Blog series of Hypothesis Testing: Components of a Hypothesis Test
Statistically, when a claim is made it has to be evaluated before believing it. This is where hypothesis testing comes into the picture. A hypothesis is a claim made about a population. A hypothesis test uses sample data to test the validity of the claim.
Let's consider a democratic country ‘XYZ’ in which there is a ruling party by the name ‘A’ and an opposition party by the name ‘B’. Pary A will claim, that during their tenure, the nation's poverty is reduced to less than 4%. Opposition Party B will criticize the claim made by Party A saying poverty of the nation is ≥ 4%. To support the claim made against Party A, the opposition party needs to showcase the evidence. If Party B gets enough evidence to support its claim (poverty ≥ 4%) then they conclude Part A has made a false claim. If Party B does not get enough evidence to support its claim then the claim made by Party A is correct. This scenario is a perfect analogy for Hypothesis testing.
Components of a Hypothesis Test
- Alternative hypothesis (H1 or Ha): The claim we make is the alternative hypothesis. Aka Research hypothesis
- Null hypothesis (H0): The claim that is done to nullify or criticize the original claim is the null hypothesis. It is the opposite of the alternative hypothesis. It says there is no relationship between variables or no differences between groups.
Example:
Null Hypothesis H0: There is no difference in the salary of factory workers based on gender.
Alternative Hypothesis Ha: Male factory workers have a higher salary than female workers.
Null Hypothesis H0: There is no relationship between pranayama and LDL cholesterol.
Alternative Hypothesis Ha: Pranayama has an impact on reducing LDL cholesterol.
The above table gives the relationship between variables in the null hypostasis based on the Alternative hypothesis.
Assuming the variable is a continuous variable that is normally distributed, the following figure illustrates the setup of a hypothesis test.
3. Level of significance(α)
In Statistics, “significance” means “not by chance” or “probably true”.
The pharmaceutical company claims that the curing rate of malaria by the newly launched drugs is 90%.
Suppose, we test the drug on 1000 patients, as per the claim it has to cure 900 patients. Consider various cases
- Drug cures 540 patients: In this case, we reject the claim.
- Drug cures 980 patients: We accept the claim.
- Drug cures 895 patients: We are doubtful whether to accept or reject the claim since the cure is close to 90% i.e. 900 patients. On the other hand, it's difficult to get precise results in real-time experiments, in our eg it's very unlikely we will get exactly 900 patients getting cured. Hence rather than reject any count less than 900 we consider certain buffer. If the value falls in this range we still accept the claim. This buffer is known as Level of significance (denoted by α).
Generally, a significance level is given as 5%(0.05) or 1%(0.01). A significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference. In the significance region, we reject H0 and accept H1.
4. Confidence level: 1-α is the confidence level, in this region, we fail to reject H0. For the 5% and 1% significance levels, we will have 95% and 99% confidence levels.
5. Critical value: Critical value is a cut-off value beyond which we will reject H0. It is the value that defines the rejection zone (the test statistic values that would lead to the rejection of the null hypothesis). It is defined by the level of significance.
From the example of Malaria drug, assume a significance level as 5% which corresponds to a z score of 1.645. Click here for the computation of critical value for a given significance level.
Please read the following series of hypothesis testing:
- Blog 2: One-tailed and Two-tailed Tests
In the coming weeks, I will publish the following blogs:
- Blog 3: How to perform hypothesis testing
- Blog 4: Type 1 and Type 2 errors
EndNote:
I hope you enjoyed reading the article on various components of hypothesis testing. Please drop your suggestions or queries in the comment section.
Would love to catch you on Linkedin. Mail me here for any queries.
Happy reading!!!!
I believe in the power of continuous learning and sharing knowledge with the community. Your contributions are invaluable in helping me create meaningful content and resources that benefit everyone. Join me on this journey of exploration and innovation in the fascinating world of data science by donating to Buy Me a Coffee.
