Hypothesis Testing: Type I Error
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Questions and Answers

What is the consequence of rejecting a true null hypothesis?

  • Failing to detect a real effect
  • Making false claims and damaging credibility
  • Wasting resources on a non-existent effect
  • All of the above (correct)

What is the typical value of alpha (α) in hypothesis testing?

  • 0.20
  • 0.05 (correct)
  • 0.10
  • 0.01

What is the effect of a larger sample size on Type I Error?

  • Increases the risk of Type I Error (correct)
  • Has no effect on Type I Error
  • Decreases the risk of Type I Error
  • Always leads to Type II Error

What is the result of a smaller significance level (α) in hypothesis testing?

<p>Decreases the risk of Type I Error (D)</p> Signup and view all the answers

What is the definition of a Type I Error?

<p>Rejecting a true null hypothesis (A)</p> Signup and view all the answers

How can Type I Error be minimized?

<p>Using a conservative significance level (α) (B)</p> Signup and view all the answers

What can be said about a one-to-one function?

<p>It maps each x to exactly one y and each y to exactly one x (D)</p> Signup and view all the answers

What is the inverse function of f denoted as?

<p>f-1 (A)</p> Signup and view all the answers

What is true about the domain and range of a one-to-one function?

<p>Each x in the domain corresponds to exactly one y in the range, and each y in the range corresponds to exactly one x in the domain (A)</p> Signup and view all the answers

What is the purpose of the inverse function of f?

<p>To correspond from the range of f back to the domain of f (A)</p> Signup and view all the answers

What type of function has an inverse function?

<p>Only one-to-one functions (A)</p> Signup and view all the answers

Study Notes

Hypothesis Testing: Type I Error

Definition: A Type I Error occurs when a true null hypothesis is rejected, resulting in a false positive.

Also known as:

  • Alpha (α) error
  • False positive error

Consequences:

  • Rejection of a true null hypothesis can lead to incorrect conclusions and misguided decisions
  • Resources may be wasted on pursuing a non-existent effect or relationship
  • False claims can be made, damaging credibility and trust

Probability of Type I Error:

  • Represented by the Greek letter alpha (α)
  • Typically set to 0.05, indicating a 5% chance of rejecting a true null hypothesis
  • The smaller the α, the lower the probability of a Type I Error, but the higher the probability of a Type II Error (failing to reject a false null hypothesis)

Factors affecting Type I Error:

  • Sample size: Larger samples increase the likelihood of detecting a true effect, but also increase the risk of Type I Error
  • Significance level (α): A smaller α reduces the risk of Type I Error, but increases the risk of Type II Error
  • Test statistic and p-value: A p-value below α indicates a statistically significant result, but does not guarantee the absence of a Type I Error

Minimizing Type I Error:

  • Use a conservative significance level (α) to reduce the risk of Type I Error
  • Use multiple tests and replication to verify results
  • Consider the consequences of a Type I Error and adjust the significance level accordingly

Type I Error

  • Occurs when a true null hypothesis is rejected, resulting in a false positive
  • Also known as Alpha (α) error or False positive error

Consequences of Type I Error

  • Leads to incorrect conclusions and misguided decisions
  • Wastes resources on pursuing a non-existent effect or relationship
  • Damages credibility and trust with false claims

Probability of Type I Error

  • Represented by the Greek letter alpha (α)
  • Typically set to 0.05, indicating a 5% chance of rejecting a true null hypothesis
  • A smaller α reduces the probability of Type I Error, but increases the probability of Type II Error

Factors Affecting Type I Error

  • Larger samples increase the likelihood of detecting a true effect, but also increase the risk of Type I Error
  • A smaller α reduces the risk of Type I Error, but increases the risk of Type II Error
  • A p-value below α indicates a statistically significant result, but does not guarantee the absence of a Type I Error

Minimizing Type I Error

  • Use a conservative significance level (α) to reduce the risk of Type I Error
  • Use multiple tests and replication to verify results
  • Consider the consequences of a Type I Error and adjust the significance level accordingly

Inverse Function of a One-to-One Function

  • A one-to-one function, f, has a unique output (y) for each input (x) in its domain.
  • For every y in the range of f, there is exactly one x in the domain of f that corresponds to it.
  • The inverse function of f, denoted as f-1, is the correspondence from the range of f back to the domain of f.
  • The inverse function f-1 reverses the direction of correspondence, taking each y in the range back to its unique corresponding x in the domain.

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Understand the concept of Type I Error, also known as Alpha error or False positive error, in hypothesis testing, including its consequences and probability.

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