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Introduction to Hypothesis Testing
What is Hypothesis Testing?
Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves testing an assumption (hypothesis) and determining whether to accept or reject it based on the evidence provided by the data.
Steps in Hypothesis Testing
1. State the Hypotheses: Formulate the null hypothesis (H0) and the alternative hypothesis (H1).
Null Hypothesis (H0): Assumes no effect or no difference.
Alternative Hypothesis (H1): Assumes there is an effect or a difference.
2. Choose a Significance Level: Decide the probability of rejecting the null hypothesis when it is true (commonly 0.05).
3. Collect Data: Gather sample data relevant to the hypotheses.
4. Perform the Test: Use statistical tests (e.g., t-test, chi-square test) to analyze the data.
5. Make a Decision: Based on the test results, decide whether to reject or fail to reject the null hypothesis.
Types of Hypotheses
One-tailed Test: Tests for an effect in one direction (e.g., greater than).
Two-tailed Test: Tests for an effect in both directions (e.g., not equal to).
Common Statistical Tests
t-Test: Compares the means of two groups.
Chi-Square Test: Tests the association between categorical variables.
ANOVA (Analysis of Variance): Compares the means of three or more groups.
Example
A researcher wants to test if a new drug is more effective than the existing one. The null hypothesis (H0) states that there is no difference in effectiveness, while the alternative hypothesis (H1) states that the new drug is more effective. By performing a t-test on the data collected from clinical trials, the researcher can determine if there is a statistically significant difference between the two drugs.
Activity
Think of a hypothesis you can test using data. Write down the null and alternative hypotheses, and outline how you would collect and analyze the data. For example, test whether the average height of students in a class is greater than the national average.
Quiz
1. What is the null hypothesis?
- a) A hypothesis that assumes there is an effect or difference
- b) A hypothesis that assumes no effect or difference
- c) A hypothesis that is always true
- d) A hypothesis that cannot be tested
2. True or False: The p-value indicates the probability of obtaining the observed results if the null hypothesis is true.
- a) True
- b) False
3. What is a type I error in hypothesis testing?
- a) Failing to reject the null hypothesis when it is false
- b) Rejecting the null hypothesis when it is true
- c) Accepting the null hypothesis when it is false
- d) Failing to accept the null hypothesis when it is true
4. What is the significance level in hypothesis testing commonly denoted as?
- a) p-value
- b) alpha (α)
- c) beta (β)
- d) gamma (γ)
5. Which step in hypothesis testing involves gathering sample data?
- a) State the Hypotheses
- b) Choose a Significance Level
- c) Collect Data
- d) Perform the Test
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