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Clojure for Data Science

You're reading from   Clojure for Data Science Statistics, big data, and machine learning for Clojure programmers

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Product type Paperback
Published in Sep 2015
Publisher
ISBN-13 9781784397180
Length 608 pages
Edition 1st Edition
Languages
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Author (1):
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Henry Garner Henry Garner
Author Profile Icon Henry Garner
Henry Garner
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Table of Contents (12) Chapters Close

Preface 1. Statistics FREE CHAPTER 2. Inference 3. Correlation 4. Classification 5. Big Data 6. Clustering 7. Recommender Systems 8. Network Analysis 9. Time Series 10. Visualization Index

The t-statistic


While using the t-distribution, we look up the t-statistic. Like the z-statistic, this value quantifies how unlikely a particular observed deviation is. For a dual sample t-test, the t-statistic is calculated in the following way:

Here, is the pooled standard error. We could calculate the pooled standard error in the same way as we did earlier:

However, the equation assumes knowledge of the population parameters σa and σb, which can only be approximated from large samples. The t-test is designed for small samples and does not require us to make assumptions about population variance.

As a result, for the t-test, we write the pooled standard error as the square root of the sum of the standard errors:

In practice, the earlier two equations for the pooled standard error yield identical results, given the same input sequences. The difference in notation just serves to illustrate that with the t-test, we depend only on sample statistics as input. The pooled standard error can be...

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