Should I Learn Calculus or Statistics First If I’m Learning on My Own?

When embarking on a journey to learn statistics, one of the earliest questions arises: should you start with calculus, or can you dive straight into statistics?

Why Not Start with Statistics?

At the beginning, when you are first learning statistics, you really don’t need any calculus. These courses are inherently applied and focus on how statistical procedures can be used to analyze data. They take a “cookbook” approach, treating the procedures as a recipe for conducting data analysis. For these introductory courses, a good understanding of high school math without calculus is more than sufficient.

Deepening Your Understanding with Calculus

If you truly want to understand how statistical procedures are developed, you will need both linear algebra and calculus, both univariate and multivariate. For very advanced work, you might also need to understand real analysis, complex analysis, and measure theory.

The Importance of Applied Statistics

At the core of statistical theory, applied statistics is about "telling a story" about the patterns in your dataset. Statistical procedures are merely tools to help you tell these stories in a compelling way. To analyze data in a way that provides insights, a researcher needs curiosity, creativity, and a solid understanding of statistical theory.

When Does Calculus Come into Play?

While applied statistics courses might not require calculus, some more advanced topics cannot be understood without it. Continuous distributions, for example, can be challenging to grasp without a solid foundation in calculus. However, discrete distributions are often more accessible to those without a strong background in calculus.

Independently or Interdependently?

Calculus and statistics can be studied independently, but having a foundational understanding of both can be beneficial. The study of statistics does not have calculus as a prerequisite at the beginning, but it can be useful to know both subjects well at a later point. Concepts like the Gamma function, marginal probabilities in continuous distributions, and even determining the area under a normal distribution require a good grasp of calculus.

Conclusion and Expert Opinion

In general, it is beneficial to start with statistics if you are new to the subject. However, if you plan to delve deeply into the theoretical underpinnings of statistics, a solid background in calculus is crucial. As one expert put it, 'Not just "yes" "Heck yes". To truly understand statistics, you need to understand integration at a minimum. Studying statistics without calculus is superficial at best.'

To further refine your understanding, consider supplementing your studies with resources that enhance both your knowledge of statistics and calculus. This will give you a well-rounded foundation, enabling you to tackle more advanced topics with confidence.