Before understanding the Null Hypothesis in detail, let us first understand the definition of the Hypothesis.
In Statistics, a hypothesis can be defined as a formal statement, which gives an explanation about the relationship between any two or more variables of the specified population.
Hypothesis helps the researcher to translate any given problem to a clear explanation for the outcome of the study.
Hypothesis clearly explains and predicts the expected outcome and it indicates the types of experimental design and directs the study of any research process.
What Is The Null Hypothesis?
We can define a null hypothesis as a general statement or a default position that says there is no relationship between two measured phenomena or there is no association among groups.
Why is Null Hypothesis Important?
Hypothesis helps the researcher to translate any given problem to a clear explanation for the outcome of the study.
Testing (which involves accepting, approving, rejecting, or disproving) the null hypothesis and thus concluding that there are or we can say that there are no grounds for believing that there is any relationship between two phenomena is basically a central task in the modern practice of science; in the field of statistics.
To be more specific, hypothesis testing gives precise criteria for rejecting or accepting a null hypothesis within a level known as the confidence level.
Null Hypothesis Symbol-
A Null Hypothesis is denoted by the symbol H0 in statistics. It is usually pronounced as “h-nought” or “H-null”. The Subscript in H is the digit 0.
Null Hypothesis Principle and When is A Null Hypothesis Rejected?
The principle followed for null hypothesis testing is basically collecting the data and determining the chances of a given set of data during the study on any given random sample, assuming that the null hypothesis is true.
Suppose, if the given data does not face the expected null hypothesis, then the outcome we will get will be quite weaker and they conclude that by saying that the given set of data does not provide strong evidence against the null hypothesis which is because of insufficient evidence.
Finally, this leads to null hypothesis rejection.
Null Hypothesis Formula or How Do You Find The Null Hypothesis :
So far, understanding the concept of null hypothesis, let’s now discuss the null hypothesis formula:
Here, the null hypothesis formula is given below.
H0: p = p0
The formula for the alternative hypothesis can be written as: Ha = p >p0, and < p0≠ p0
The formula for the test static is denoted by:
\[Z=\frac{P-P_{0}}{\sqrt{\frac{P-P_{0}}{n}}}\]
Remember that, p0 here is the null hypothesis.
Types of Null Hypothesis.
There are 4 different types of Null hypothesis. Each of them is explained below with examples.
Simple Hypothesis:
A simple Hypothesis is the one in which the relationship between two variables is predicted. One is an independent variable and the other is a dependent variable. A simple Hypothesis completely specifies the population distribution. An example of a simple Hypothesis is
“Consuming sugar drinks daily leads to being overweight.”Composite hypothesis.
A Composite hypothesis describes the relationship between two or more independent variables and two or more dependent variables. In this hypothesis, the population distribution is not specified. An example of the Composite hypothesis is stated below.
“Individuals who consume sugar drinks daily and have a family history of health issues are more likely to become overweight and develop diabetes.”Exact hypothesis.
In this hypothesis, the exact value of the parameter or variable is defined. All the assumptions made during the derivation of the hypothesis are met in the exact hypothesis. An example of an exact hypothesis is,
“Students in a division score an average 17 out of 25 in exams. Hence, μ=17.”Inexact hypothesis.
Unlike the exact hypothesis, the exact value of the parameter or variable is not defined in the Inexact type of Hypothesis. Instead, a specific range or interval of the parameter is stated. For example,
Students in class score an average between 12 to 15 out of 20 in exams. Hence,
12< μ< 15.
Null Hypothesis Problem
Problem: A researcher thinks that if the knee surgery patients go to physical therapy twice a week (instead of going 3 times), their recovery period will be longer. Given average recovery time knee surgery patients are given 8.2 weeks.
Step 1:
First, we need to figure out the hypothesis from the problem. The hypothesis is usually hidden in a word problem that you need to figure out. The hypothesis that has been given in the above question is “I expect the average recovery period to be greater than 8.2 weeks.”
Step 2:
You need to convert the hypothesis to math. Remember that the average can be sometimes written as μ.
H1: μ > 8.2(average)
Step 3:
Now state what will happen if the hypothesis doesn’t come true. If the recovery time is not greater than the given average that is 8.2 weeks, there are only two possibilities, that the recovery time is equal to 8.2 weeks or it is less than 8.2 weeks.
H0: μ ≤ 8.2
H0 (The null hypothesis): μ (the average) ≤ (is less than or equal to) 8.2
H0 🡪 μ1 = μ2 where
H0 is the null hypothesis,
μ1 is the mean of population 1, and
μ2 is the mean of population 2.
A stronger null hypothesis denotes that if two samples are drawn from the same given population, such that the variances and shapes of the given distributions are also equal.
Examples of situations where hypothesis tests are used in the real world.
Is there a 100% chance of getting affected by dengue?
Answer: There could be chances of getting affected by dengue but the chances of getting affected by dengue are not 100%.
Do teenagers these days use mobile phones more than adults to access the internet?
