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Hypothesis Testing, State a Hypothesis, Assumptions, Logic of Hypothesis…
Hypothesis Testing
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Power
Only two possible outcomes IF test has an effect:
- fail to reject null hypothesis (Type II error)
- Reject null hypotheses
When effect is measured, probability for 1 of these = 100%
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Null Hypothesis
Sample Means close to 0 effect, M=μ
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Assumptions
All participants are randomly selected,
All observations are independent, no consistent predictable relationship between one observation and the next
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σ, pop. standard deviation is the same after treatment (for unknown) as pre-treatment(known), effect of treatment is a constant +/- to every score
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hypothesis is directional, specifying an increase or decrease in the effect
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- Compute z-score for alternative distribution to find power
- Locate Critical Regions and Compare M(critical)
Critical region in null distribution, overlaps with alternative distribution at M(critical)- shows how often a sample will reject null hypothesis
- sketch distributions for null and alternative hypotheses next to each other (directions for hypothesis suggesting increase. For decrease, reverse distribution locations
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Greater sample size will reduce the overlap (more of alt distribution above Mcrit) - increasing power
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Greater effect (average score difference between null and alt), will also reduce overlap and increase power
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when a null hypothesis is rejected, but is actually true (seemed like there was an effect to treatment, but actually there wasn't)
Type I Error (Alpha)
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the lower the alpha level, the less risk of error, but more evidence required for hypothesis test
when a researcher FAILS to reject the null hypothesis when they should have. (Treatment had an effect, but researchers failed to detect it)
Type II Error (Beta)
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impossible to determine exact probability, but represented by β
statistical procedure using sample data to draw inferences about a population (unmeasureable) of interest, combining Z-score, probability, and distribution of sample means
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H₀ = ZERO EFFECT or Independent Variable (treatment) has no change or effect on Dependent Variable (scores)
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level of significance, α, small probability value (.05, .01, .001) used to identify low-probability samples, and separate them
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measures the absolute magnitude of treatment effect, separate from size of sample
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