ISDS 361B Test 1 Review

March 27, 2018 | Author: Augustus Chan | Category: Student's T Test, P Value, Standard Error, Statistical Hypothesis Testing, Errors And Residuals


Comments



Description

ISDS 361B REVIEW FOR EXAM #1I. Hypothesis Tests/Confidence Intervals of 1, 2 and More than Two Means Basic Concepts • • • “Can you conclude…HA?” -- Yes if p-value < α = .05 Requirement (one of the following): o Must be sampling from approximately normal distributions or o Must take large samples Begin by getting z or t-value o z or t is the number of standard errors the point estimate is from the hypothesized value – that is: Confidence Interval: x ± (z α/2 or t α/2, n -1 ) * (Standard Error) Then – σ known (given) – use z; σ unknown (not given) – use t (Point Estimate) - (Hypothesi zed Value) Standard Error • • Tests of One Population Mean • • • Point estimate = x Standard Error = σ/ n if σ known or s/ n if σ is unknown P-values By hand > Tests < Tests ≠ Tests Area above z or t value Area below z or t value 2* (Area in the tail) Excel z-test p-value/interval 1-NORMSDIST(z) NORMSDIST(z) Assuming z > 0: 2*(1-NORMSDIST(z)) Assuming z < 0: 2*NORMSDIST(z) x = AVERAGE(.. CONFIDENCE ..) (α, σ, n) zα/2 * (standard error) = Excel t-test p-value/interval Assuming t > 0: TDIST(t,df,1) Assuming t < 0: TDIST(-t,df,1) Assuming t > 0: TDIST(t,df,2) Assuming t < 0: TDIST(-t,df,2) Go to Descriptive Statistics x =M ean t α/2, n -1 = Confidence Interval x ±(z α/2 or t (S tandard α n -1 ) * /2, E r) rro Confidence Level DF)* SQRT(Var/Obs1+Var2/Obs2) (Mean1 – Mean2) ± TINV(α.Do z-test/z-interval 3. Determine if data is paired (Paired if problem is set up with something in common between each entry from one sample and a corresponding entry in the second sample) If YES -.DF)* SQRT(Pooled Var*(1/Obs1+1/Obs2)) • 2.Tests of the Differences Between 2 Population Means How to proceed: 1.Do t-test/t-interval with equal variances Standard Error Excel p-value t-test Paired 2 Sample for Means z-test 2 Sample for Means t-test 2 Sample Assuming Unequal Variances t-test 2 Sample Assuming Equal Variances Excel Confidence Interval BOLD/ITALIC from output 1.Create column of differences 2. Descriptive Statistics (Mean)±(Confidence Level) (Mean1 – Mean2) ± NORMSINV(1-α/2)* SQRT(Var/Obs1+Var2/Obs2) (Mean1 – Mean2) ± TINV(α. Can you conclude variances differ? (F-test – low p-value  σ’s differ. p-value for F-test = 2*(one-tail p-value printed by Excel)) If YES – Do t-test/t-interval with unequal variances If NO -.Paired Difference Test/Confidence Interval Do you know the variances? (Variances or standard deviations given) If YES -. • • • Experimental Point Design Estimate Paired Difference Known Variances Unknown ≠ Variances xD x1 − x 2 sD nD 2 σ1 σ 2 + 2 n1 n 2 x1 − x 2 2 s1 s2 + 2 n1 n 2 Unknown = Variances x1 − x 2 1 1  s  +  n   1 n2  2 p . μi and μj differ if | x i .DFE)*SQRT(MSE*(1/n1+1/n2) o Comparing all pairs of k different means Any pair of means. proceed to the next steps below Can we conclude Factor A alone affects changes in mean values? -p-value of F-test for MSA/MSE Can we conclude Factor B alone affects changes in mean values? -p-value of F-test for MSB/MSE • Excel: Two Factor With Replication Must include one row and one column of labels Rows Per Sample = number of entries for each two factor treatment 1 1  MSE  +  n   1 n 2  where c = k(k-1)/2 1 1  MSE  +  n   1 n2    • • • • • .