Answer: Age has no limit and is not a factor that we can use mobile phones to access the internet.
Does having the fruit apple daily will not cause fever?
Answer: Having an apple daily does not assure of not having fever, but on the other hand it does increase the immunity to fight against such diseases.
Are children better at performing mathematical calculations than adults?
Answer: Again in this example too, age has no effect on Mathematical skills.
Hypothesis tests are often conducted in botany to determine whether some new treatment, fertilizer or chemical can cause increased growth, stamina or immunity in plants and animals.
Suppose, a botanist believes that a certain fertilizer will cause plants to grow more during a 1 month period than what they actually grow. Currently, they grow to 20 inches. To test the effectiveness of the fertilizer, the botanist applies the fertilizer to each of the plants in her lab for a month.
Then performs a hypothesis test using the following hypothesis:
H0: μ = 20 inches as the effect is nil on the mean plant growth by the fertilizer.
HA: μ > 20 inches (the fertilizer will cause mean plant growth to increase)
If the p-value of the test is significantly less then it will reject the null hypothesis and as a result, the fertilizer leads to increased plant growth.
In clinical trials, hypothesis tests are often used to determine whether some new treatment, drug, procedure, etc. cause improved outcomes in patients and thus elevate the treatment levels.
Suppose a doctor wishes to test a new drug that reduces blood pressure in obese patients. To test its effectiveness, the doctor may measure the blood pressure of 40 patients before and after using the new drug for a month.
Then a hypothesis test is performed using the following hypothesis.
H0: μafter = μbefore means the mean blood pressure is the same before and after using the drug
HA: μafter < μbefore (the mean blood pressure is less after using the drug)
Hypothesis tests are often conducted in business organizations to determine whether a new advertising campaign will get more leads and cause an increase in sales.
Suppose, the executive team of an organization believes that spending more on digital advertising leads to increased sales. To test this, the organization may increase money spent on digital advertising during a 3 month period and collect data to see if overall sales have increased or not.
A hypothesis test can be performed using the following hypothesis.
H0: μafter = μbefore signifies the mean sales is the same before and after spending more on advertising
HA: μafter > μbefore (the mean sales increased spending more on advertising)
Apart from just the above 3 examples, hypothesis testing is widely used in research centers, chemical laboratories, stock market predictions, the Investment industry and several business organizations.
Decision errors
There are two types of decision errors that can happen when doing a hypothesis test. They are described below.
Type I error:
This happens when one rejects the null hypothesis despite the null hypothesis being true. The probability of making a type I error is equal to the alpha level significantly
Type II error.
This happens when one fails to reject the null hypothesis when it is actually false. The probability of committing a type II error is the power of the test.
Importance of Hypothesis testing in real life and examples
The main aim of a hypothesis statement in statistics is to determine whether or not some hypothesis of a population parameter is true or false. It is an essential part of the procedures in statistics.
A hypothesis test evaluates two mutually exclusive statements and determines which statement is best supported by sample data. A discovery or a new finding holds a significant value when supported by a hypothesis test. Because the hypothesis test provides sufficient evidence to check the credibility of the given data.
To conduct a hypothesis test in the practical world, researchers obtain a random sample from the population and perform a hypothesis test on the sample data using Null and Alternative hypotheses.
Difference between Null Hypothesis and Alternative Hypothesis.
FAQs on Null Hypothesis
1. Why is a null hypothesis important and can you accept a null hypothesis?
The purpose and the importance of the null hypothesis and alternative hypothesis are that they provide an approximate description of any given phenomena. The purpose of the null hypothesis is to provide the researcher or an investigator with the relational statement that is directly tested in any research study.
A null hypothesis is a hypothesis that is never acceptable. We either reject them or we fail to reject them. Hence, failing to reject the null hypothesis does not mean that we have shown that there is no difference in accepting the null hypothesis.
2. State one example where a Null hypothesis is applied in a practical life scenario?
The concept of null hypothesis has a variety of practical applications. Let us take the example of stock investment, buying shares of a company. The annual return of company stock when invested for a long duration is assumed to be 7.5%.
Now to test if the assumption is true or false, we consider the null hypothesis to be, ”the mean annual return for XYZ company shares is not 7.5%”. To test this hypothesis, we first accept the null hypothesis.
We then check the history of the stock performance of the last 5 years of XYZ company and then calculate the mean of the annual return. The result is then compared to the assumed annual return of 7.5%.
If it turns out that the average annual return of the last 5 years is 7.5%, then the null hypothesis is rejected. And the alternative hypothesis is accepted.
3. What is the purpose of Hypothesis testing?
Hypothesis testing is a statistical process of testing an assumption regarding a particular phenomenon or parameter. Often a good theory can make accurate predictions. However, for an analyst, hypothesis testing is a rigorous way of backing up his prediction with statistical analysis to support the predictions. It is also helpful to determine sufficient statistical evidence that can favor a certain hypothesis about the specified parameter.
In simple words, hypothesis testing is a systematic approach to assessing theories through observations and then determining whether the stated statement is true or false.