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Introduction to Hypothesis Testing - Coggle Diagram
Introduction to Hypothesis Testing
Hypothesis testing is a statistical method that uses sample data to determine whether there is enough evidence to support or reject a claim about a population.
hypothesis-testing procedure
Make a guess about the population.
Example: We think American adults gain an average of 7 pounds between Thanksgiving and New Year’s.
Predict what our sample should look like.
If the true population average is 7 pounds, we expect our sample average to be close to 7, but not necessarily exactly 7 because of sampling error.
Take a random sample.
We measure the weight change of some American adults and calculate their sample mean.
Compare the sample result with our prediction.
If the sample mean is close to 7, the hypothesis seems reasonable.
If the sample mean is far from 7, the hypothesis may be wrong.
Unknown population: The population after treatment, whose characteristics we do not know and want to determine using a sample.
Hypothesis testing is used to determine whether a treatment changes the population mean compared with a known or assumed value.
A sample is a small group selected from the population to collect data and determine whether the treatment has an effect.
Four Steps of a Hypothesis Test
State the hypotheses – Make a claim about the population.
Set the criteria – Decide how much evidence is needed to reject the hypothesis.
Collect and analyze data – Take a sample and calculate the test statistic.
Make a decision – Decide whether to reject or fail to reject the hypothesis.
Test statistic: A single number calculated from sample data that is used to test a hypothesis.
Hypothesis testing is an inferential process that uses sample data to make a conclusion about a population.
Type I Error: Rejecting a true null hypothesis.
Probability of a Type I Error: The probability of rejecting a true null hypothesis
Alpha level (α): The probability of making a Type I error, rejecting the null hypothesis when it is actually true.
Type II Error: Failing to reject a false null hypothesis
β = probability of a false negative.
Selecting an Alpha Level: Choosing the acceptable probability of making a Type I error.
If the z-score falls in the critical region, we reject the null hypothesis and conclude that the treatment has a significant effect.
Random Sampling: Selecting participants randomly from a population so that the sample is representative of the population and the results can be generalized to the population.
Independent Observations: Each observation is not affected by or related to another observation.
Nondirectional (two-tailed) test: A hypothesis test that looks for an effect in either direction;the result could be higher or lower than the expected value
Directional (one-tailed) test: A hypothesis test that looks for a difference in one specific direction, higher or lower.
Because the researcher expects the treatment to increase tips, this is a directional (one-tailed) test.
Null hypothesis (H₀): The red shirt does not increase tips.
Alternative hypothesis (H₁): The red shirt increases tips.
One-Tailed vs. Two-Tailed Tests
One-tailed test: Looks for an effect in one specific direction (higher or lower).
Two-tailed test: Looks for an effect in either direction (higher or lower).
Critical Region: The range of sample results that are very unlikely to occur if the null hypothesis is true.
Power of a hypothesis test: The probability of correctly rejecting the null hypothesis when the treatment really has an effect.
Researchers calculate power to determine whether an experiment is likely to detect a real treatment effect when one exists.
Simple definition:
Effect size: The amount or size of the treatment effect
Alpha level: A lower alpha level means a lower probability of Type I error, but it also reduces the power of the test.