One-Tailed Test
A one-tailed test is a statistical test wherein the critical area of a distribution is one-sided with the goal that it is either greater than or under a certain value, but not both. On the off chance that the sample being tested falls into the one-sided critical area, the alternative hypothesis will be accepted instead of the null hypothesis.
Financial analysts utilize the one-tailed test to test an investment or portfolio hypothesis.
What Is a One-Tailed Test?
A fundamental concept in inferential statistics is hypothesis testing. Hypothesis testing is run to determine whether a claim is true or not, given a population parameter. A test that is conducted to show whether the mean of the sample is significantly greater than and significantly not exactly the mean of a population is considered a two-tailed test. While the testing is set up to show that the sample mean would be higher or lower than the population mean, it is alluded to as a one-tailed test. The one-tailed test gets its name from testing the area under one of the tails (sides) of a normal distribution, although the test can be utilized in other non-normal distributions.
Before the one-tailed test can be performed, null and alternative hypotheses must be established. A null hypothesis is a claim that the scientist hopes to reject. An alternative hypothesis is the claim supported by rejecting the null hypothesis.
A one-tailed test is otherwise called a directional hypothesis or directional test.
Example of the One-Tailed Test
Let's say an analyst wants to prove that a portfolio manager outperformed the S&P 500 index in a given year by 16.91%. They might set up the null (H0) and alternative (Ha) hypotheses as:
H0: \u03bc ≤ 16.91
Ha: \u03bc > 16.91
The null hypothesis is the measurement that the analyst hopes to reject. The alternative hypothesis is the claim made by the analyst that the portfolio manager performed better than the S&P 500. On the off chance that the outcome of the one-tailed test results in rejecting the null, the alternative hypothesis will be supported. Then again, assuming that the outcome of the test neglects to reject the null, the analyst might carry out further analysis and investigation into the portfolio manager's performance.
The region of rejection is on just a single side of the sampling distribution in a one-tailed test. To determine how the portfolio's return on investment compares to the market index, the analyst must run an upper-tailed significance test in which extreme values fall in the upper tail (right half) of the normal distribution curve. The one-tailed test conducted in the upper or right tail area of the curve will show the analyst how much higher the portfolio return is than the index return and whether the difference is significant.
1%, 5% or 10%
The most common significance levels (p-values) utilized in a one-tailed test.
Determining Significance in a One-Tailed Test
To determine how significant the difference in returns is, a significance level must be specified. The significance level is almost consistently represented by the letter p, which stands for probability. The level of significance is the probability of incorrectly reasoning that the null hypothesis is false. The significance value utilized in a one-tailed test is either 1%, 5%, or 10%, although some other probability measurement can be utilized at the discretion of the analyst or statistician. The probability value is calculated with the assumption that the null hypothesis is true. The lower the p-value, the stronger the evidence that the null hypothesis is false.
On the off chance that the resulting p-value is under 5%, the difference between both observations is statistically significant, and the null hypothesis is rejected. Following our example above, in the event that the p-value = 0.03, or 3%, the analyst can be 97% confident that the portfolio returns didn't rise to or fall below the return of the market for the year. They will, therefore, reject H0 and support the claim that the portfolio manager outperformed the index. The probability calculated in just a single tail of a distribution is half the probability of a two-tailed distribution in the event that comparative measurements were tested utilizing both hypothesis testing tools.
While utilizing a one-tailed test, the analyst is testing for the possibility of the relationship in one direction of interest and completely ignoring the possibility of a relationship in another direction. Utilizing our example over, the analyst is interested in whether a portfolio's return is greater than the market's. In this case, they don't have to statistically account for a situation in which the portfolio manager underperformed the S&P 500 index. Thus, a one-tailed test is possibly appropriate when it isn't important to test the outcome at the flip side of a distribution.
Highlights
- A one-tailed test is a statistical hypothesis test set up to show that the sample mean would be higher or lower than the population mean, but not both.
- Before running a one-tailed test, the analyst must set up a null and alternative hypothesis and establish a probability value (p-value).
- While utilizing a one-tailed test, the analyst is testing for the possibility of the relationship in one direction of interest and completely ignoring the possibility of a relationship in another direction.
FAQ
When Should a Two-Tailed Test Be Used?
You would utilize a two-tailed test when you want to test your hypothesis in both directions.
What Is a One-Tailed T Test Used for?
A one-tailed T-test checks for the possibility of a one-direction relationship but doesn't think about a directional relationship in another direction.
How Do You Determine If It Is a One-Tailed or Two-Tailed Test?
A one-tailed test searches for an increase or lessening in a parameter. A two-tailed test searches for change, which could be a decline or an increase.
