Significance Level

A Significance Level is the probability of committing a Type I error.

• AKA: Type I Error Rate, α.
• Context:
  • It can also be defined as the probability of rejecting the null hypothesis given that is true, i.e. [math]\displaystyle{ P\big( \mbox{reject } H_0 \big| H_0 \mbox{ is true} \big) }[/math].
  • It can be defined as [math]\displaystyle{ \alpha=1 - \frac{\text{confidence level}}{100} }[/math]
• Example(s):
  • A False Positive Error Rate.
  • Given a confidence level of [math]\displaystyle{ 95\% }[/math] the significance level is [math]\displaystyle{ \alpha=1-(95/100)=0.05 }[/math]
• Counter-Example(s):
  • Confidence Level.
  • Confidence Interval.
  • Statistical Power.
  • P-value.
• See: Region of Rejection, Null Hypothesis, Hypothesis Test Acceptance Region, Statistical Hypothesis Testing Task.

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References

2017a

• (Wikipedia, 2017) ⇒ http://en.wikipedia.org/wiki/Type_I_and_type_II_errors#Type_I_error
  • A type I error occurs when the null hypothesis (H₀) is true, but is rejected. It is asserting something that is absent, a false hit. A type I error may be likened to a so-called false positive (a result that indicates that a given condition is present when it actually is not present).

The type I error rate or significance level is the probability of rejecting the null hypothesis given that it is true. It is denoted by the Greek letter α (alpha) and is also called the alpha level. Often, the significance level is set to 0.05 (5%), implying that it is acceptable to have a 5% probability of incorrectly rejecting the null hypothesis.

2017b

• (Stat Treak, 2017) ⇒ http://stattrek.com/statistics/dictionary.aspx?definition=P-value Retrieved: 2017-03-07
  • A Type I error occurs when the researcher rejects a null hypothesis when it is true. The probability of committing a Type I error is called the significance level, and is often denoted by α.

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