What is hypothesis testing used for?
Hypothesis testing is a statistical method used to make inferences about a population based on sample data. It helps determine whether there is enough evidence to support or reject a specific claim (hypothesis) about a population parameter.
It is commonly used in research to evaluate assumptions, compare groups, and assess relationships between variables under uncertainty.
What are the five steps in hypothesis testing?
1) State the null (H0) and alternative (H1) hypotheses. 2) Choose a significance level (alpha, e.g., 0.05). 3) Select the appropriate test and calculate the test statistic. 4) Determine the p-value or critical value. 5) Make a decision to reject or fail to reject H0.
These steps provide a structured way to evaluate evidence and ensure consistency in statistical decision-making.
How do you determine if a null hypothesis should be rejected?
You reject the null hypothesis if the p-value is less than or equal to the chosen significance level (alpha), indicating strong evidence against H0. Alternatively, you reject H0 if the test statistic falls within the critical region.
If the p-value is greater than alpha, you fail to reject the null hypothesis, meaning there is insufficient evidence to support the alternative hypothesis.
What is the difference between a directional and a non-directional hypothesis?
A directional hypothesis specifies the expected direction of the effect or relationship (e.g., greater than or less than). A non-directional hypothesis only states that there is a difference or effect, without specifying direction.
Directional hypotheses are more specific and typically tested with one-tailed tests, while non-directional hypotheses use two-tailed tests.
What is the difference between a one-tailed and a two-tailed hypothesis test?
A one-tailed test evaluates the possibility of an effect in one direction only (either greater than or less than). A two-tailed test evaluates both directions, checking for any significant difference from the null hypothesis.
One-tailed tests have more power in one direction but cannot detect effects in the opposite direction, while two-tailed tests are more conservative and widely used.
What is a decision error?
A decision error occurs when the conclusion made from a hypothesis test does not reflect the true state of reality. It arises because decisions are based on sample data, which may not perfectly represent the population.
There are two main types of decision errors: Type I and Type II errors.
What is the difference between a Type I Error and a Type II Error?
A Type I Error occurs when the null hypothesis is incorrectly rejected when it is actually true (a false positive). A Type II Error occurs when the null hypothesis is not rejected when it is actually false (a false negative).
The probability of a Type I Error is alpha, while the probability of a Type II Error is beta; reducing one often increases the other.
