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Hypothesis is making an assumption. In Statistics a Hypothesis or an assumption is taken first and then the Hypothesis is tested as how accurate it is or not. Hypothesis testing is a study based on statistical accuracy of an experiment. If the result is positive i.e. if the assumption is correct or approximate, then it is called Statistically Significant. 

There are two types of statistical hypotheses

  • Null Hypothesis: Denoted by H0, it is actually an assumption that the sample observations are purely from chance.
  • Alternate Hypothesis: Denoted by H1 or Ha, it assumes that the sample is influenced by a non-random cause. 

Reject the null hypothesis and accept the alternative hypothesis or Fail to reject the null hypothesis and state that there is not enough evidence to support the alternative hypothesis.

  • When we test a hypothesis we proceed as follows.
  • Formulate the null and alternative hypothesis.
  • Level of significance has to be determined.
  • The size of the sample has to be chosen.
  • With the help of the table, determine if the z score falls within the acceptance region. 

Statisticians follow a formal process to determine whether to accept or reject null-hypothesis, based on sample data. This process is called hypothesis testing and consists of four steps.

  • State the hypotheses: The first step involves stating the null and alternate hypotheses. The hypotheses have to be stated in such a way that they are mutually exclusive.
  • Formulate an analysis plan: The analysis plan describes how to use sample data to evaluate the null hypothesis. This evaluation focuses around a single test statistic.
  • Analyze sample data:  Find the value of the test statistic (mean score, proportion, t-score, z-score, etc.) described in the analysis plan
  • Interpret results: Apply the decision rule described in the analysis plan. If the value of the test statistic is unlikely, based on the null-hypothesis, reject the null hypothesis. 

Decision Errors - Two types of errors can result from a hypothesis test

  • Type I Error: A Type I Error occurs when the researcher rejects a null-hypothesis when it is actually true. The probability of committing a Type I error is called the significance level. This probability is called alpha and is often denoted by α.
  • Type II Error: A Type II Error occurs when the researcher fails to reject a null-hypothesis when it is false. The probability of committing a Type II Error is called Beta and is often denoted by β. 

Decision Rules - The analysis plan includes decision rules for rejecting the null-hypothesis. In practice, statisticians describe these decision rules in two-ways with reference to a P-value or with reference to a region of acceptance.

  • P-value:  The strength of evidence in support of a null-hypothesis is measured by the p-value. Suppose the test statistic is equal to S. The P-value is the probability of observing a test statistic as extreme as S, assuming the null hypothesis is true. If the P-value is less than the significance level, we reject the null hypothesis.
  • Region of acceptance: The region of acceptance is a range of values. If the test statistic falls under the region of acceptance the null-hypothesis is not rejected. The region of acceptance is defined so that the chance of making a Type I error is equal to the significance level. 

The set of values outside the region of acceptance is called the region of rejection. If the test statistic falls under the region of rejection, the null-hypothesis is rejected. In such cases, we say that the hypothesis has been rejected at the α level of significance.  

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