Table of Contents
Null hypothesis definition
The null hypothesis is a general statement that states that there is no relationship between two phenomenons under consideration or that there is no association between two groups.
- A hypothesis, in general, is an assumption that is yet to be proved with sufficient pieces of evidence. A null hypothesis thus is the hypothesis a researcher is trying to disprove.
- A null hypothesis is a hypothesis capable of being objectively verified, tested, and even rejected.
- If a study is to compare method A with method B about their relationship, and if the study is preceded on the assumption that both methods are equally good, then this assumption is termed as the null hypothesis.
- The null hypothesis should always be a specific hypothesis, i.e., it should not state about or approximately a certain value.
Null hypothesis symbol
- The symbol for the null hypothesis is H_{0,} and it is read as H-null, H-zero, or H-naught.
- The null hypothesis is usually associated with just ‘equals to’ sign as a null hypothesis can either be accepted or rejected.
Null hypothesis purpose
- The main purpose of a null hypothesis is to verify/ disprove the proposed statistical assumptions.
- Some scientific null hypothesis help to advance a theory.
- The null hypothesis is also used to verify the consistent results of multiple experiments. For e.g., the null hypothesis stating that there is no relation between some medication and age of the patients supports the general effectiveness conclusion, and allows recommendations.
Null hypothesis principle
- The principle of the null hypothesis is collecting the data and determining the chances of the collected data in the study of a random sample, proving that the null hypothesis is true.
- In situations or studies where the collected data doesn’t complete the expectation of the null hypothesis, it is concluded that the data doesn’t provide sufficient or reliable pieces of evidence to support the null hypothesis and thus, it is rejected.
- The data collected is tested through some statistical tool which is designed to measure the extent of departure of the date from the null hypothesis.
- The procedure decides whether the observed departure obtained from the statistical tool is larger than a defined value so that the probability of occurrence of a high departure value is very small under the null hypothesis.
- However, some data might not contradict the null hypothesis which explains that only a weak conclusion can be made and that the data doesn’t provide strong pieces of evidence against the null hypothesis and the null hypothesis might or might not be true.
- Under some other conditions, if the data collected is sufficient and is capable of providing enough evidence, the null hypothesis can be considered valid, indicating no relationship between the phenomena.
When to reject null hypothesis?
- When the p-value of the data is less than the significant level of the test, the null hypothesis is rejected, indicating the test results are significant.
- However, if the p-value is higher than the significant value, the null hypothesis is not rejected, and the results are considered not significant.
- The level of significance is an important concept while hypothesis testing as it determines the percentage risk of rejecting the null hypothesis when H_{0} might happen to be true.
- In other words, if we take the level of significance at 5%, it means that the researcher is willing to take as much as a 5 percent risk of rejecting the null hypothesis when it (H_{0}) happens to be true.
- The null hypothesis cannot be accepted because the lack of evidence only means that the relationship is not proven. It doesn’t prove that something doesn’t exist, but it just means that there are not enough shreds of evidence and the study might have missed it.
Null hypothesis examples
The following are some examples of null hypothesis:
- If the hypothesis is that “the consumption of a particular medicine reduces the chances of heart arrest”, the null hypothesis will be “the consumption of the medicine doesn’t reduce the chances of heart arrest.”
- If the hypothesis is that, “If random test scores are collected from men and women, does the score of one group differ from the other?” a possible null hypothesis will be that the mean test score of men is the same as that of the women.
H_{0}: µ_{1}= µ_{2}
H_{0}= null hypothesis
µ_{1}= mean score of men
µ_{2}= mean score of women
Alternative hypothesis definition
An alternative hypothesis is a statement that describes that there is a relationship between two selected variables in a study.
- An alternative hypothesis is usually used to state that a new theory is preferable to the old one (null hypothesis).
- This hypothesis can be simply termed as an alternative to the null hypothesis.
- The alternative hypothesis is the hypothesis that is to be proved that indicates that the results of a study are significant and that the sample observation is not results just from chance but from some non-random cause.
