In hypothesis testing, there are two important values you should be familiar with: alpha (α) and beta (β). These values are used to determine how meaningful the results of the test are. So, let’s talk about them!
Alpha
Alpha is also known as the level of significance. This represents the probability of obtaining your results due to chance. The smaller this value is, the more “unusual” the results, indicating that the sample is from a different population than it’s being compared to, for example. Commonly, this value is set to .05 (or 5%), but can take on any value chosen by the research not exceeding .05.
Alpha also represents your chance of making a Type I Error. What’s that? The chance that you reject the null hypothesis when in reality, you should fail to reject the null hypothesis. In other words, your sample data indicates that there is a difference when in reality, there is not. Like a false positive.
Multiple Hypothesis Testing
When a study includes more than one hypothesis test, the alpha of the test will not match the alpha for each test. There is a cumulative effect of alpha when multiple tests are being conducted such that three tests using alpha=.05 each would have a cumulative alpha of .15 for the study. This exceeds what is acceptable for quantitative research. Therefore, researchers should consider making an adjustment, such as aBonferroni Correction. Using this method, the researcher takes the alpha of the study and divides it by the number of tests being conducted: .05/5 = .01. The result is the level of significance that will be used for each test to determine significance.
Beta
The other key-value relates to the power of your study. Power refers to your study’s ability to find a difference if there is one. It logically follows that the greater the power, the more meaningful your results are. Beta = 1 – Power. Values of beta should be kept small, but do not have to be as small as alpha values. Values between .05 and .20 are acceptable.
Beta also represents the chance of making a Type II Error. As you may have guessed, this means that you came to the wrong conclusion in your study, but it’s the opposite of a Type I Error. With a Type II Error, you incorrectly fail to reject the null. In simpler terms, the data indicates that there is not a significant difference when in reality there is. Your study failed to capture a significant finding. Like a false negative.
Examples:
Type I Error: Testing positive for antibodies, when in fact, no antibodies are present.
Type II Error: Testing negative for antibodies when in fact, antibodies are present.
FAQs
Alpha is the probability of rejecting the null hypothesis when it is true. By convention, typical values of alpha specified in medical research are 0.05 and 0.01. Beta () is the probability of accepting the null hypothesis when it is false. A type II error occurs when a false null hypothesis is accepted.
What is alpha and beta error in statistics? ›
Making a statistical decision always involves uncertainties, so the risks of making these errors are unavoidable in hypothesis testing. The probability of making a Type I error is the significance level, or alpha (α), while the probability of making a Type II error is beta (β).
What is alpha vs beta data? ›
Both alpha and beta are historical measures of past performances. Alpha shows how well (or badly) a stock has performed in comparison to a benchmark index. Beta indicates how volatile a stock's price has been in comparison to the market as a whole.
When to use 0.01 and 0.05 level of significance? ›
How to Find the Level of Significance? If p > 0.05 and p ≤ 0.1, it means that there will be a low assumption for the null hypothesis. If p > 0.01 and p ≤ 0.05, then there must be a strong assumption about the null hypothesis. If p ≤ 0.01, then a very strong assumption about the null hypothesis is indicated.
What is alpha and beta in simple terms? ›
Though both greek letters, alpha and beta are quite different from each other. Alpha is a way to measure excess return, while beta is used to measure the volatility, or risk, of an asset. Beta might also be referred to as the return you can earn by passively owning the market.
What is a good beta value in statistics? ›
Values of beta should be kept small, but do not have to be as small as alpha values. Values between . 05 and . 20 are acceptable.
How to reduce alpha and beta error? ›
Ideally alpha and beta errors would be set at zero, eliminating the possibility of false-positive and false-negative results. In practice they are made as small as possible. Reducing them, however, usually requires increasing the sample size.
What does Alpha error 0.05 mean? ›
An alpha of 0.05 means you are willing to accept a 5% chance of incorrectly rejecting the null hypothesis (Type I error). To test the hypothesis at the 0.05 level, you would: 1. State your null hypothesis (H0) and alternative hypothesis (H1).
Is P value the same as alpha error? ›
The term significance level (alpha) is used to refer to a pre-chosen probability and the term "P value" is used to indicate a probability that you calculate after a given study.
What does alpha tell us in statistics? ›
Before you run any statistical test, you must first determine your alpha level, which is also called the “significance level.” By definition, the alpha level is the probability of rejecting the null hypothesis when the null hypothesis is true. Translation: It's the probability of making a wrong decision.
Analysts use beta when they want to determine a stock's risk profile. High-beta stocks, which generally means any stock with a beta higher than 1.0, are supposed to be riskier but provide higher return potential; low-beta stocks, those with a beta under 1.0, pose less risk but also usually lower returns.
How to calculate alpha and beta? ›
Calculation of alpha and beta in mutual funds
- Fund return = Risk free rate + Beta X (Benchmark return – risk free rate)
- Beta = (Fund return – Risk free rate) ÷ (Benchmark return – Risk free rate)
- Fund return = Risk free rate + Beta X (Benchmark return – risk free rate) + Alpha.
Conventionally, p < 0.05 is referred as statistically significant and p < 0.001 as statistically highly significant.
What is a good p-value? ›
The lower the p-value, the greater the statistical significance of the observed difference. A p-value of 0.05 or lower is generally considered statistically significant. P-value can serve as an alternative to—or in addition to—preselected confidence levels for hypothesis testing.
What is the p-value for dummies? ›
The p value, or probability value, tells you how likely it is that your data could have occurred under the null hypothesis. It does this by calculating the likelihood of your test statistic, which is the number calculated by a statistical test using your data.
What is an alpha and a beta? ›
Alpha and beta are two different parts of an equation used to explain the performance of stocks and investment funds. Beta is a measure of volatility relative to a benchmark, such as the S&P 500. Alpha is the excess return on an investment after adjusting for market-related volatility and random fluctuations.
What are α and β and what is the relationship between them? ›
Relation between α and β:
The common-emitter current gain (β) is the ratio of the transistor's collector current to the transistor's base current, i.e. And the common base DC current gain (α) is a ratio of the transistor's collector current to the transistor's emitter current, i.e.
What does an alpha level of .05 mean? ›
For the current example, the alpha is 0.05. The level of uncertainty the researcher is willing to accept (alpha or significance level) is 0.05, or a 5% chance they are incorrect about the study's outcome. Now, the researcher can perform the research.
How do α and β differ? ›
Answer: The key difference between the two lies in the orientation of the hydroxyl group which is on the same side in α-glucose and on the opposite sides in the β-glucose.
