One Tailed and Two Tailed Test
Understanding One Tailed and Two Tailed Test
One Tailed and Two Tailed Test in Statistics are the backbone of data analytics, helping us make informed decisions using data. One of the foundational concepts in inferential statistics is hypothesis testing which includes One Tailed and Two Tailed Test.
Within this category, we often come across the terms “one tailed” and “two tailed” tests. Although these may sound technical, the concept is quite simple when explained in everyday language.
In this article, we’ll explore what one tailed and two tailed tests are, when to use them, and how they differ. We’ll also walk through some real world examples for your understanding.
What is Hypothesis Testing ?
Before diving into one and two tailed tests, let’s quickly recap hypothesis testing.
Hypothesis testing is a statistical method that allows us to test assumptions (or hypotheses) about a population based on sample data. For example, a company might want to know if a new marketing strategy leads to higher sales than the old one.
There are two main types of hypotheses:
Null Hypothesis (H0): Assumes there is no effect or difference.
Alternative Hypothesis (H1 or Ha): Assumes there is an effect or difference.
Our goal is to determine whether the sample data provides enough evidence to reject the null hypothesis in favor of the alternative.
What is a One tailed test?
One tailed test looks for an effect in one direction. It is used when the alternative hypothesis is directional.
A one tailed test checks whether a sample mean is significantly greater than or less than a population mean or a specified value, but not both.
When to Use:
When you’re only interested in deviations in one direction.
Examples:
Testing if a new drug is more effective than the current one.
Checking if a machine produces items lighter than the standard weight.
Types:
Right Tailed Test: If we want to know whether the mean is greater than a certain value.
H0: μ ≤ μ0
Ha: μ > μ0
Left Tailed Test: If we want to know whether the mean is less than a certain value.
H0: μ ≥ μ0
Ha: μ < μ0
What is a Two tailed test?
A two tailed test checks for the possibility of an effect in both directions.
It evaluates whether the sample mean is significantly different from the population mean, either higher or lower.
When to Use:
- When you’re interested in any significant deviation, regardless of direction.
- Examples:
Testing if a new teaching method results in different test scores (could be higher or lower).
Verifying if a machine’s output weight is different from the standard.
Structure:
H0: μ = μ0
Ha: μ ≠ μ0
Visualizing the Difference
Imagine a bell shaped curve (normal distribution).
In a 1 tailed test, you only shade one tail (left or right), depending on your hypothesis.
In a 2 tailed test, you shade both tails because you’re testing for any extreme values in either direction.
This helps understand how the critical region (where we reject the null hypothesis) differs:
One-tailed test has the entire alpha level (e.g., 5%) in one tail.
Two-tailed test splits the alpha into 2.5% in each tail (if alpha = 5%).
One Tailed vs Two Tailed Tests
Important Questions to Ask:
Do I care about only one direction (greater or less)? → One-tailed
Do I care about any difference (greater or less)? → Two-tailed
Practical Tip for Testing:
Always define your hypotheses before looking at the data. Choosing a one-tailed test just to get significant results is considered bad practice.
Advantages and Disadvantages of One Tailed and Two Tailed Test
| Feature | One-Tailed Test | Two-Tailed Test |
|---|---|---|
| Simplicity | Easier to get significance in one direction | More balanced test |
| Flexibility | Less flexible (only one direction) | Tests for any difference |
| Acceptance | Less accepted in scientific journals | Widely accepted |
| Risk of Misuse | Higher, if chosen after seeing data | Lower, more conservative |
p-Values and Significance Levels
In a 1 tailed test, the p-value represents the probability in one tail.
In a 2 tailed test, the p-value includes both tails (it’s effectively doubled if the test was originally one-tailed).
For a significance level (α) of 0.05:
One tailed: Reject H0 if p < 0.05
Two tailed: Reject H0 if p < 0.025 in each tail (total 0.05)
Practical Implementation One Tailed and Two Tailed Test
Scenario:
A coffee shop claims that their average cup size is 300 ml. You collected a random sample of 10 cups and want to test if the actual average differs.
Your data (in ml):[290, 295, 305, 310, 300, 298, 299, 303, 297, 308]
Step By Step In Excel
2 Tailed Test (Is the mean ≠ 300 ml?)
- Entering the Data In Excel
290
295
305
310
300
298
299
303
297
308 Mean:
=AVERAGE(A1:A10)Standard Deviation:
=STDEV.S(A1:A10)Sample Size (n): 10
Standard Error (SE):
=B2/SQRT(10)t-statistic:
(Mean - 300)/SEDegrees of Freedom:
n - 1 = 9Two-tailed p-value:
=2*T.DIST.2T(ABS(t), 9)
1 Tailed Test (Is mean < 300 ml?)
Use:
=T.DIST(t, 9, TRUE)
Interpretation:
If p-value < 0.05, reject the null hypothesis.
2-tailed: Any significant difference.
1-tailed: Only test if it’s less than 300 ml.
Python Implementation
import scipy.stats as stats
import numpy as np
# Sample data
data = [290, 295, 305, 310, 300, 298, 299, 303, 297, 308]
mu = 300 # Claimed average
# One-sample t-test
t_stat, p_value_two_tailed = stats.ttest_1samp(data, mu)
# One-tailed p-value (less than 300)
p_value_one_tailed = p_value_two_tailed / 2 if t_stat < 0 else 1 - p_value_two_tailed / 2
print(f"Mean: {np.mean(data):.2f}")
print(f"Two-Tailed Test: t = {t_stat:.4f}, p = {p_value_two_tailed:.4f}")
print(f"One-Tailed Test (mean < 300): p = {p_value_one_tailed:.4f}")
-
Use 2-tailed if you’re checking for any difference.
-
Use 1-tailed if you want to test specifically if it’s less than 300.
Real Life Examples of One Tailed and Two Tailed Test
Example 1: Drug Effectiveness
Scenario: A pharmaceutical company wants to test if a new drug lowers blood pressure more than the existing one.
Test Type: One-tailed (we care only if it’s better, not worse).
Example 2: Manufacturing Tolerance
Scenario: A company checks if the average weight of a product is different from the required 500g.
Test Type: Two-tailed (too high or too low, both are issues).
Example 3: Employee Performance
Scenario: HR tests if a new training program has any effect (positive or negative) on productivity.
Test Type: Two-tailed
Conclusion:
Understanding one and two tailed tests is crucial in statistics and data analytics. The key is to match the test type with the research question. If your hypothesis is directional, go for a one tailed test. If it’s non directional, a two-tailed test is your best bet.
Always remember to define your hypotheses clearly, choose the right test before analyzing the data, and interpret results carefully. With these principles, you’ll be well-equipped to make data-driven decisions that are statistically sound.
Quick Recap:
One-tailed: Test for difference in one direction only
Two-tailed: Test for any difference
Choose based on your hypothesis, not the outcome
Whether you’re running A/B tests, checking product quality, or analyzing surveys, this understanding will make you a smarter, more reliable data analyst.
If you want to learn more, you can check out our PrepInsta Prime’s ML / AI and Data Analytics Course.
