LEVEL OF SIGNIFICANCE

• Type 1 error


  The probability of committing the Type 1 error is called the level of significance
• Level of significance (α)

  The probability of making an error in rejecting the null hypothesis when it is actually true
• The choice for the value of the significance level is determined by the researcher
• The commonly used levels of significance are 0.05 and 0.01
• The level of significance should be set before testing the hypothesis
• 0.01 level of significance

  The researchers is willing to take 1% error in making a decision, and is 99% confident that they will make a right decision
• 0.05 level of significance

  The researchers is willing to take 5% error in making decision, and is 95% confident that they will make a right decision
• Critical or rejection Region


  Consists of values that support the alternative hypothesis Ha and leads to the rejection of null hypothesis Ho, with an area given by the level of significance α
• Nonrejection Region


  Consists of values that support the null hypothesis Ho and leads to nonrejection, with an area given by the confidence level 1-α
• Determining the Criteria (Rejection) Region


  Distribution of test statistics is divided into critical/rejection region and nonrejection region
• Two-tailed test


  If a nondirectional alternative hypothesis (Ha involving the quantified ≠) is formulated, the critical region is divided into two equal regions located in each tail of the distribution, each with an area of α/2
• One-tailed test


  If a directional alternative hypothesis (Ha involving the quantifier > or <) is formulated, the critical region is concentrated on one tail of the distribution having an area of α
• Right-tailed or upper-tailed test


  If a directional alternative hypothesis (Ha involving the quantifier >) is formulated, the critical region is located at the right-tail or upper-tail of the distribution
• Left-tailed or lower-tailed test


  If a directional alternative hypothesis (Ha involving the quantifier <) is formulated, the critical region is located at the left-tail or lower-tail of the distribution
• The level of significance, denoted by alpha, is the probability of committing a Type I error.