μ2: | x1 . μ1 and μ2 differ if | x1 .DFE EXCEL LSD = TINV(α.DFE)*SQRT(MSE*(1/n1+1/n2) o Confidence interval for μ1 .DFE EXCEL LSDEW = TINV(α/c.Tests for Differences of More Than 2 Means • Must Also Assume Variances are Equal How to proceed: Determine if there is: • One Factor With No Blocks  Can we conclude Treatment means vary? -.x 2 | ± LSD One Factor With Blocks (only one entry for each factor/block pair)  Can we conclude Treatment Means vary? -.x 2 | > LSD LSD = tα/2.x j | > LSDEW =   tα/2c.p-value for F-test of MSB/MSE • Excel: Two Factor Without Replication Include one row and one column of labels and check Labels Two Factor (More than one entry for each combination of the two factors)  Can we conclude the factors interact to affect changes in mean values? p-value of F-test for MSI/MSE – IF p-value low – conclude INTERACTION and STOP – if NOT.p-value for F-test of MSTr/MSE • Excel: Single Factor ANOVA Include one row labels and check Labels • Which means differ? o Comparing just 2 means  Two means.p-value for F-test of MSTr/MSE Can we conclude Block Means vary? -. o Ft+k = (Cell containing b0) + (t+k)*(Cell containing b1) o o o o o • Ft+k+1 = (Cell containing b0) + (t+k+1)*(Cell containing b1) + (Cell containing S1) Ft+k+2 = (Cell containing b0) + (t+k+2)*(Cell containing b1) + (Cell containing S2) …. T3 = γ*(L3-L2)+(1-γ)*T2 o Drag down L3. F3 = α*y2 + (1. Ft+2k = (Cell containing b0) + (t+2k)*(Cell containing b1) Etc. F3 = L2+T2.Then MAD = AVERAGE(these values) • MSE: Square Error =(y-F)^2 -.. T2 = y2-y1.drag down to Ft+1 • Exponential smoothing: F2 = y1. Decomposition – See PowerPoint PERFORMANCE MEASURES o Do for all periods that have both a forecast and a time series value • MAD: Abs Dev = ABS(y – F) -. L3 = α*y3 + (1-α)*F3.drag down to Ft+1 • All approaches: Ft+k = Ft+1 LINEAR TREND ONLY MODELS • Regression: F1 = b0+b1*(cell denoting period = 1) – drag down to Ft+1 and beyond • Holts: L2 = y2.Then MSE = AVERAGE(these values) ..α)*F2 -. o Ft+2 = (cell with Ft+1) + (absolute reference to cell with Tt) o Drag cell containing Ft+2 down to Ft+3 and beyond LINEAR TREND AND SEASONAL MODELS (with k seasons) • Regression Approach o Add k-1 dummy variables and create columns 0’s and 1’s to denote season o REGRESSION on period and dummy variables o Ft+1 = (Cell containing b0) + (t+1)*(Cell containing b1) + (Cell containing S1) o Ft+2 = (Cell containing b0) + (t+2)*(Cell containing b1) + (Cell containing S2) o …. and F3 down to period t o Ft+1 = Lt + Tt.FORECASTING • • o o Do a scatterplot to determine if seasonality or cyclical effects exist To determine long term trend: Do Regression High p-value for β1  Stationary Model Low p-value for β1  Model with Linear Trend The following assumes there are n time series values: STATIONARY MODELS • Last period: F2 = y1 – drag down to Ft+1 • Moving average: Fn+1 = AVERAGE(highlight first n y’s) – drag down to Ft+1 • Weighted Moving Average: Fn+1 = wn*yn + wn-1*yn-1 … + w1y1 -. T3. • For either method: Choose the approach with lowest value .
Copyright © 2024 DOKUMEN.SITE Inc.