Blog series of Hypothesis Testing: One-tailed and Two-tailed Test

Pallavi Padav
Women in Technology
4 min readApr 4, 2024
https://www.whale-images.com/articles/tile/killer-whale-tail-display-northern-vancouver-island-158.htm

Welcome to the series of hypothesis testing Part 2!. Click here to read about Part 1 ‘Components of a Hypothesis Test’’.

Hypothesis a.k.a Claims are simple English statements representing a change in the previous condition.

Example of Claims:

  1. The average weight of the chocolate bars is not equal to 35g.
  2. A baseball coach believes a certain 4-week program will increase the mean hitting percentage of his players, which is currently 0.285.
  3. A biologist believes that a certain pesticide will cause plants to grow less during a month than they normally do, which is currently 10 inches.

1. Converting claims statement into mathematical/statistical form:

Ask, "Does the statement represent a change in the previous condition?”

  • If the answer is ‘Yes, there is change’ then it is an alternative hypothesis, H1.
  • No, there is no change’, then it is the null hypothesis, H0.

Now look out for clue words and convert them into symbols:

Created by author

Example 1: The average weight of the chocolate bars is not equal to 35g.

  • In this example, the alternative hypothesis (Ha) would be the average weight of the chocolate bars ≠ 35g. This wouldn’t specify whether the average weight of the bar is less or more than 35g.
  • The null hypothesis (H0) would be the average weight of the chocolate bars = 35g.

Example 2: A baseball coach believes a certain 4-week program will increase the mean hitting percentage of his players, which is currently 0.285.

  • The program will cause mean hitting percentage to increase, hence alternative hypothesis (Ha) is μ > 0.285.
  • The null hypothesis (H0) would be the program will not affect the mean hitting percentage. μ = 0.285.

Example 3: A biologist believes that a certain pesticide will cause plants to grow less during a month than they normally do, which is currently 10 inches.

  • The pesticide will cause mean plant growth to decrease, alternative hypothesis (Ha) μ < 10 inches.
  • The null hypothesis (H0) would be the pesticide will not affect the mean plant growth i.e. μ = 10 inches.

2. One-tailed and two-tailed tests?

Compare the signs of the alternative hypothesis (Ha) in all three examples. Example 1 contains the not equal (“≠”) sign hence its Non-directional hypothesis. The remaining two examples contain the less than (“<“) or greater than (“>”) sign.

Directional hypothesis tests are also called “one-tailed” tests and Non-directional hypothesis tests are also called “two-tailed” tests.

https://courses.lumenlearning.com/suny-natural-resources-biometrics/chapter/chapter-3-hypothesis-testing/

where c is the known value.

2.a One-tailed test

In the Directional hypothesis tests /one-tailed test critical region is present in only one part of the bell curve (the red area below). It can be a left-tailed test or a right-tailed test. Left-tailed test: The critical region is in the extreme left region (tail) under the curve. Right-tailed test: The critical region is in the extreme right region (tail) under the curve.

https://www.nipissingu.ca/sites/default/files/One-tailed-Test-or-Two-tailed-Test.pdf

2.b Two-tailed tests

In the Non-directional hypothesis tests /two-tailed tests, the critical region is present on both sides of the bell curve.

https://www.nipissingu.ca/sites/default/files/One-tailed-Test-or-Two-tailed-Test.pdf

For the 5% and 1% significance levels, each side will have 2.5% or 0.5% significance levels.

Please read the following series of hypothesis testing:

In the coming weeks, I will publish the following blogs:

  • Blog 3: How to perform hypothesis testing
  • Blog 4: Type 1 and Type 2 errors

EndNote:

I hope you enjoyed reading the blog on one-tailed and two-tailed hypothesis testing. Please drop your suggestions or queries in the comment section.

Would love to catch you on Linkedin. Mail me here for any queries.

Happy reading!!!!

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