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disc4 - Notes on week 4 material Intro to hypothesis...

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Notes on week 4 material
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Intro to hypothesis testing Logic of hypothesis testing Testing against the null hypothesis Significance level Region of rejection Critical values – Tails/directionality How to do the z-test Decision making Kinds of errors
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Logic All tests compare means How different are the means? They should vary a little by chance • Z-test: – Compare sample mean to population mean – Factor out chance difference – Are the means still different?
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Logic We always test against the null hypothesis Null = no effect of our experimental manipulation (IV) Notation: H 0 Not intuitive! Hypothesizes that sample mean and population mean are not different To visualize: plot distribution of means based on null hypothesis
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Logic μ σ X This is the distribution of means under the null hypothesis Where does the sample mean fall in this distribution?
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So We want to know where the sample mean falls relative to the population mean We want to know if they are different enough to be considered statistically different Remember that some variation is just due to chance Samples will always be different than populations This is going to depend on sample size N affects variability
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The point Statistical hypothesis testing lets us answer this question: How likely is it that the sample mean came from this population ? If not very likely, we assume the difference is due to our manipulation Not likely = <5% or <1%
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Logic μ Remember the proportions of area under the distribution 34%
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Logic μ And confidence intervals: Under H 0 : 95% of the time the sample mean will fall within 1.96 standard errors of μ z = -1.96 z = 1.96
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Difference between means This is why, in some tests, we use a critical value of z=1.96 Here is another way to think about it:
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Difference between means How big must this be to be significant?
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