- If a study is to compare method A with method B about their relationship and we assume that the method A is superior or the method B is inferior, then such a statement is termed as an alternative hypothesis.
- Alternative hypotheses should be clearly stated, considering the nature of the research problem.
Alternative hypothesis symbol
- The symbol of the alternative hypothesis is either H_{1} or H_{a} while using less than, greater than or not equal signs.
Alternative hypothesis purpose
- An alternative hypothesis provides the researchers with some specific restatements and clarifications of the research problem.
- An alternative hypothesis provides a direction to the study, which then can be utilized by the researcher to obtain the desired results.
- Since the alternative hypothesis is selected before conducting the study, it allows the test to prove that the study is supported by evidence, separating it from the researchers’ desires and values.
- An alternative hypothesis provides a chance of discovering new theories that can disprove an existing one that might not be supported by evidence.
- The alternative hypothesis is important as they prove that a relationship exists between two variables selected and that the results of the study conducted are relevant and significant.
Alternative hypothesis principle
- The principle behind the alternative hypothesis is similar to that of the null hypothesis.
- The alternative hypothesis is based on the concept that when sufficient evidence is collected from the data of random sample, it provides a basis for proving the assumption made by the researcher regarding the study.
- Like in the null hypothesis, the data collected from a random sample is passed through a statistical tool that measures the extent of departure of the data from the null hypothesis.
- If the departure is small under the selected level of significance, the alternative hypothesis is accepted, and the null hypothesis is rejected.
- If the data collected don’t have chances of being in the study of the random sample and are instead decided by the relationship within the sample of the study, an alternative hypothesis stands true.
Alternative hypothesis examples
The following are some examples of alternative hypothesis:
1. If a researcher is assuming that the bearing capacity of a bridge is more than 10 tons, then the hypothesis under this study will be:
Null hypothesis H_{0}: µ= 10 tons
Alternative hypothesis H_{a}: µ>10 tons
2. Under another study that is trying to test whether there is a significant difference between the effectiveness of medicine against heart arrest, the alternative hypothesis will be that there is a relationship between the medicine and chances of heart arrest.
Null hypothesis vs Alternative hypothesis
Basis of comparison |
Null hypothesis |
Alternative hypothesis |
Definition | The null hypothesis is a general statement that states that there is no relationship between two phenomenons under consideration or that there is no association between two groups. | An alternative hypothesis is a statement that describes that there is a relationship between two selected variables in a study. |
Symbol | It is denoted by H_{0}. | It is denoted by H_{1} or H_{a}. |
Mathematical expression | It is followed by ‘equals to’ sign. | It is followed by not equals to, ‘less than’ or ‘greater than’ sign. |
Observation | The null hypothesis believes that the results are observed as a result of chance. | The alternative hypothesis believes that the results are observed as a result of some real causes. |
Nature | It is the hypothesis that the researcher tries to disprove. | It is a hypothesis that the researcher tries to prove. |
Result | The result of the null hypothesis indicates no changes in opinions or actions. | The result of an alternative hypothesis causes changes in opinions and actions. |
Significance of data | If the null hypothesis is accepted, the results of the study become insignificant. | If an alternative hypothesis is accepted, the results of the study become significant. |
Acceptance | If the p-value is greater than the level of significance, the null hypothesis is accepted. | If the p-value is smaller than the level of significance, an alternative hypothesis is accepted. |
Importance | The null hypothesis allows the acceptance of correct existing theories and the consistency of multiple experiments. | Alternative hypothesis are important as it establishes a relationship between two variables, resulting in new improved theories. |
References
- R. Kothari (1990) Research Methodology. Vishwa Prakasan. India.
- https://www.statisticssolutions.com/null-hypothesis-and-alternative-hypothesis/
- https://byjus.com/maths/null-hypothesis/
- https://en.wikipedia.org/wiki/Null_hypothesis
- https://www.statisticssolutions.com/null-hypothesis-and-alternative-hypothesis/
- https://keydifferences.com/difference-between-null-and-alternative-hypothesis.html
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