Hypothesis Testing

Hypothesis testing is a statistical method that is used in making statistical decisions using experimental data. It is basically an assumption that we make about the population parameter.

Steps of Hypothesis Testing

Hypothesis testing is carried out in four steps:

  1. Formulate the Hypotheses: The first step is to formulate the null hypothesis (H₀) and the alternative hypothesis (H₁ or Hₐ). The null hypothesis is generally an assertion of no effect or no difference and is the default assumption unless we have sufficient evidence to reject it. The alternative hypothesis is usually the hypothesis that we want to prove or establish.

  2. Choose the Significance Level (α): The significance level, also denoted as alpha or α, is a probability threshold that determines when you reject the null hypothesis. Commonly used values are 0.05 (5%), 0.01, and 0.1.

  3. Compute the Test Statistic: Depending on the nature of the data and the reason for the analysis, different test statistics may be used. For example, a Z-test uses the Z-statistic, a T-test uses the T-statistic, and a chi-square test uses the chi-square statistic.

  4. Make a Decision: If the test statistic falls within the critical region, we reject the null hypothesis in favor of the alternative hypothesis. If the test statistic falls outside the critical region, we do not reject the null hypothesis.

Type I and Type II Errors

When we make a decision based on a statistical test, there are four possible outcomes:

  • True positive: We reject the null hypothesis, and it's false.
  • True negative: We do not reject the null hypothesis, and it's true.
  • Type I error (False positive): We reject the null hypothesis, but it's true.
  • Type II error (False negative): We do not reject the null hypothesis, but it's false.

In hypothesis testing, we control for the probability of making a Type I error with our significance level, but reducing the probability of a Type I error increases the probability of a Type II error, and vice versa. This is known as the Type I and Type II error trade-off.

Hypothesis testing is an essential procedure in statistics and is used to make statistical decisions about population parameters based on a sample of data.