Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating a hypothesis, collecting data, and then determining whether the evidence supports the hypothesis or not. The process generally involves the following steps:
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Formulate the Hypotheses:
- Null Hypothesis (H0): The hypothesis that there is no effect or no difference. It is the statement that the test seeks to disprove.
- Alternative Hypothesis (H1 or Ha): The hypothesis that indicates the presence of an effect or a difference. It is what you want to prove.
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Choose a Significance Level (α):
- The significance level is the threshold for rejecting the null hypothesis. Common choices are 0.05, 0.01, or 0.10. It represents the probability of making a Type I error (rejecting a true null hypothesis).
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Collect Data:
- Gather sample data relevant to the hypotheses being tested.
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Calculate the Test Statistic:
- Depending on the type of test (t-test, z-test, chi-square test, etc.), calculate the test statistic using the sample data.
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Determine the p-value or critical value:
- The p-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true.
- Alternatively, one can use a critical value approach where you compare the test statistic to a critical value derived from statistical tables based on the significance level.
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Make a Decision:
- If the p-value is less than or equal to α (or if the test statistic exceeds the critical value), reject the null hypothesis. Otherwise, do not reject it.
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Draw Conclusions:
- Based on the decision, conclude whether there is enough evidence to support the alternative hypothesis.
Example Scenario
Suppose a new drug is believed to lower blood pressure compared to a placebo. You would:
- H0: The mean blood pressure of patients using the drug is equal to that of patients taking the placebo.
- H1: The mean blood pressure of patients using the drug is lower than that of patients taking the placebo.
After collecting your data and running the appropriate statistical test, you would evaluate the p-value and decide whether to reject H0 in favor of H1.
Considerations
- Type I Error: Rejecting the null hypothesis when it is true.
- Type II Error: Failing to reject the null hypothesis when it is false.
- The power of a test is the probability of correctly rejecting the null hypothesis when it is false.
Hypothesis testing is commonly used in various fields such as psychology, medicine, business, and social sciences to validate theories and make informed decisions based on empirical data.