Hypothesis testing refers to the systematic and scientific method of examining whether the hypothesis set by the researcher is valid or not. Hypothesis testing verifies that the findings of an experiment are valid and the particular results did not happen by chance. If the particular results have occurred by chance then that experiment can not be repeated and its findings won’t be reliable. For example, if you conduct a study that finds that a particular drug is responsible for the blood pressure problem in diabetic patients. But, when you repeat this experiment and it does not give the same results, no one would trust this experiment’s findings. Hence, hypothesis testing is a very crucial step to verify the experimental findings. The main criterion of hypothesis testing is to check whether the null hypothesis is rejected or retained. The null hypothesis assumes that there does not exist any relationship between the variables under investigation, while the alternate hypothesis confirms the association between the variables under investigation. If the null hypothesis is rejected, it means that alternative hypotheses (research hypothesis) are accepted, and if the null hypothesis is accepted, the alternate hypothesis is rejected automatically. In this article, we’ll learn about hypothesis testing and various real-life examples of hypothesis testing.
Understanding Hypothesis Testing
The hypothesis testing broadly involves the following steps,
- Step 1: Formulate the research hypothesis and the null hypothesis of the experiment.
- Step 2: Set the characteristics of the comparison distribution.
- Step3: Set the criterion for decision making, i.e., cut off sample score for the comparison to reject or retain the null hypothesis.
- Step:4 Set the outcome of the sample on the comparison distribution.
- Step 5: Make a decision whether to reject or retain the null hypothesis.
Let us understand these steps through the following example,
Suppose the researcher wants to examine whether the memorizing power of students improves after consuming caffeine or not. To examine this he conducts experiments, the experiment involves two groups say group A (experimental group) and group B (control group). Group A consumed the coffee before the memory test, while group B consumed the water before the memory test. The average normally distributed score of the people of the experimental group has a standard deviation of 4 and a mean of 19. On the basis of the score, the researcher can state that there is an association between the two variables, i.e., the memory power and the caffeine, but the researcher can not predict any particular direction, i.e., which out of the experimental group and the control group had performed better in the memory tests. Hence, the level of significance value, i.e., 5 per cent will help to draw the conclusion. Following is the stepwise hypothesis testing of this example,
Step 1: Formulating Null hypothesis and alternate hypothesis
There exist two sample populations, i.e., group A and group B.
Group A: People who consumed coffee before the experiment
Group B: People who consumed water before the experiment.
On the basis of this, the null hypothesis and the alternative hypothesis would be as follows.
Alternate Hypothesis: Group A will perform differently from Group B, i.e., there exists an association between the two variables.
Null Hypothesis: There will not be any difference between the performance of both groups, i.e., Group A and Group B both will perform similarly.
Step 2: Characteristics of the comparison distribution
The characteristics of the comparison distribution in this example are given below,
Population Mean = 19
Standard Deviation= 4, normally distributed.
Step 3: Cut off score
In this test the direction of effect is not stated, i.e., it is a two-tailed test. In the case of a two-tailed test, the cut off sample scores is equal to +1.96 and -1.99 at the 5 per cent level.
Step 4: Outcome of Sample Score
The sample score is then converted into the Z value. Using the appropriate method of conversion this value is turned out to be equal to 2.
Step 5: Decision Making
The Z score value of 2 is far more than the cut off Z value, ie., +1.96, hence the result is significant, ie., rejection of the null hypothesis, i.e., there exists an association between the memory power and the consumption of the coffee before the test.
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Hypothesis Testing Real Life Examples
Following are some real-life examples of hypothesis testing.
1. To Check the Manufacturing Processes
Hypothesis testing finds its application in the manufacturing processes such as in determining whether the implication of the new technique or process in the manufacturing plant caused the anomalies in the quality of the product or not. Let us suppose, that manufacturing plant X decides to verify that the particular method results in an increase in the defective products per quarter, say this number to be 200. Now, to verify this the researcher needs to calculate the mean of the number of defective products produced before the start and the end of the quarter.
Following is the representation of the Hypothesis testing of this example,
Null Hypothesis (Ho): The average of the defective products produced is the same before and after the implementation of the new manufacturing method, i.e., μ after = μ before
Alternative Hypothesis (Ha): The average number of defective products produced are different before and after the implementation of the new manufacturing method, i.e., μ after ≠ μ before
If the resultant p-value of the hypothesis testing comes lesser than the significant value, i.e., α = .05, then the null hypothesis is rejected and it can be concluded that the changes in the method of production lead to the rise in the number of defective products production per quarter.
2. To Plan the Marketing Strategies
Many businesses often use hypothesis testing to determine the impact of the newly implemented marketing techniques, campaigns or other tactics on the sales of the product. For example, the marketing department of the company assumed that if they spend more the digital advertisements it would lead to a rise in sales. To verify this assumption, the marketing department may raise the digital advertisement budget for a particular period, and then analyse the collected data at the end of that period. They have to perform hypothesis testing to verify their assumption. Here,
Null Hypothesis (Ho): The average sales are the same before and after the rise in the digital advertisement budget, i.e., μafter = μbefore
Alternative Hypothesis (Ha): The average sales increase after the rise in the digital advertisement budget, i.e., μafter > μbefore
If the P-value is smaller than the significant value (say .05), then the null hypothesis can be rejected by the marketing department, and they can conclude that the rise in the digital advertisement budget can result in a rise in the sales of the product.
