Alternative hypothesis

The word hypothesis denotes a working statement. In statistics, mathematicians have a keen interest in proving whether a hypothesis is true or false. A true hypothesis can be a fact or a historical event. A null hypothesis denotes a ‘no change’ event or fact. It is denoted by H0. An alternative hypothesis is an alternative of null. It is denoted by Ha or H1. For example, a null hypothesis is that your friend is going to win a lottery. An alternative hypothesis of this event will be that your friend is going to win a double lottery. An alternative hypothesis is the opposite of a null hypothesis. The event or fact should be clear-cut to cancel the null hypothesis. In hypothesis testing, one will choose a statement that they think will be true and ultimately cancel or reject the null hypothesis. One can also choose an alternative statement to replace the null statement.

Types of alternative hypothesis

Left-tailed – In the left-tailed alternative hypothesis, the sample portion is less than the specified value. It is denoted by π0, such that H1: π0> π
Right-tailed – In this, the sample portion is greater than the value, such that H1: π0< π
Two-tailed – According to the two-tailed hypothesis, the sample portion is not equal to some value. It is denoted by H1: π0 ≠ π.
Non-directional – It is concerned to prove the null hypothesis is not true. Whatever be the region, reason or point of rejection, it doesn’t matter.

Note: The null hypothesis in this case will be represented by H1: π0= π.

Why do we use the alternative hypothesis?

Researchers and scholars across the globe use the alternative hypothesis. They do their research by using null hypotheses and consider whatever research they have done is true. Alternative hypothesis opposes null hypothesis so that the research work comes out stronger. How? The more the contradiction to a hypothesis, the more vital it will prove correct. Statistics, medicine, technology, psychology, science, and mathematics, the alternative hypotheses, are used everywhere to make the research or the product more robust.

Points to Ponder

1. Both the hypotheses have their significant value. It depends upon the researchers what they chose. They can reject a null hypothesis and can accept an alternative hypothesis, or can do vice versa.
2. Jerzy Neyman and Egon Pearson brought up the concept of the alternative hypothesis. The Neyman-Pearson lemma forms a crucial component in today’s statistical hypothesis testing.
3. There can be two types of errors in hypothesis testing. Type I error (known as false positive) means one has mistakenly rejected a hypothesis. For example, an innocent person was convicted. Type II error (known as false negative) means someone has mistakenly accepted a hypothesis. For example, a guilty person was not convicted.
4. The ultimate goal of a hypothesis is to eliminate errors and come out with the best possible outcome of research in different fields of science and technology.