How do you find Alpha?

在统计学中，"Alpha"（α）通常指的是错误发现率（false discovery rate），它是在假设检验中犯第一类错误（错误地拒绝一个真实的零假设）的概率。在进行假设检验时，研究者需要设定一个显著性水平，即他们愿意接受犯第一类错误的最高概率。这个水平通常用α表示，并且通常设置为0.05或0.01，意味着研究者愿意接受5%或1%的错误拒绝零假设的概率。

### **Step 1: Understanding Alpha in Statistical Testing**

Alpha is a fundamental concept in statistical hypothesis testing. It is the probability of rejecting a true null hypothesis (Type I error). When conducting a hypothesis test, researchers set a significance level, which is the threshold for deciding whether the results are statistically significant. This significance level is the alpha level (α), and it is typically set at 0.05, indicating a 5% risk of a Type I error.

#### Setting the Alpha Level

The alpha level is set before conducting the test and is a key factor in determining the outcome of the test. It is a measure of the stringency of the test. A lower alpha level means a more stringent test, which is less likely to produce a Type I error but also less likely to detect a true effect if one exists (increasing the risk of a Type II error).

#### One-Tailed vs. Two-Tailed Tests

The concept of alpha also applies to the type of test being conducted. A one-tailed test focuses on the possibility of the outcome being on one side of the distribution (either greater than or less than the null hypothesis value). A two-tailed test considers the possibility of the outcome being on either side of the distribution. For a two-tailed test, the alpha level is divided by 2, which effectively makes the test more stringent.

#### Calculating Confidence Intervals

Confidence intervals provide a range within which we can be confident that the true value lies. The relationship between alpha and confidence intervals is given by the formula:

\[ \text{Confidence Level} = 1 - \alpha \]

For example, if you want to be 95% confident that your analysis is correct, the alpha level would be:

\[ \alpha = 1 - 0.95 = 0.05 \]

This means there is a 5% chance that the interval does not contain the true value. For a two-tailed test, you would divide the alpha level by 2:

\[ \alpha_{\text{two-tailed}} = \frac{\alpha}{2} = \frac{0.05}{2} = 0.025 \]

#### Practical Implications

Choosing the right alpha level is crucial. Setting it too low can lead to underpowered tests that fail to detect true effects. Setting it too high can increase the likelihood of false positives. The decision on the alpha level should be based on the costs of Type I and Type II errors in the context of the study.

### Step 2:

To get -- subtract your confidence level from 1. For example, if you want to be 95 percent confident that your analysis is correct, the alpha level would be 1 -C .95 = 5 percent, assuming you had a one tailed test. For two-tailed tests, divide the alpha level by 2.Nov 6, 2012