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Chapter 8: Hypothesis Testing - Coggle Diagram
Chapter 8: Hypothesis Testing
The purpose of collecting data from samples is to answer questions about the population
Hypothesis Testing: A statistical method that uses sample data to evaluate a hypothesis about a population
What is needed for hypothesis testing?
Hypothesis: A predicted outcome
Null Hypothesis: The hypothesis that states the treatment will have no (null) effect
Sometimes includes change in one direction that is not anticipated by the alternative hypothesis. For instance, if the alternative hypothesis predicts a decrease in headache pain from a medicine, the null hypothesis may include increases in pain (since that is not a desired outcome)
In these cases, the alpha level refers just to one side of the distribution!
Called a Directional Hypothesis Test or One-Tailed Test
If the test statistic lies in the critical region, the null hypothesis is
rejected
If the test statistic does not lie in the critical region, the null hypothesis is
not rejected
Alternative Hypothesis: The hypothesis that there will be change after the treatment
Sometimes called the "scientific hypothesis"
A hypothesis test does not accept or reject the alternative hypothesis!
Decision Criteria: A way to decide if the hypothesis is sufficiently supported or not based on the sample data
Alpha Level: Probability value that is used to define the concept of "very unlikely" in a hypothesis test
Provides a metric by which to determine the answer to if a hypothesis is supported or not
Also called level of significance
Critical Region: Values defined as "highly unlikely" to be observed if the Null Hypothesis is true
Defined by the Unit Normal Table
Represented by a decimal, such as a=.05 or a=.01
The smaller the alpha level, the more stringent the test is and the less likely it is that a true null hypothesis will be rejected
Type I Error: When a true null hypothesis is rejected
There is a 5% chance of making a Type I error if a=.05, as if the null hypothesis is true then only 5% of samples should have a sample mean in that range
The decimal indicates what percentage of the distribution is identified as extreme, so if a=.05 then the upper and lower 2.5%s would be extremes
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Errors occur and fantastical results do happen. That's why it's important to retest!
Type II Error: When a false null hypothesis is not rejected
Usually happens if the treatment effect is small, additional testing and/or larger sample sizes may eventually successfully observe a small treatment effect
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Power: The probability that the test will correctly reject a false null hypothesis
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This is usually the less egregious error to make, so typically researchers err on the side of lower alpha levels
Known/Unknown Population: The known population is the population before the treatment (change) occurs. The unknown population is the known population after treatment, when we are not sure if there will be change
Sample: A sample is pulled from the known population, measured, then treated. This sample then (theoretically) becomes representative of a sample from the unknown population (which doesn't exist, because you can't treat the entire population)
Larger sample means more accurate results
Needs to be a random sample to be generalizable
Helps to ensure independent obserations
Step 1: State the hypotheses and select an alpha level
Step 2: Locate the critical region
Step 3: Compute the test statistic
Step 4: Make a decision about the null hypothesis
Assumptions
The treatment will add or subtract a constant amount from the scores
This lets the standard deviation remain the same for the known and unknown populations, so that it can be used to compute the z-score
The distribution of sample means from the population is normal
This lets us use the unit normal table to find the critical region
Effect Size: A measure of the magnitude of a treatment
Cohen's d: The difference between the known and unknown population means (typically represented as positive regardless of difference direction)