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Introduction to Hypothesis Testing - Coggle Diagram
Introduction to Hypothesis Testing
The Logic Of Hypothesis Testing
The Logic of Hypothesis Testing
Hypothesis testing is a statistical method that uses sample data to evaluate a hypothesis about a population
Typically used in the context of a research study
We state a hypothesis about a population. Usually the hypothesis concerns the value of a population parameter
ex: we hypothesize that an American adults gain an average of (u) = 7 lbs, between Thanksgiving and New Year's Day
Next we obtain a random sample from the population
ex: select a sample of n=200 American adults
Before we select a sample, we use the hypothesis to describe what values we should expect for the sample mean, if the hypothesis is really true. Ex: If we predict the average weight gain to be 7lbs, then we would expect our sample to have a mean around 7 lbs
the sample should be similar to population, but expect a certain amount of error
We compare the obtained sample data with the prediction made from the hypothesis.
If the sample mean is consistent with our prediction, we conclude the hypothesis is reasonable. If there's a big discrepnancy between the data and prediction, we decide the hypothesis is probably wrong.
The Elements of a Hypothesis Test
The Unknown Population
The unknown population is the focus of the research question
The researcher begins with a known population- individuals as they exist before treatment
The Sample in the Research Study
The goal of the hypothesis test is to determine whether the treatment has any affect on the individuals in the population
The original population (before treatment) and the unknown population (after treatment)
The unknown population is actually the hypothetical (the treatment is never administered to the entire population)
The Four Steps of a Hypothesis Test
State the hypothesis... make predictions about the population parameters
Set the criteria for a decision
null hypothesis: states the treatment has no effect, no difference, or no relationship
alternative hypothesis: states the treatment has an effect, a difference, or a relationship
Collect data and compute sample statistics
z= sample mean-hypothesized population mean/standard error between M and (u)
Make a decision about the null hypothesis
Closer Look at z-Score Statistic
test statistic: indicates that the sample data are converted into a single, specific statistic that's used to test hypotheses
Uncertainty and Errors in Hypothesis Testing
Type I Errors
Occurs when a researcher rejects a null hypothesis that's actually true
Means the researcher concludes there's evidence for a treatment effect, when in fact the treatment has no effect
The problem isn't with the researcher, it's that the info from the sample is misleading
Usually occurs when a researcher unknowingly obtains an extreme or nonrepresentative sample
The alpha level hypothesis test is the probability that the test will lead to a type I error
Type II Errors
Occurs when a researcher fails to reject a null hypothesis that is in fact false
Hypothesis test has failed to detect a real treatment effect
Means the research data did not show the results the researcher had hoped to obtain
Impossible to determine a single exact probability for error
Selecting Alpha Level
Alpha helps determine the boundaries for the critical region by defining the concept of "very unlikely" outcomes
Alpha determines the probability of a Type 1 error
Directional (One-Tailed) Hypothesis Tests
One-trailed test: the statistical hypothesis specify either an increase or decrease in the population mean... make a statement about the direction of the effect
H0: Tips are not increased (treatment doesn't work)
H1: Tips are increased (the treatment works as predicted
Critical region is defined by sample outcomes that are very unlikely to occur if the null hypothesis is true
One tailed test requires 2 changes in the step-by-step hypothesis testing procedure
the directional prediction is incorporated into the statement of the hypotheses
the critical region is located entirely in one tail of the distribution
Comparison of One-Tails vs. Two-Tailed Tests
A one-tailed test allows you to reject the null hypothesis when the difference between the sample and the population is relatively small, provided the difference is in the specified direction
A two-tailed test, on the other hand, requires a relatively large difference independent of direction. This point is illustrated in the following example.
Concerns about Hypothesis Testing: Measuring Effect Size
Statistically significant treatment effect doesn't necessarily indicate a substantially large treatment effect
A measure of effect size is intended to provide a measurement of the absolute magnitude of a treatment effect, independent of the size of samples being used
Statistical Power
The power of a statistical test is the probability that the test will correctly reject a false null hypothesis. That is, power is the probability that the test will identify a treatment effect if one really exists.
