Hypothesis Testing: Type I Error
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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</p> Signup and view all the answers

    What is the definition of a Type I Error?

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

    How can Type I Error be minimized?

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

    What is the inverse function of f denoted as?

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

    What type of function has an inverse function?

    <p>Only one-to-one functions</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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    Description

    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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