Hypothesis Testing: Concepts, Steps, and Result Interpretation

Posted on Feb 18, 2025 in Road Engineering Technology

Hypothesis Testing: Concepts, Steps, and Interpretation

Background:

  • A statistical hypothesis is an assumption about a population parameter. This assumption may or may not be true.
  • The best way to determine whether a statistical hypothesis is true would be to examine the entire population.

Since that is often impractical, researchers typically examine a random sample from the population.

If sample data are not consistent with the statistical hypothesis, the hypothesis is rejected.

The question of interest is simplified into two competing claims (hypotheses) between which there is a choice:

  • Null hypothesis (H0): Theory that has been put forward, either because it is believed to be true or because it is to be used as a basis for argument, but has not been proved.
  • Alternative hypothesis (H1): Statement of what a statistical hypothesis test is set up to establish.

Steps in Hypothesis Testing

  • All hypothesis tests are conducted the same way: the researcher states a hypothesis to be tested, formulates an analysis plan, analyses sample data according to the plan, and accepts or rejects the null hypothesis, based on results of the analysis.
  • 1. State the hypotheses:
    • This involves stating the null and alternative hypotheses.
    • The hypotheses are stated in such a way that they are mutually exclusive: if one is true, the other must be false.
  • 2. Formulate an analysis plan:
    • The plan describes how to use sample data to evaluate the null hypothesis.
    • The evaluation often focuses around a single test statistic.
    • It should specify the Significance level:
      • Often, researchers choose significance levels equal to 0.01, 0.05, or 0.10; but any value between 0 and 1 can be used.
  • 3. Test the method:
    • Typically, the test method involves a test statistic and a sampling distribution.
    • It is computed from sample data, the test statistic might be a mean score, proportion, difference between means, difference between proportions, z-score, t-score, chi-square, etc.
    • Given a test statistic and its sampling distribution, a researcher can assess probabilities associated with the test statistic.
    • If the test statistical probability is less than the significance level, the null hypothesis is rejected.
  • 4. Final conclusion:

Example:

The final conclusion once the test has been carried out is always given in terms of the null hypothesis: “Reject H0 in favour of H1” or “do not reject H0”.

If H0 is not rejected, it does not necessarily mean that the null hypothesis is true, it only suggests that there is not sufficient evidence against H0 in favour of H1.

If H0 is rejected, it suggests that the alternative hypothesis may be true.

Consider a clinical trial of a new drug – claiming that a new drug is better than the current drug for treatment of the same symptoms.

Null hypothesis (H0): The new drug is no better, on average, than the current drug – there is no difference between the two drugs on average.

Alternative hypothesis (H1): The new drug has a different effect, on average, compared to that of the current drug – there is a difference between the two drugs on average.

Give special consideration to the null hypothesis because it relates to the statement being tested, whereas the alternative hypothesis relates to the statement to be accepted if/when the null is rejected.

Final conclusion is driven once the test has been carried out (“Reject H0” or “do not reject H0”).

Errors in Hypothesis Testing

Conclusions are only probabilities, and can have errors.

  • Types of errors:
  • Type I: The null hypothesis is rejected when it is true.
    • Equal to a chosen level of significance (5% or 1%).
  • Type II: The null hypothesis is not rejected when it is false.