What is One Tailed and Two tailed Hypothesis Testing?

Data Science, AI and ML
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One-tailed and two-tailed Hypothesis Testing

If the alternate hypothesis gives the alternate in both directions (less than and greater than) of the value of the parameter specified in the null hypothesis, it is called a Two-tailed test.

If the alternate hypothesis gives the alternate in only one direction (either less than or greater than) of the value of the parameter specified in the null hypothesis, it is called a One-tailed test.

Alternate Hypothesis(H1 or Ha) – As previously mentioned that Null Hypothesis and Alternate Hypothesis are mutually exclusive statements. So if the Null Hypothesis is commonly accepted facts then the Alternate Hypothesis is a real fact-based on observation from the sample data. It is denoted by H1 or Ha. If it is a test of means then we say that H1 : µ1 ≠ µ2 , which states that there is a significant difference in 2 population means.

  • Critical Region – The critical region is defined as the region of values in distribution that leads to the rejection of the null hypothesis at some given probability level.
  • One-Tailed Test – A one-tailed test is a statistical hypothesis test in which the critical area of distribution is either greater than or less than a certain value, but can’t be both. For this the alternate hypothesis formulation is H1 : µ1 > µ2 or H1 : µ1 < µ2 .
  • Two-Tailed Test – A two-tailed test is a statistical hypothesis test in which the critical area of distribution is on either of the sides. It tests whether the sample means of 2 or more populations are unequal (in the test of means). For this alternate hypothesis, the formulation is H1 : µ1 ≠ µ2 .

e.g. if H0: mean= 100 H1: mean not equal to 100 here according to H1, mean can be greater than or less than 100. This is an example of a Two-tailed test Similarly, if H0: mean>=100 then H1: mean< 100 Here, the mean is less than 100. It is called a One-tailed test.