Hypothesis Test
A statistical method that uses sample data to evaluate a hypothesis about a population
Goal of Hypothesis Testing
To rule out sampling error as a reason for the results of a research study
Sample and Population difference
-Explained by sampling error (no treatment effect)
-Too large to be explained by sampling error (treatment effect)
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Hypothesis Test Assumptions
1.)These are the characteristics we want the population we sample from to have
2.)Help us make accurate inferences
3.)Always check test’s assumptions
Assumptions w/ Z-statistics
1.)Participants are randomly sampled from the population
2.)Sample values are independent observations
3.)Standard deviation is constant
4.)Sampling distribution is normally distributed
5.)Scale dependent/nominal independent variable
Alpha level
-Establishes a cut off for making a decision for a null hypothesis
-Determines/Minimize Type 1 Error Risk
-0.05 is most used, 0.01, 0.001
Hypothesis Test Steps
1.)State hypothesis about population
2.)Set criteria for decision
3.)Calculate sample statistics
4.)Reject/fail to reject null hypothesis
When the Alpha Level is lowered….?
The hypothesis test demands more evidence from research results
Alpha Levels tend to have….?
Small probability values
Critical Region
-Outcomes are very unlikely to occur if the null hypothesis is true.
-They are defined by sample means that are unlikely to be obtained if the treatment has no effect.
Critical Values
Values that define the critical region
Type 1 Errors
Incorrectly rejecting a true null hypothesis (false positive) You reject even though it’s true
Type 2 Errors
Incorrectly failing to reject the null hypothesis when it’s actually false (miss) You don’t reject when you’re supposed to
One-tailed Tests/Directional Tests
-Critical region in one tail of the distribution
-a=0.05 we put all 5% in one tail (upper or lower)
Two-tailed Tests/Non-Directional Tests
-Critical region divided between two tails of the distribution
-a=0.05 we put 2.5% in each tail (more conservative reduces power in a particular tail)
Two types of Non Errors
-Correct non rejection: fail to reject H0 when true
-Correct rejection: rejecting H0 when its false
Point Estimates
Single-number summary statistic
from a sample that is used as an estimate of the population parameter
Interval Estimates
Include the population mean a certain percentage of the time if we sample from the same
population repeatedly
95% Confidence interval
-We’re 95% confident the range values includes the true population mean.
Benefits of using confidence intervals
-Give a range of values for a pop parameter
-Same information as hypo test, but additional info
Effect Size
It shows how big or strong a difference/relationship is, no matter how large the sample is.
Cohen’s D
mean difference/standard deviation (measures effect size)
Cohen’s D Interpretation
-0.2= small effect
-0.5= medium effect
-0.8= large effect
Statistical Power
The likelihood that we
will reject the null hypothesis, given its false. (to find; use mcrit, power equation, then find the number on unit table)
