Hypothesis Testing: Type I Error

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.