Hypothesis Testing

What is Hypothesis Testing in Statistics? Types and Steps

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Hypothesis testing is the process of evaluation and testing of a proposed  hypothesis or a claim about a population parameter. It is tested against the evidence inferred from the sample data.

The scope of this article aims to discuss the underlying concept of Hypothesis Testing in statistics, its types and steps, significance level, p-value and common errors in hypothesis testing.

What is Hypothesis testing?

Hypothesis testing is a critical part of statistical and scientific research, which, on the basis of a sample of data, makes inferences about a population by assessing the likelihood of the observations taking the assumption that the null hypothesis is true. 

Hypothesis testing is used in different domains like business, healthcare, and engineering to make informed decisions. 

Types of Hypothesis Testing

  • Null Hypothesis (H0) and Alternative Hypothesis (Ha) –

Null hypothesis represents the hypothesis that there is no significant association between  between variables. It is the hypothesis that is to be tested and any observed difference is merely due to chance. Alternative hypothesis represents the hypothesis that there is difference or association between variables. It is the accepting hypothesis if the null hypothesis is rejected and the observed difference is not due to chance.

  • Simple and Composite Hypothesis Testing –

In hypothesis testing, null and alternative hypotheses can be simple and composite hypotheses. Simple hypothesis specifies a particular value for a population parameter. For example, the null hypothesis that the mean height of a population is 173 cm is a simple hypothesis. Composite hypothesis specifies a range of values for a population parameter. For example, the alternative hypothesis that the mean height of a population is not 173 cm is a composite hypothesis.

  • One-Tailed and Two-Tailed Hypothesis Testing –

In hypothesis testing, alternative hypotheses can be one-tailed and two-tailed. One-tailed alternative hypothesis specifies the direction of difference between variables. Here, the distribution of the test sample is one-sided, meaning, it is either greater or lesser than a specific value. Two-tailed alternative hypothesis does not specify the direction of difference between variables. Here, the distribution of the test sample is two-sided, meaning, it is checked to be greater or less than a range of values.

Steps in Hypothesis Testing

Steps in Hypothesis Testing

Step 1: Stating the hypotheses

Begin with stating  the null and alternative hypotheses on the basis of the research area. Typically, the null hypothesis is the default assumption and the alternative hypothesis as the assumption of the desired result.

Step 2: Setting the significance level

The significance level, denoted by alpha (α). It is the probability of rejecting the null hypothesis when it is true. The significance level is usually 0.05 or 0.01, meaning the chance of 5% or 1% in accepting to make a Type 1 error (rejection of true null hypothesis). 

Step 3: Collecting the data

The data is collected by conducting a study or experiment to test the hypothesis. Here the focus should be on the random data such that the results are unbiased. 

Step 4: Calculating the test statistic

The test statistic measures the deviation of sample data from the null hypothesis. Frequently used test statistics are- chi-square test, t-test, z-test and F-test. The type of test statistic being used depends on the type of hypothesis being tested and the level of data measurement.

Step 5: Calculating the p-value

The p-value is the probability of observing the test statistic with the assumption of the null hypothesis being true or the probability of the null hypothesis being rejected. A small p-value (less than significance level) indicates rejection of the null hypothesis and a large p-value (greater than significance level) indicates that the null hypothesis cannot be rejected.

Step 6: Making a decision and interpreting the results

Finally, on the basis of p-value and the significance level, a decision is made. In case p-value is less than significance level, the null hypothesis is rejected in favor of the alternative hypothesis and the results are said to be statistically significant. For cases where p-value is greater than the significance level, the null hypothesis is not rejected and results are not statistically significant.

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Hypothesis Testing in Statistics Example:

Example: Suppose a factory produces light bulbs, and the manufacturer claims that the average lifespan of a bulb is 1000 hours. However, you suspect that the bulbs may not actually last that long. To test your hypothesis, you randomly select a sample of 50 bulbs and test their lifespans. You find that the average lifespan of the sample is 980 hours with a standard deviation of 50 hours.

For performing a hypothesis test on the above problem, the steps need to be followed are:

  1. The null and alternative hypotheses are defined, wherein, the null hypothesis (H0) is the average lifespan of bulbs which is 1000 hours and the alternative hypothesis (Ha) is that it is less than 1000 hours.
  2. Choose a significance level of 0.05, i.e., acceptance of 5% risk of rejecting the null hypothesis when it is true.
  3. The test statistic is calculated with the use of t-test as population standard division is not known. The formula for the t-test is:

t = ( – ? ) / (s /√n  )

where,  is the sample mean, ? is the population mean (to be tested), s is the sample standard deviation, and n is the sample size.

Putting in the values,

t = (980 – 1000) / (50/√50 ) = -2.24

  1. To calculate the p-value, we use the one-tailed hypothesis (as we only want to find whether the lifespan is less than 1000 hours), so we have to find the area under the t-distribution to the left of our test statistic. By using a t-table or a calculator, p-value is found out to be 0.014.
  2. On comparing the p-value (0.014) to the significance level (0.05), we conclude that p-value is less than the significance level, which means the average lifespan of bulbs is less than 1000 hours.

Note: This is just a simple illustrative example and hypothesis testing in statistics can be more complex involving more variables, sample sizes and assumptions.

Common Errors in Hypothesis Testing:

There are two types of error in hypothesis testing: 

  • Type 1 Error – This is the error of rejecting the null hypothesis when it is true. The probability of occurrence of Type 1 error is denoted as alpha (α).
  • Type 2 Error – This is the error of failing to reject the null hypothesis when it is false. The probability of occurrence of Type 2 error is denoted as beta (β).

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Conclusion

Hypothesis testing meaning in statistics defines a tool which models a hypothesis about a population to be true or false. It majorly takes in account of assumptions and interpretations based on probability, and hence it can be erroneous at times. Hypothesis testing is widely used for large sample data such as in psychology, biology, advertising, and many more.

Author

  • Rahul Kumar

    Written by:

    I am Rahul Kumar final year student at NIT Jamshedpur currently working as Data Science Intern. I am dedicated individual with a knack of learning new things.