Blog series of Hypothesis Testing: One-tailed and Two-tailed Test
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:
- The average weight of the chocolate bars is not equal to 35g.
- A baseball coach believes a certain 4-week program will increase the mean hitting percentage of his players, which is currently 0.285.
- 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:
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.
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.
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.
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:
- Blog 1: Components of a Hypothesis Test
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:
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