321_09_slides3

# 321_09_slides3 - Week 2 Review of Econ 221 Econ 321...

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Week 2 Review of Econ 221 Econ 321 Introduction to Econometrics Econ 321-Stéphanie Lluis 1 Wooldridge: appendices B & C + chapters 1

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Additional Tools and Issues in Statistical Analysis Hypothesis Testing Confidence Intervals Covariance/Correlation Simple regression Causality Econ 321-Stéphanie Lluis 2
Hypothesis Testing Step 1 State hypotheses What are our beliefs or our predictions? We make what we do not believe our null hypothesis H 0 μ = μ 0 We lay out what we believe as our alternative hypothesis H A : μ < μ 0 or H A : μ > μ 0 or H A : µ ≠ µ 0 Will determine whether one-tail or 2-tail test

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Hypothesis Testing Step 2 What is the statistic of the test ? Are you testing a mean or a relationship between two variables? Sample mean Y or OLS estimator beta hat Under H 0 T= Is the variance of the population 2 known? This will also determine which distribution to use: z (standard normal) or t n-1 student distribution) Compute the value of the statistic (based on the sample info) denoted T when σ is unknown and use S Y standard deviation of Y σ/(n ½ )= standard error
Hypothesis Testing Step 3 Conclude Always in terms of reject or cannot reject H 0 Choose a level of significance Level of significance α = P(Reject H 0 | H 0 true) Find critical values c for 1% or 5% level tests For α =5% and a one-tailed test P(T >c .05 | H 0 )=.05 For α =5% and a two-tailed test P(|T|>c .025 | H 0 )=.05 P(-c 025 < T ≤ c 025 | H 0 ) Uses stat called T here (assumes σ unknown)

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One Tailed Test H A “Greater than” 0 H A “Less than” 0 c α -c α Example based on the t n-1 distribution with n> 120 obs: Reject H 0 at 5% level if Reject H0 at 5% level if t value > 1.645=c 5% t value < -1.645=-c 5% t value Reject H 0 at the α% level And c 1% = 2.326
Two Tailed Test H A “Different from” 0 P(t value ≤ -t α/2 )= α/2 -t α/2 t α/2 P(t vaue > t α/2 )= α/2 Reject at α% if t value > t α/2 or t value < -t α/2 P(-c α/2 < T ≤ c α/2 | H0)= α %

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Hypothesis Testing Step 3 Conclude based on the p-value instead of choosing a significance level p-value: what is the largest significance level (probability) at which we reject H 0 In this case, we don’t fix the rejection area at 5% or 1%, we calculate it based on the t value and compare the probability with the 5% or 1% level test
One Tailed Test and p-value H A “Greater than” 0 H A “Less than” 0 P(T > t value )=p t value P(T ≤ -t value )=p -t value Reject H 0 at 10% level if p < 0.10 Reject H0 at 5% level if p < 0.05 Reject H0 at 1% level if p < 0.01

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Two Tailed Test and p-value H A “Different from” 0 P(T ≤ -t value ) -t value P( | T | > t value ) = P(T ≤ -t value ) + P(T> t value ) =2*P(T > t value ) t value P(T > t value )