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Hypothesis Interpretation From the Calculated P-Value.
The calculated p-value is 0.0686. This means that the hypothesis that there is no difference between the two groups is not rejected at the 5% significance level.
P-Value Example:
A statistician is testing the hypothesis that a certain medication is effective in treating a certain type of cancer. A sample of 100 patients is taken, and the results of the treatment are analyzed. The statistician finds that in the sample, 60 of the patients were successfully treated.
The statistician tests the hypothesis that the medication is effective in treating the cancer by calculating the p-value. The p-value is the probability of obtaining a result as extreme as the one observed, or more extreme, if the null hypothesis is true. In this case, the p-value is the probability of obtaining a result as extreme as 60 successes out of 100 patients, or more extreme.
The p-value is calculated by comparing the observed value of 60 successes out of 100 patients to the value of the distribution of successes that would be expected if the null hypothesis were true. If the p-value is less than a predetermined cutoff value, such as 0.05, then the statistician concludes that the medication is effective in treating the cancer.
How to Find P Value Formula:
P-value is the probability of obtaining the observed or a more extreme result, assuming the null hypothesis is true. It is calculated using the following formula:
P-value =
where:
O is the observed result
E is the most extreme result that could have been obtained, given the null hypothesis is true
N is the sample size
Real-Life P-Value Examples:
1. A study is conducted to determine whether there is a relationship between stress levels and heart disease. A total of 100 people are studied, and it is found that 50 of them have heart disease and 50 do not. The stress levels of each person are measured, and it is found that the average stress level of those with heart disease is 9, while the average stress level of those without heart disease is 5.
The null hypothesis is that there is no relationship between stress levels and heart disease.
The alternative hypothesis is that there is a relationship between stress levels and heart disease.
The p-value is calculated to be 0.023.
This p-value indicates that the probability of the null hypothesis being true is 2.3%. This means that there is a 97.7% chance that the alternative hypothesis is true.
2. A study is conducted to determine whether there is a relationship between stress levels and heart disease. A total of 100 people are studied, and it is found that 50 of them have heart disease and 50 do not. The stress levels of each person are measured, and it is found that the average stress level of those with heart disease is 9, while the average stress level of those without heart disease is 5.
The null hypothesis is that there is no relationship between stress levels and heart disease.
The alternative hypothesis is that there is a relationship between stress levels and heart disease.
Also Check For:
Level of Significance in Statistics – Definition, P-value Significance Level and FAQs
