Statistical Hypothesis Testing- Steps, Errors, Interpretation

What is hypothesis testing?

Hypothesis testing is used to determine whether a premise is valid or not in relation to a statistical parameter. The goal of hypothesis testing is to make decisions about a population based on the interpretation of hypothesis testing on sample data drawn from the population data.

How Hypothesis Testing is done?

The testing of a hypothesis is done by forming a null and alternate hypothesis, where the null hypothesis states that the prevailing belief or premise in relation to a statistical parameter is true whereas the alternate hypothesis states that the prevailing belief or premise in relation to a statistical parameter is not true and thus alternate hypothesis is accepted.

Null and alternate hypothesis are mutually exclusive in nature. If one is true automatically another hypothesis becomes false and thus both are proposed simultaneously in relation to a statistical parameter.

Let us go through the steps of conducting hypothesis testing-

  1. Propose a null hypothesis (H0) and alternate hypothesis (Ha) is proposed in relation to the statistical parameter you want to interpret from the population.
  2. Specify the significance level (α) for accepting or rejecting the null hypothesis where the significance level is about the probability of error when the null hypothesis is true. The researcher decides on the significance level based on research problem. Generally, as a thumb rule, an alpha level of 0.05 (5%) is used.
  3. Conduct the experiments, and collect data to run statistical tests.
  4. Select an appropriate statistical test to calculate test statistics and p-value (In the null hypothesis, the p-value measures the probability of obtaining the observed results).
  5. Analyze the output and form conclusions.

Interpretation of the test results

Based on the output of the statistical test, the p-value is compared with the significance level (α). If the p-value is lower than the threshold level of acceptable error specified in the alpha value then observations are considered to be significant. Usually, the significance level for a study is set at 0.05 or 5%. A p-value that is below the significance level indicates that your results were statistically significant and supported the alternative hypothesis. If your p-value was greater than the significance level, then the results were statistically insignificant.

The interpretation of statistical hypothesis testing thus helps in making decisions on the validity of the hypothesis on the population data based on the statistical tests drawn on sample data drawn from that population data.

Types of Error in Hypothesis Testing

There are few types of errors that occur during hypothesis testing based on discrepancy between actual results and statistical results. Those types of errors are-

  1. Type I error – Type I errors are false positive errors when results appear to be statistically significant but they are actually purely by chance or the result of unrelated factors. This type of error can be prevented by choosing a higher alpha value (α).
  2. Type II error – Type II errors mean failing to reject the null hypothesis when it is actually false. This is not the same as accepting the null hypothesis as a test can only conclude whether to reject the null hypothesis. A type II error occurs when the statistical study failed to conclude the effect of stimuli on a statistical parameter when there actually was. This type of error can be prevented by increasing the statistical power of the study. The Type II error rate is also known as beta (β).

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