.6	-5.3	10.6	0.0
...	...	...	...	...	...	...	...	...	...	...
71338	2022	Apr	4	26	116	15.2	4.1	9.7	11.1	0.0
71339	2022	Apr	4	27	117	10.7	2.6	6.7	8.1	0.0
71340	2022	Apr	4	28	118	12.7	3.9	8.3	8.8	0.0
71341	2022	Apr	4	29	119	11.7	6.7	9.2	5.0	0.0
71342	2022	Apr	4	30	120	17.6	1.0	9.3	16.6	0.0

71343 rows × 10 columns

1.7.3. Get descriptive statistics#

We will look at indexing in the context of getting descriptive statistics for the different variables in a dataframe, and/or for a selection of rows.

Pandas has a number of built-in functions to get descriptive statistics:

df.mean() - gets the mean
df.median() - gets the median
df.var() - gets the variance
df.std() - gets the standard deviation
df.min() - gets the minimum value
df.max() - gets the maximum value
df.corr() - gets the correlation coefficient (Pearson or Spearman)

in the function names above, df is just a placeholder for “dataframe”

You can replace df with the name of your dataframe (and we need to tell the function to use only columns containing numerical data)

weather.mean(numeric_only=True)

YYYY           1924.165174
MM                6.516210
DD               15.729154
DD365           182.917077
Tmax             13.890153
Tmin              6.156018
Tmean            10.046208
Trange            7.734244
Rainfall_mm       1.786964
dtype: float64

Which columns from the dataframe are missing from the table of means?

Month is missing because the values are strings (words); we only get the mean for numerical columns

1.7.4. Decriptives for a single column#

Format:

df.column.mean()

You might just want the mean for one column, in which case you can include the column name as follows:

weather.Tmax.mean()

13.890153065515406

Instead of a whole table of means, many of which were irrelevant, we now just have the single number we wanted - the mean of Tmax

Think check that the value obtained this way matches the one in the table above.

Why does it work?#

The commmand weather.Tmax.mean() has two steps.

Step 1:

The syntax weather.Tmax (or more generally, df.column) returns just the one column of the dataframe as a series (essentially a one-column table).

Look:

weather.Tmax

       8.3
       2.2
      -2.2
      -1.7
       0.0
         ... 
  15.2
  10.7
  12.7
  11.7
  17.6
Name: Tmax, Length: 71343, dtype: float64

If we liked, we could give this single-column series a name a ‘save’ it:

DailyMaxima  = weather.Tmax
print(DailyMaxima)

       8.3
       2.2
      -2.2
      -1.7
       0.0
         ... 
  15.2
  10.7
  12.7
  11.7
  17.6
Name: Tmax, Length: 71343, dtype: float64

However, we don’t need to do that as we can just tack the .mean() function onto it directly as follows:

Step 2:

The syntax .mean() gets the mean of the thing before the dot (i.e. the series you created with the command weather.Tmax)

weather.Tmax.mean()

13.890153065515406

Exercises#

Complete the following quick practice questions.

Note that the numerical answers are provided so you can check that you have done it correctly.

# get the mean daily rainfall
# answer = 1.79

# get the median daily rainfall
# answer = 0.0
# think - why??

# get the standard deviation of the maximum daily temperature
# answer = 5.63

# find the minimum value of "year" 
# answer = 1827

1.7.5. Get descriptives for a subset of rows#

df.query('columnname == number')
df.query('columnname == "string"')
df.query('columnname1 == value1 and columnname2 == value2')

Say I want to know the mean daily maximum temperatures for the year 1921.

Step 1: find the relevant rows#

I first need to somehow pull out the rows of the table where the value for YYYY is 1921

I can do this using the function df.query, for example weather.query(‘YYYY == 1921’)

note the quote marks surrounding the whole query
note the double equals sign ==, which is used for checking if two values are equal (as opposed to setting a value)

# get all the rows where year is 1921
weather.loc[weather.YYYY == 1921]

	YYYY	Month	MM	DD	DD365	Tmax	Tmin	Tmean	Trange	Rainfall_mm
34333	1921	Dec	12	31	1	9.1	3.3	6.2	5.8	0.0
34334	1921	Jan	1	1	2	12.2	7.1	9.7	5.1	9.7
34335	1921	Jan	1	2	3	11.9	8.7	10.3	3.2	6.1
34336	1921	Jan	1	3	4	9.9	5.9	7.9	4.0	0.0
34337	1921	Jan	1	4	5	12.3	9.8	11.1	2.5	5.5
...	...	...	...	...	...	...	...	...	...	...
34693	1921	Dec	12	26	361	10.8	-3.1	3.9	13.9	5.6
34694	1921	Dec	12	27	362	11.2	5.4	8.3	5.8	1.3
34695	1921	Dec	12	28	363	13.9	3.9	8.9	10.0	0.0
34696	1921	Dec	12	29	364	7.6	1.7	4.7	5.9	0.8
34697	1921	Dec	12	30	365	11.7	1.9	6.8	9.8	4.5

365 rows × 10 columns

Note the size of this table - there are 365 rows. Why?

