Simpson’s Paradox: A Real-Life Example (from Marketing)

When people say, "Lies, damned lies, and statistics," they mean that the persuasive power of numbers can lead to misguided decisions when statistics are carelessly interpreted. This article explains and illustrates Simpson's paradox, a statistical trick that can be misleading.

How Simpson’s Paradox May Occur in Marketing

Introduction:

Simply put, Simpson’s Paradox means that when you look at statistics in small groups and then combine them, the results can be entirely different. This paradox occurs in various fields like healthcare, sociology, climatology, and more. Let’s explore an example from the world of marketing.

Simpson’s Paradox in Advertisement Analysis

Results of Advertising Campaign

Marketing specialists once grappled with a challenging decision: how to allocate their advertising budget between Android and iOS users. Here’s what happened:

They conducted an online advertising campaign and obtained the following results:

  • Advertisement reached 188,000 Android users.
  • Approximately 49.5% (93,000) of them clicked on the advertisement.
  • Advertisement was presented to 101,000 iOS users.
  • Around 56.5% (57,000) of iOS users engaged with the advertisement.

If you were a marketing specialist in this scenario, you might initially lean towards allocating more budget to iOS users, given their seemingly higher responsiveness (56.5%). However, let’s delve deeper into the data.

A Closer Look at the Results

Out of the 188,000 Android users, 172,000 were phone users, and 16,000 were tablet users. Among phone users, approximately 46% (79,000) clicked on the advertisement. Among tablet users, 87.5% (14,000) engaged with the advertisement. Does this suggest that the advertisement was remarkably more effective for Android tablet users?

To gain clarity, a similar breakdown for iOS users is needed:

Out of the total 101,000 iOS users, 62,000 were iPhone users, and 39,000 were iPad users. Among iPhone users, around 42% (26,000) clicked on the advertisement. Among iPad users, 79.5% (31,000) engaged with the advertisement.

So, to sum up:

Android Users:

  • Shown: 188,000
  • Clicked: 93,000 (49.5%)

iOS Users:

  • Shown: 101,000
  • Clicked: 57,000 (56.5%)

Further breakdown:

Android Phone Users:

  • Shown: 172,000
  • Clicked: 79,000 (46%)

Android Tablet Users:

  • Shown: 16,000
  • Clicked: 14,000 (87.5%)

iOS iPhone Users:

  • Shown: 62,000
  • Clicked: 26,000 (42%)

iOS iPad Users:

  • Shown: 39,000
  • Clicked: 31,000 (79.5%)

Emergence of Simpson’s Paradox

Now it’s contradictory! Initially, it appeared that iOS users responded better (49.5% vs. 56.5%). However, a detailed analysis suggests that Android users, for both phones and tablets, actually clicked on advertisements more frequently. This contradiction is what Simpson’s paradox is. It highlights the challenge of interpreting statistics accurately.

Conclusion:

This example is an excellent demonstration of why people say there are lies, damned lies, and statistics. While statistics are a powerful tool, they must be used professionally and with care. Regardless of your career aspirations, understanding the main principles of using statistics is crucial and, incidentally, taught in school.

References:

Video Version

If you enjoyed exploring these numbers and want a more comprehensive understanding of what happened with Android and iOS users and why statistics showed opposite results, feel free to subscribe to our video content. In the video version of this blog post, we visualize this information conveniently in the form of tables and explain why statistics seemingly played tricks. Enjoy the preview of the video below.

Further reading:

In general, mathematics is frequently employed to analyze business and marketing data. Explore more articles on the usage of mathematics in business and marketing in our blog:

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