3. In Clinical Trials
Many pharmacists and doctors use hypothesis testing for clinical trials. The impact of the new clinical methods, medicines or procedures on the condition of the patients is analysed through hypothesis testing. For example, a pharmacist believes that the new medicine is resulting in the rise of blood pressure in diabetic patients. To test this assumption, the researcher has to measure the blood pressure of the sample patients (patients under investigation) before and after the intake of the new medicine for nearly a particular period say one month. The following procedure of the hypothesis testing is then followed,
Null Hypothesis (H0): The average blood pressure is the same after and before the consumption of the medicine, i.e., μafter = μbefore
Alternative Hypothesis (Ha): The average blood pressure after the consumption of the medicine is less than the average blood pressure before the consumption of the medicine, i.e., μafter < μbefore
If the p-value of the hypothesis test is less than the significance value (say .o5), the null hypothesis is rejected, i.e., it can be concluded that the new drug is responsible for the rise in the blood pressure of diabetic patients.
4. In Testing Effectiveness of Essential Oils
Essential oils are gaining popularity nowadays due to their various benefits. Various essential oils such as ylang-ylang, lavender, and chamomile claim to reduce anxiety. You might like to test the true healing powers of all these essential oils. Suppose you assume that the lavender essential oil has the ability to reduce stress and anxiety. To check this assumption you may conduct the hypothesis testing by restating the hypothesis as follows,
Null Hypothesis (Ho): Lavender essential has no effect on reducing anxiety.
Alternative Hypothesis (Ha): Lavender oil helps in reducing anxiety.
In this experiment, group A, i.e., the experimental group are provided with the lavender oil, while group B, i.e., the control group is provided with the placebo. The data is then collected using the various statistical tools and the stress level of both the groups, i.e., the experimental and the control group is then analysed. After the calculation, the significance level, and the p-value are found to be 0.25, and 0.05 respectively. The p values are less than the significance values, hence the null hypothesis is rejected, and it can be concluded that the lavender oil helps in reducing the stress among the people.
5. In Testing Fertilizer’s Impact on Plants
Nowadays, hypothesis testing is also used to examine the impact of pesticides, fertilizers, and other chemicals on the growth of plants or animals. Let us suppose a researcher wants to check his assumption that the particular fertilizer may result in the faster growth of the plant in a month than its usual growth of 10 inches. To verify this assumption he consistently gave that fertilizer to the plant for nearly a month. Following is the mathematical procedure of the hypothesis testing in this case,
Null Hypothesis (H0): The fertilizer does not have any influence on the growth of the plant. i.e., μ = 20 inches
Alternative Hypothesis (Ha): The fertiliser results in the faster growth of the plant, i.e., μ > 20 inches
Now, if the p-value of the hypothesis testing comes smaller than the level of significance, say .05, then the null hypothesis can be rejected, and you can conclude that the particular fertilizer is responsible for the faster plant growth.
Suppose the researcher assumes that Vitamin E helps in the faster growth of the Hair. He conduct an experiment in which the experimental group is provided with vitamin E for three months while the controlled group is provided with the placebo. The results are then analysed after the duration of three months. To verify his assumption he restates the hypothesis as follows,
Null Hypothesis (H0): There is no association between the Vitamin E and the hair growth of the sample group, i.e., μafter = μbefore
Alternative Hypothesis (Ha): The group of people who consumed the vitamin E shows faster hair growth than the average hair growth of them before the consumption of the Vitamin E provided other variables remains constant. Here, μafter > μbefore.
After performing the statistical analysis, the significance level and the p-value in this scenario are o.o5, and 0.20 respectively. Hence, the researcher can conclude that the consumption of vitamin E results in faster hair growth.
7. In Testing the Teaching Strategy
Suppose the two teachers say Mr X and Mr Y argue about the best teaching strategy. Mr X says that children will perform better in the annual exams if they are given the weekly tests, while Mr Y argues that the weekly test would not impact the performance of the children in the annual exams and it is waste of time. Now, to verify who is right between the both, we may conduct hypothesis testing. The researcher may formulate the hypothesis as follows,
Null Hypothesis (Ho): There is no association between the weekly tests on the performance of the children in the annual exams, i.e., the average marks scored by the children when they were given the weekly exams and when not, were the same. (μafter = μbefore)
Alternative Hypothesis (Ha): The children will perform better in the annual exams, when they have to give the weekly tests, rather than just giving the annual exams, i.e., μafter > μbefore.
Now, if the p-value of the hypothesis testing comes smaller than the level of significance, say .05, then the null hypothesis can be rejected, and the researcher can conclude that the children will perform better in the annual exams if the weekly examination system would be implemented.
8. In Verifying the Assumption related to Intelligence
Suppose a principle states that the students studying in her school have an IQ level of above average. To support her statement, the researcher may take a sample of around 50 random students from that school. Let’s say the average IQ score of those children is around 110, and the average IQ score of the mean population is 100 with a standard deviation of 15. The hypothesis testing is given as follows,
Null Hypothesis (Ho): The population mean IQ score of 100 is a general fact, i.e., μ = 100.
Alternative Hypothesis (Ha): The average IQ score of the students is above average, i.e., μ > 100
It’s a one-tailed test as we are aiming for the ‘greater than’ assumption. Let us suppose the alpha level or we can say the significance level, in this case, is 5 per cent, i.e., 0.05, and this corresponds to the Z score equal to 1.645. The Z score is found by the statistical formula given by (112.5 – 100) / (15/√30) = 4.56. Now, the final step is to compare the values of the expected z score and the calculated z score. Here, the calculated Z score is lesser than the expected Z score, hence, the Null Hypothesis is rejected, i.e., the average IQ score of the children belonging to that school is above average.