In the original table weather, there is one row per day
365 of those rows (days) match the criterion ‘YYYY = 1921’ because there are 365 days in a year.

If I wanted to, I could give this table a name and ‘save’ it for later use:

weather1921 = weather.query('YYYY == 1921') # create a new dataframe for just 1921
weather1921 # look at my new dataframe

	YYYY	Month	MM	DD	DD365	Tmax	Tmin	Tmean	Trange	Rainfall_mm
34333	1921	Dec	12	31	1	9.1	3.3	6.2	5.8	0.0
34334	1921	Jan	1	1	2	12.2	7.1	9.7	5.1	9.7
34335	1921	Jan	1	2	3	11.9	8.7	10.3	3.2	6.1
34336	1921	Jan	1	3	4	9.9	5.9	7.9	4.0	0.0
34337	1921	Jan	1	4	5	12.3	9.8	11.1	2.5	5.5
...	...	...	...	...	...	...	...	...	...	...
34693	1921	Dec	12	26	361	10.8	-3.1	3.9	13.9	5.6
34694	1921	Dec	12	27	362	11.2	5.4	8.3	5.8	1.3
34695	1921	Dec	12	28	363	13.9	3.9	8.9	10.0	0.0
34696	1921	Dec	12	29	364	7.6	1.7	4.7	5.9	0.8
34697	1921	Dec	12	30	365	11.7	1.9	6.8	9.8	4.5

365 rows × 10 columns

… but I don’t need to do this as I can tack on more commands to complete my goal in a single line of code.

Step 2: find the relevant column#

Now that I have grabbed the relevant rows, I narrow it down to column Tmax

weather.query('YYYY == 1920').Tmax

   3.2
  13.2
   4.5
   3.7
   3.7
         ... 
  12.1
  11.9
  12.3
  12.4
  12.1
Name: Tmax, Length: 366, dtype: float64

Step 4: add in the actual function#

FInally, I can tack on teh function I want to run on my selected rows and column: mean():

weather.query('YYYY == 1920').Tmax.mean()

13.701092896174861

Exercises#

Complete the following quick practice questions:

# Get the mean daily maximum temperature in 2006
# answer = 15.7

# Get the mean daily minimum temperature in 1947
# answer = 6.16

1.7.6. Get descriptives for one category#

What about getting the mean daily maximum temperatures for, say, October? So I need to pull out all the rows in which ’MM’ matches ’Oct’

The syntax is very similar, but now I am matching a string "Oct", so it needs to be in quotes:

weather.query('Month == "Oct"').Tmax.mean()

14.112638544251446

note you can actually use single and double quotes interchangeably in Python, but in cases like this where you have quotes within quotes, it is better to use both types to avoid the computer getting confused about which opening and closing quotes to pair up.

so you could do either of these

weather.query(‘Month == “Oct”’).Tmax.mean()
weather.query(“Month == ‘Oct’”).Tmax.mean()

but not these

weather.query(‘Month == ‘Oct’’).Tmax.mean()
weather.query(“Month == “Oct””).Tmax.mean()

Exercises#

Complete the following quick practice questions:

# Get the mean daily rainfall in January
# answer = 1.77

# Get the mean daily rainfall in June
# answer = 1.81
# Is this surprising? why?

1.7.7. Match multiple conditions#

What if I want to know the mean daily maximum temperature in 1920 for June only?

We can simply use and or & to pass df.query() multiple conditions:

# mean daily maximum temperature in 1920
weather.query('YYYY == 1920').Tmax.mean()

13.701092896174861

# mean daily maximumm temperature in 1920
weather.query('YYYY == 1920 & MM == 6').Tmax.mean()

19.553333333333335

Think hopefully the value for June is higher than the average for the whole year? If not something has gone wrong!

Exercises#

Complete the following quick practice questions:

# Get the mean daily rainfall in June 2007
# answer = 2.62

# Get the minimum temperature in January 1947
# answer = -12.4. This was an unusually cold winter.
# note that you were asked for the min temperature in that month, not the mean of the daily minimum Tmin)

1.7.8. Syntax for correlation#

When we run a correlation, we need to index two columns - the two we are correlating.

