Evaluation Of Decision Error

  • Four possible outcomes that determine whether a decision is correct or an error:
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  • It is not possible to simultaneously commit a Type I(α) error and Type II (β)decision error.
  • In short, either an alpha (α) or beta (β) decision error can be made, but not both.
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Type I Error

  • Probability of rejecting the null hypothesis when it is true is called type I error, designated by Greek letter α Alpha.
  • Example
    - A toy manufacturing company set a limit of 2% defective from the woodenparts it receives from its vendor.
    - A sample of 500 parts out of 4000 lot size received revealed that 11 parts were defective, translating to 2.2% greater than 2%.
    - The customer rejectedthe Shipment.
    - A 100% inspection from the vendor revealed that only 50 parts were defective out of 4000 parts, i.e., 1.25% defective.
    - In this case, only 1.25% of the parts were defective against an acceptable level of 2% defective, and rejecting the shipment was an error.
    - In terms of hypothesis testing language, we say that we rejected the Null Hypothesis, but the shipment wasnot substandard.
    - We committed a Type 1 Error.

Type II Error

  • Probability of committing another type of error , called a type II error, designated by Greek letter β ,beta
  • Type II error – Accepting the null hypothesis when it is actually false
  • Example
    - In the example, the toy manufacturer would commit a type II error if a shipment from a supplier containing greater than 2% defective, yetthe shipment was accepted.
    - How could this happen?
    - Suppose 9 out of the 500 parts in the sample tested were substandard, leading to 1.8% defective. As per the guideline, the sample contained less than 2% defective and hence was accepted.
    - What if, by chance, the 90 defective parts out of 4000 lots leading to 2.25% defective greater than 2%
    - Since the person doing analysis cannot study every item in the population, thus there is the possibility of two types of errors, Alpha error α, and beta errorβ