What is null and alternative hypothesis?

By Riya Jain and Priya Chetty on June 19, 2020

A hypothesis is an idea or assumption expressed in the form of a single statement. It aims to explore a new phenomenon, examine the who, what, why, where, and how, OR check the relationship between two elements. For instance, to answer how does online learning affect students’ skill development? The hypothesis is generally presented in the null and alternative format.

Types of hypotheses
Figure 1: Types of hypotheses

What is a null hypothesis?

The null hypothesis is something to which the researcher aims to find evidence against its perception. Thus, it negates the researcher’s perception or assumption. As it is a weak prediction i.e. though the researcher is not able to find evidence in support of their claim still the existence of the negation is just a matter of chance. It is denoted by H0, which is a statement in the hypothesis showing that there is a relationship between the concerned variables or elements. In mathematical form, the null hypothesis is described with an equal or greater than or less than sign i.e.

Mathematical symbols for null hypothesis
Figure 2: Mathematical symbols for null hypothesis

Example 1- Explanatory hypothesis

Explanatory hypotheses seek to explain patterns in problems. For example, in a study where the purpose is to examine the average physical development of transitional age male youth (16-24 years). The researcher has hypothesized the average height to be more than 68 inches i.e.

H0: µ ≤ 68

Herein, as the researcher has claimed that transitional age male youth has average height as greater than 68 inches thus, the null hypothesis is represented as the negation of the assumption in presence of equality, i.e.:

Null hypothesis (H0): The average height of male youth of transitional age is not greater than 68 inches.

Example 2- Exploratory hypothesis

Exploratory hypotheses explain the relationship between two observed variables. For example, in a study, the objective is to determine the influence of social factors like relatives, reference groups, family members, or society on consumer behaviour. For this, the null hypothesis will be:

H0: There is no significant impact of social factors on consumer behaviour.

The above hypotheses negate the claim of the researcher but also state that there is not much evidence that supports the presence of a relationship between variables. Thus, it could be a chance-based linkage.

Non-rejection of the sample hypothesis does not yield an appropriate prediction. Thus, the purpose of the hypothesis testing is to nullify, reject or disapprove the stated null hypothesis.

What is an alternative hypothesis?

An alternative hypothesis symbolized by HA or H1 is the opposite of the null hypothesis. It depicts that there is a presence of an observed effect between the variables. It is something that a researcher aims to indirectly verify by stating the assumption. It mentions that there is the existence of a significant linkage between the characteristics of the measurable population parameters. Mathematically, the alternative hypothesis can be denoted as:

Mathematical symbols for alternative hypothesis
Figure 3: Mathematical symbols for alternative hypothesis

Example 1- Explanatory hypothesis

In the example stated in the null hypothesis i.e. where the researcher claims to that the height of transitional youth is more than 68 inches, the alternative hypothesis would be:

HA: µ > 68

Example 2- Exploratory hypothesis

For the previous example i.e. impact of social factors on consumer behaviour, the alternative hypothesis can be stated as:

HA: There is a significant impact of social factors on consumer behaviour.

Herein, the alternative hypothesis mentions what the researcher believes. Thus, for verifying this claim, the researcher wants to test the alternative of the above hypothesis and state the prediction by rejecting the null hypothesis.

The direction of the relationship, two-tailed and one-tailed

Furthermore, the alternative hypothesis does not just depict the relationship between variables but also the direction of the relationship. As in the above example, the height is more than 68 inches, depicting a ‘right-tailed test’. Basically, based on the direction of the relationship, the alternative hypothesis could be categorized as a two-tailed and one-tailed test.

Form of Alternative hypothesis
Figure 4: Form of Alternative hypothesis

Two-tailed is a non-direction test wherein just the existence of a relationship between the variables is stated and not the form of relationship. On the other hand, a one-tailed test represents the direction of the linkage between the variables. Herein, for the two-tailed tests, the significance level of the hypothesis testing is split into two parts i.e. right and left area like 5% significance level would be distributed into two parts – 2.5% on the right side and 2.5% on the left

Two-tailed distribution at 5% significance level
Figure 5: Two-tailed distribution at 5% significance level (Frost, J; 2018)

However, the one-tailed test represents the direction of the linkage thus the distribution of the significance level of the hypothesis depends on the side of the direction. In case of the right-tailed or upper bound test, the 5% significance level would be entirely distributed on the rights side i.e.

One-tailed right side distribution at 5% significance level
Figure 6: One-tailed right side distribution at 5% significance level (Frost, J; 2018)

While the left-side one-tailed test shows that 5% significance level would be entirely distributed on the left side i.e.

One-tailed left side distribution at 5% significance level
Figure 7: One-tailed left side distribution at 5% significance level (Frost, J; 2018)

In all these forms of alternative hypothesis, the mathematical notation varies. For two-tailed test the mathematical symbol is ≠, for right-tailed test is >, and for left side test symbol is <. Thus, representing in different forms, alternative hypothesis is something which the researcher aims to accept by finding evidence against the negation of the claim.

Following the sample stated in the null hypothesis, the alternative hypothesis is

HA: There is a significant impact of social factors on the customer behaviour

The above sample states the prediction of the researcher by showing that it is a strong conclusion because the existence of linkage is shown to have significant changes and not just the random case scenario.

Hence, as the stated hypothesis is something which is statistically derived from the experiment by rejecting the null hypothesis in the form of an alternate, thus it is referred to as the alternative hypothesis.

Why the inclusion of null and alternative hypothesis is important for hypothesis testing?

The clear statement of both the hypothesis and these fragmentations before the data collection and interpretation process is essential for indicating that the researcher has knowledge about the concerned area. Following the systematic procedure of statement of hypothesis, clear identification of the research problem could be done by these statements. Although research aims to prove the alternative hypothesis, stating the null hypothesis is important. Failing to represent the null hypothesis leads to faulty results and misinterpretation of the dataset.

References

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