Say we want to get the correlation between the minimum and maximum daily temperatures,Tmin and Tmax:

Correlation is ‘symmetrical’ (it doesn’t matter which variable is \(x\) and which is \(y\)) but for the purposes of the pandas function we are using, we first find one of the columns (doesn’t matter which one):

weather.Tmin

… and call the pandas function df.corr() to operate on it:

weather.Tmin.corr()

Inside the brackets, we tell it which column to correlate against weather.Tmin:

# get the correlation between columns Tmin and Tmax of dataframe weather
weather.Tmin.corr(weather.Tmax)

0.8414800914062079

We could change what we correlate against Tmin by changing what is inside the brackets, eg:

# get the correlation between columns Tmin and Tmean of dataframe weather
weather.Tmin.corr(weather.Tmean)

0.9502479355058366

Since correlation is ‘symmetrical’ (it doesn’t matter which variable is \(x\) and which is \(y\)) we can also switch the variables around:

# get the correlation between columns Tmin and Tmean of dataframe weather
weather.Tmean.corr(weather.Tmin)

0.9502479355058366

… we just need one column specified outside the brackets and one inside

Correlation type#

We can set the type of correlation to Pearson or Spearman as appropriate (the default is Pearson’s \(r\)):

# get the correlation between columns Tmin and Tmax of dataframe weather
weather.Tmin.corr(weather.Tmax, method='spearman')

0.8438796074978867

Exercises#

Complete the following practice questions to help you get to grips with the syntax for correlation:

# Find the Spearman correlation between daily mean temperature Tmean, and rainfall
# answer = -0.019

# Find the correlation between year and daily mean temperature
# answer = 0.083

Think - are these strong or weak correlations? Is this surprising, did you expect something different?

All-by-all correlation matrix#

We can also quickly output all the correlations between all possible pairs of columns in a dataframe by simply not giving any column index (but we do have to tell it to only use the numeric columns):

weather.corr(numeric_only=True)

	YYYY	MM	DD	DD365	Tmax	Tmin	Tmean	Trange	Rainfall_mm
YYYY	1.000000	-0.003411	-0.000059	-0.003372	0.071631	0.089683	0.083044	-0.001257	0.008117
MM	-0.003411	1.000000	0.010567	0.995580	0.179681	0.235401	0.213082	-0.018820	0.043672
DD	-0.000059	0.010567	1.000000	0.092771	0.001217	0.002876	0.002035	-0.002055	0.005315
DD365	-0.003372	0.995580	0.092771	1.000000	0.177016	0.233248	0.210545	-0.020536	0.043925
Tmax	0.071631	0.179681	0.001217	0.177016	1.000000	0.841480	0.967881	0.593339	-0.008807
Tmin	0.089683	0.235401	0.002876	0.233248	0.841480	1.000000	0.950248	0.064379	0.086181
Tmean	0.083044	0.213082	0.002035	0.210545	0.967881	0.950248	1.000000	0.371965	0.035037
Trange	-0.001257	-0.018820	-0.002055	-0.020536	0.593339	0.064379	0.371965	1.000000	-0.144654
Rainfall_mm	0.008117	0.043672	0.005315	0.043925	-0.008807	0.086181	0.035037	-0.144654	1.000000

The problem with this is that the figure we want is often buried amongst a lot of irrelevant correlation coefficients.

Correlation using `scipy.stats`#

Note that here we are using the pandas function df.corr()

Later in the course we will use two functions from a library called scipy.stats:

stats.pearsonr()
stats.spearmanr()

These are actually a bit more useful as they give us a \(p\)-value for the correlation as well as the correlation coefficient

don’t worry if you don’t know what a \(p\)-value is yet - this will be covered later in the course

scipy.stats will be used extensively in the module on hypothesis testing

Python: Descriptives and Indexing

Contents

1.7. Python: Descriptives and Indexing#

1.7.1. Set up Python Libraries#

1.7.2. Import a dataset to work with#

1.7.3. Get descriptive statistics#

1.7.4. Decriptives for a single column#

Why does it work?#

Exercises#

1.7.5. Get descriptives for a subset of rows#

Step 1: find the relevant rows#

Step 2: find the relevant column#

Step 4: add in the actual function#

Exercises#

1.7.6. Get descriptives for one category#

Exercises#

1.7.7. Match multiple conditions#

Exercises#

1.7.8. Syntax for correlation#

Correlation type#

Exercises#

All-by-all correlation matrix#

Correlation using scipy.stats#

Correlation using `scipy.stats`#