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# Number of Samples for Hypothesis Test

**Hypothesis Testing** - it is the process of using statistical tests to determine if the observed differences between two or more samples is statistically significant or not. A null hypothesis (Ho) is a stated assumption that there is no difference or the difference is due to a random chance while the alternate hypothesis (Ha) is a statement that there is a true difference. With the help of hypothesis testing, we arrive at one of the following conclusions.

1. Fail to reject the Null hypothesis (accept the Null hypothesis)

2. Reject the Null hypothesis (accept the Alternate hypothesis)

From a practical point of view, hypothesis testing allows to collect sample sizes and make decisions based on facts and it takes away the decisions based on gut feeling or experience or common sense. You have statistical proof of whatever you "feel" or "think" is right.

**Sample Size **is the number of observations or data points or objects in a sample. Sufficiency of sample size is a key element in hypothesis testing to be able to make inferences about the population. The right sample size is primarily dependent on the cost & time involved in data collection and the need for statistical significance. Statistically, sample size is affected by the following parameters

a. Significance Level (σ) or the maximum allowed probability of committing Type I error

b. Power of the test (1-β), where β is the maximum allowed probability of committing Type II error

c. Minimum difference (in the test statistic) to be detected.

An application-oriented question on the topic along with responses can be seen below. The best answer was provided by Rajesh Patwardhan on 27th November 2019.

Applause for all the respondents - Rajesh Patwardhan, Abhishek Mitra, Nilesh Gham, Mukul Kandpal, Deepak Pardasani, Shashank Parihar

## Question

## Vishwadeep Khatri

Q 213.

It is common to see two aproaches in Hypothesis testing. These are mentioned below.Take a certain number of samples (whatever is feasible practically), and test the decided hypothesis. If the statistical significance is not proved, take some more samples. Keep increasing samples as long as possible and stop if significance is proved. This aproach keeps initial cost low.Decide the number of samples using a sample size calculation (considering alpha, beta, difference to be detected and hypothesized value etc.) and take a decision based on the outcome of hypothesis testing. This approach provides decision in one go.Which of the two approaches for Hypothesis testing will you select? Why?

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