Hypothesis Testing

Hypothesis Testing

Hypothesis testing is a fundamental tool in statistical analysis and helps researchers and analysts make objective decisions based on data. It provides a structured approach for drawing conclusions about populations from limited sample information.

In order to make a decision based on the data, it is very useful to make some assumptions about the population. Such an assumption, which may or may not be true, is known as a “hypothesis.”. In simple words, we can say that hypothesis testing is useful for accepting or not accepting assumptions.

The null hypothesis (H0) and alternative hypothesis (Ha) are key components of hypothesis testing. Here’s a brief explanation of each:

H0 and H1

1. Null Hypothesis (H0): The null hypothesis represents the default assumption. It assumes that there is no significant difference, effect, or relationship in the population being studied. In other words, any observed differences or effects in the sample data are due to chance or random variability. So, we can say that the null hypothesis treats everything as equal and similar. The null hypothesis is typically denoted as “H0.”
2. Alternative Hypothesis (Ha/H1): The alternative hypothesis proposes a different or opposing claim to the null hypothesis. It suggests that there is a significant difference, effect, or relationship in the population being studied. The alternative hypothesis is what the researcher or analyst is trying to gather evidence for. It can take various forms depending on the nature of the study, such as stating that a mean is greater or less than a certain value, that two groups are significantly different, or that a correlation exists. The alternative hypothesis is denoted as “Ha” or “H1.”

In hypothesis testing, the goal is to assess the evidence in the sample data and determine whether it provides enough support to reject the null hypothesis in favor of the alternative hypothesis. The choice between the null and alternative hypotheses depends on the research question and the hypothesis the researcher wants to test.

Process of Hypothesis Testing:

a. Collect the data

b. Define the significance level:

To define the significance level, we have to do certain tests:

1. t-test
2. chi-square test
3. ANOVA test
4. z-test

In general, we take significance level = 0.05. It means if we take 100 data points at random, then in 5% the null hypothesis will be valid or our assumption is true.

On the basis of these tests, we will find the significance level, and from the significance level, we can find the strength of the null hypothesis or with what confidence we can accept or not accept the null hypothesis.

So,

if p-value < α → Not accept HO

if p-value ≥ α → Accept HO

Here,

α = significance level

c. Accept/Not Accepting the Null Hypothesis:

If the Null hypothesis(Ho) is not accepted, then we will opt for the alternative hypothesis (Ha).

Type — I and Type—II errors:

When we test the null hypothesis (Ho) against the alternative hypothesis (Ha), there will be four possibilities:

a. Ho is accepted → when Ho is true [correct]

b. Ho rejected→ when Ho is true [Type-I error]

c. Ho accepted→ when Ho is false [Type-II error]

d. Ho rejected→ when Ho is false [correct]

So we can say that

α = probability of Type-I error or probability of rejecting Ho/Ho being true)

β = probability of Type-II error or probability of (accept Ho/Ha is true)

Points to remember:

1. α, and β cannot be zero simultaneously when inferences are based on samples.
2. However, α and β can be zero when a complete (population) enumeration is done.
3. If one of them is said to be zero, the other becomes 1. It means if α = 0 then β = 1 or, α = 1then β = 0.
4. The above point does not mean that α + β = 1.
5. α and β should be kept low.
6. Usually α = 0.01 or 0.05 and for that, we take a large sample size so that will also be low.

Conclusion:

In conclusion, the article offers a comprehensive overview of hypothesis testing, encompassing the significance of assumptions, the pivotal role of null and alternative hypotheses, the step-by-step process of hypothesis testing, and the consideration of Type-I and Type-II errors. It provides valuable insights into how hypothesis testing allows researchers and analysts to make informed decisions based on limited sample information, contributing to the foundation of statistical analysis.