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When studying the effects of a drug, it would be possible to determine the effects by administering the drug to all people who need it, but this is not possible. Therefore, in a clinical trial, a drug is administered to a subset of the population to verify whether the data obtained from the trial applies to many people worldwide.
For example, we hypothesize that the new antipyretic drug Y has an antipyretic effect in the population and use a test method to confirm whether this hypothesis is true. This method is called a “hypothesis test.” A hypothesis test is also called a population test or statistical test.
In this article, we will explain hypothesis testing and what p-value indicates probability.
The null and alternative hypothesis
In statistical hypothesis testing, we first formulate the null and alternative hypotheses.
Let us first explain the null and alternative hypotheses.
When the new drug Y is superior in antipyretic action, we can say that the decreasing body temperature is greater than 0°C. Therefore, if we assume that the decreasing body temperature in the population is 0°C, the hypothesis will most likely not be confirmed. Therefore, if we assume that the hypothesized decrease in body temperature in the population is 0°C, then the hypothesized event is unlikely to occur.
In this case, the hypothesis that the decreasing body temperature is 0°C is the null hypothesis. The null hypothesis is a hypothesis that is rejected and returns to “nothing.” The opposite of the null hypothesis is called the alternative hypothesis. The alternative hypothesis is what we want to reveal for the purpose of analysis.
If the null hypothesis can be shown to be an event that rarely occurs, that is, the null hypothesis can be rejected, then the alternative hypothesis is adopted.
Hypothesis testing procedure
Hypothesis testing is performed according to the following procedure.
- Formulate the null and alternative hypotheses.
- Calculate the basic statistics.
The mean, standard deviation, and standard error (SE) are calculated for the survey data.
Calculate the test statistics.
The test statistic is calculated by applying the standard error (SE) to the hypothesis testing formula.
The three test statistics are the t-value, p-value, and confidence interval. - Determination of significance.
The t-value and p-value are compared with the values determined by statistics (significance level) to determine the significance difference.
How to perform a hypothesis test with a p-value
This section explains how to perform a hypothesis test with a p-value.
The p-value is an acronym for “probability” and is a value between 0 and 1.
The p-value is closely related to the t-value, and the larger the t-value, the smaller the p-value.
The smaller the p-value, the more accurate the conclusion that there is an effect (difference) in the population.
The p-value is compared with the value of the criterion established by statistics, and if the “p-value < significance level”,” the null hypothesis is rejected, and the alternative hypothesis is adopted. In other words, we conclude that “the new drug Y has an antipyretic effect in the population.”
The significance level is usually constant at 0.05 (5%).
When the p-value is less than the significance level, we can determine that there is a difference (effect, significant difference).
The p-value means that the percentage of occurences of incorrectly rejecting the null hypothesis is less than 5% when the hypothetical test is conducted several times.
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