Learn Stats for Python III: Probability and Sampling
BY IVÁN PALOMARES CARRASCOSAPOSTED ON SEPTEMBER 9, 2024

Probability and Sampling

About Part III: Probability and Sampling

Part III dives into applied probability theory, concretely by modeling discrete and continuous probability distributions in Python. Basics of probability theory are recommended to make the most of the tutorials recommended in the sections below. The following post is a good starting point to acquaint or refresh basic probability concepts. Following probability distribution modeling with Python, we suggest some tutorials focused on data sampling methods: most of these methods rely on the principles behind probability distributions.

1. Probability Distributions

There are plenty of Python tutorials that introduce key probability distributions, each focused on describing how data behaves under different scenarios. Understanding these distributions is essential for statistical analysis because they constitute the basis for performing inferences about data populations from samples (as we will cover in part IV of the series).

How commonly do used distributions in most fields, like Normal, Binomial, and Poisson, behave? To find the answer through a bit of practice, we suggest you get acquainted with probability distribution modeling for Python with these five tutorials related to the most commonly utilized distributions in the majority of applications:

How to use the uniform distribution in Python
How to use the binomial distribution in Python
How to generate a Normal Distribution in Python
How to plot a Normal Distribution in Python
How to use the Poisson distribution in Python
How to Use the Exponential Distribution in Python

2. Critical Values and p-values

In statistical inference -which we will focus on in the next post of this series through hypothesis testing methods-, critical values and p-values are essential concepts. Finding these values for datasets modeled by diverse probability distributions, and interpreting them, is important to yield conclusions about the data such as the existence or absence of significant differences between populations or groups. Getting familiar with these statistics paves the way for assessing the significance of your data analyses and making reliable data-driven decisions.

How to find the Z critical value in Python
How to find the T critical value in Python
How to find a value from a Z-score in Python
How to find a value from a t-score in Python

Note that the concepts covered in the four suggested tutorials above are closely interrelated to hypothesis testing methods which will be covered in more detail in part IV of this tutorial series.

3. Cumulative Distribution Functions (CDFs) and Specific Functions

These tutorials dive into the concept of cumulative distribution functions (CDFs), which are used to quantify the probability that tells us the probability that a random variable takes on a value less than or equal to some threshold value. They are another crucial element in various statistical inference and hypothesis testing approaches. CDFs are pivotal in understanding the probability of events up to a certain threshold. For example, the probability that daily rainfall will be less than or equal to 5 inches per squared meter.

How to Calculate & Plot a CDF in Python
How to Calculate & Plot the Normal CDF in Python

4. Sampling Methods

Sampling techniques are vital for collecting representative data from larger populations, often to perform subsequent hypotheses testing methods on them. These methods include stratified, cluster, and systematic sampling, and they can be done with or without replacement depending on the scenario and particular data needs and constraints. Data sampling methods help ensure that the samples drawn are unbiased, representative of the overall population, and statistically valid, leading to more accurate and reliable conclusions.

Sampling with replacement in Pandas
Stratified sampling in Pandas
Systematic sampling in Pandas
Cluster sampling in pandas

Coming Up Next

Now that we are acquainted with probability distributions and laid the foundations for performing inferential statistical analysis, the next post in this series will focus on formal statistical inference methodologies for such analysis tasks, including confidence interval analysis and hypothesis tests.