Hypothesis Testing
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Hypothesis Testing

The Steps to Performing Hypothesis Testing

  1. Write the original claim and identify whether it is the null hypothesis or the alternative hypothesis.
  2. Write the null and alternative hypothesis. Use the alternative hypothesis to identify the type of test.
  3. Write down all information from the problem.
  4. Find the critical value using the tables
  5. Compute the test statistic
  6. Make a decision to reject or fail to reject the null hypothesis. A picture showing the critical value and test statistic may be useful.
  7. Write the conclusion. 

    Null Hypothesis (H0)

         Statement of zero or no change. If the original claim includes equality (<=, =, or >=), it is the null hypothesis. If the original claim does not include equality (<, not equal, >) then the null hypothesis is the complement of the original claim. The null hypothesis always includes the equal sign. The decision is based on the null hypothesis.

    Alternative Hypothesis (Ha or H1)

         Statement which is true if the null hypothesis is false. The type of test (left, right, or two-tail) is based on the alternative hypothesis. 

    Left Tailed Test

    H: parameter < value
    Notice the inequality points to the left
    Decision Rule: Reject H if t.s. < c.v. 

    Right Tailed Test

    H: parameter > value
    Notice the inequality points to the right
    Decision Rule: Reject H if t.s. > c.v. 

    Two Tailed Test

    H: parameter not equal value
    Another way to write not equal is < or >
    Notice the inequality points to both sides
    Decision Rule: Reject H if t.s. < c.v. (left) or t.s. > c.v. (right)

    Type I error

    Rejecting the null hypothesis when it is true (saying false when true). Usually the more serious error.

    Type II error

    Failing to reject the null hypothesis when it is false (saying true when false).

    Probability of committing a Type I error.

    alpha

    Probability of committing a Type II error.

    beta

    Test statistic

    Sample statistic used to decide whether to reject or fail to reject the null hypothesis.

    Critical region

    Set of all values which would cause us to reject H0

    Critical value(s)

    The value(s) which separate the critical region from the non-critical region. The critical values are determined independently of the sample statistics.

    Significance level ( alpha )

    The probability of rejecting the null hypothesis when it is true. alpha = 0.05 and alpha = 0.01 are common. If no level of significance is given, use alpha = 0.05. The level of significance is the complement of the level of confidence in estimation.

    Decision

    A statement based upon the null hypothesis. It is either "reject the null hypothesis" or "fail to reject the null hypothesis". We will never accept the null hypothesis. 

    Conclusion

    A statement which indicates the level of evidence (sufficient or insufficient), at what level of significance, and whether the original claim is rejected (null) or supported (alternative).