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Midterm

The Return of The Greatest Stats Sheet Ever..pdf

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Department
Commerce
Course
COMM 291
Professor
Jonathan Berkowitz
Semester
Winter

Description
T HE R ETURN OF THE G REATEST S TATS S HEET EVER BERKOWITZ –“W HAT T OU SEW HEN T ABLE” Type of Test Outcome Variable (Y) Explanatory Variable (X) Two Sample t-test Measurement Binary ( 2 categories ex. M/F) Two Sample z-test Binary (M/F) Binary (B/W) χ test Categoric (≥2 categories) Categoric(≥2 categories) Simple Linear Regression Measurement Measurement Multiple Linear Regression Measurement Many Measurements or Categoric One-Way ANOVA Measurement Categoric “t” for means, “z” for proportions Questions to ask in pursuit of an appropriate hypothesis test: 1.▯ What kind of data do you have? Measurement/ Binary/ Categoric 2.▯ What parameter is of interest? Mean/ Proportion 3.▯ How many populations/samples do you have? ▯▯ is there matching or pairing? B ERKOWITZ ON “ERROR ” Ho is true Ho is false Accept Ho Correct Type II error Reject Ho Type I error Correct Ho: Defendant is not guilty Type I error – False positive (convict an innocent person) Pr(Type I error) = α Type II error – False negative (let a guilty person go free) Pr(Type II error) = β Power = Pr(correctly rejecting Ho) = (1-β) Test-statistic affects power: power goes up as Z increases)- σ , n , ( 0 ▯▯ by increasing n you reduce the chance of getting errors. A DDITIONAL FORMULAS N OT INCLUDED IN O VERVIEW T ABLE To find a required sample size in a One-sample z-test for p with given margin of error (E): z2α p(1− p) n = 2* E2 If 95% confidence interval(generally the ͧse…):; E= Margin of Error 1 n1 n2 2 1 2 2 2 n s ns 1 2 − n ▯ σ ▯ ▯ ▯ p 1 2 ▯ α, ▯ ( ) ▯ α 2 αdf = + − df p p ± ▯where▯ ▯wher1▯ 1 α2 x z n d n df n n = − − s s df n± n α,2 df − ± +1 2± + p z df x1 x2 whet s ( x ) t2 ± ± = − ( = − ) Confidence▯Interval▯(α=1▯C)▯ d t df n df n ▯where▯ min( 1, 1) 2 0 2 + − 2 0 ▯ n ▯0 0 + 1 2 − n ▯−▯ ▯σ▯ ▯− s n ▯ − s d n ▯ 1 n1 −2 n + n ▯ − 2 1+ 212 2▯− 1( ) ▯ x x d d − − 1 1 −2 s − 2s n p p0 p0 = = = x1 xsp D 0( 1) x1 x21) D 0 z t t ( ) ( ) Test▯Statistic▯ = = = z t sp t ABLE T where▯▯ VERVIEW O 0 0 2 ▯0▯ ▯2 ▯0▯ 0 ▯ ▯ 0 ▯ ▯2 ▯=≠<> 2 ▯=0≠<> ▯0 Hypotheses▯ 0 =d 0 =▯ ≠<>▯ ▯▯▯▯ =▯≠<>▯ ▯▯ ▯▯ ▯=▯≠<>▯ ▯=▯▯=<>▯ ▯ ▯≠d ▯1 ▯ ▯ ▯1 ▯ ▯1 ▯1 ▯ =p P=<>p 0▯a▯ :0 a▯ 0▯:a 0could▯be:0)a▯ 0▯:a 0▯:a :0 a▯ :0Pa▯ H H H H H H (d H H ▯▯▯▯Or▯▯▯▯▯▯ H H ▯▯▯▯Or▯▯▯▯▯ H H ▯ ▯ = )▯ )▯ 1 2 σ ssmaller smaller ▯ ▯2med ▯10▯ σis▯known▯ ▯10▯ Assumptions▯ sbigger▯ ≠1 sig2er▯ n n(1Not▯Normality▯ ▯ ▯▯CLT▯(lar▯▯N▯rmealtd▯ent▯Popns▯srn▯femt.ed σ (if▯σ ▯Normality▯(small▯n)▯ ▯ ▯ ▯ ▯d −1 2 1 2 s ▯ ▯ ▯ ▯ s ▯ ▯ ▯ )▯ ▯ 0 Test▯ Ontee▯ss▯orple▯Zt▯tesm▯foMe▯attteet▯▯pati▯sat▯ver▯sion)▯ti9Tewt▯tfs▯m▯p▯le▯ooled▯ne▯▯tamtpf▯ ▯ ▯ ▯ ▯ ▯ ▯ ) ) b b0 ( ( SE SE version▯above▯ × × p ▯▯▯▯ − − ▯▯▯ , 2 α,2 t t ± ±0 b b 1 0: same▯as▯pooled Note▯further▯calc’s▯listed▯on▯last▯page… Confidence▯Interval▯(α=1▯C)▯ CI for β CI for β ----------------------------------------- ▯ 2 ) ) 0 0 0 b1 ( ) ij − ( − ( −ij E ij b0 SE b1 SE ) O E 0---- = ▯ + ( ) t t ▯ − − p −p 1D 0 − ∑ all cells------β ------β1-----F= MSM/MSE F=MSM/MSE▯ ( ( n ) 1= n Where▯df=(r▯1)(c▯1)▯ F= MSM/MSE Where▯df=DFE=N▯p▯▯ Test▯Statistp1▯ p1 p2 p2 Test-stat: Test-stat:
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