Introductory Applied Statistics for Engineers
Introductory Applied Statistics for Engineers STAT 324
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Mrs. Triston Collier
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This 4 page Class Notes was uploaded by Mrs. Triston Collier on Thursday September 17, 2015. The Class Notes belongs to STAT 324 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 29 views. For similar materials see /class/205089/stat-324-university-of-wisconsin-madison in Statistics at University of Wisconsin - Madison.
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Date Created: 09/17/15
STAT 324 Discussion 5 TBS Bleng Song O ice 1270 MSC Phone 262 3230 Email songm statwiscedu O ice hour 1100 1200 AM and 100 200 PM Tue My Website wwwstatwiscedusongm 1 Examples 11 Example 1 Perform a simulation study of samples of size 3 from a normal distribution with mean 50 and standard deviation 10 For each sample store the difference between the observed and theoretical means divided by the theoretical standard error of the mean nsamplelt 3 sample size Nsimlt 2000O Number of simulation mlt 50 sd1O theolt replicateNsimmeanrnormnsamplemsd msdsqrtnsample Dens ity plot librarylattice densityplot theo plot pointFALSE QQmathplot qqmath theof valseqfrom0005 toO995 by0005 typec g p What will you find Now we change the sample size to 30 nsamplelt 30 theollt replicate Nsim meanrnorm nsample m sd m sdsqrt nsample densityplot theol plot pointFALSE qqmath theol f valseqfrom0005to0995by0005 typec g p 12 Example 2 Use the observed standard deviation from the sample to calculate the standard error of the mean nsamplelt 3 emplt replicateNsimsamplt rnormnsamplemsdmeansamp msdsampsqrtnsample densityplot empplotpointF qqmath empfvalseqfrom0005to0995by0005typec g p Is it normal Check t distribution qqmath empfvalseqfrom0005to0995by0005typec g p distributionfunctionp qtpdfnsample 1 Now we Change the sample size to 30 nsamplelt 30 emplt replicateNsimsamplt rnormnsamplemsdmeansamp msdsampsqrtnsample densityplot empplotpointF qqmath empfvalseqfrom0005to0995by0005typec g p Is it normal Check t distribution qqmath empfvalseqfrom0005to0995by0005typec g p distributionfunctionp qtpdfnsample 1 STAT 324 Discussion 9 TA Jiale Xu Webpage wwwstatwisceduxujialestat324 1 ANOVA 11 One Way ANOVA The model yij M ai 61739 617 N N07 02 12Ij12 DecomPOSitioni yij y i 91739 i 22 Zr yij 2T yij where y Zlgfm Relation among Sum Squares I m I m I m Z 91739 i y2 Z i y2 Z i 902 i1 j1 i1 j1 i1 j1 I m SST Z y 2 i1 j1 I m I SSE Z 2 7 y2 2 MW 7 y2 i1 j1 i1 I m 8va SSE 22m 7 102 i1 j1 Test the Null Hypothese The means in different groups are same Mathematically a1a2a10 ANOVA Table Source df SS MS F value p value Group I l SSB MSbSSBI 1 MSbMSe PFgtMSbMSe Residerror n SSE MSeSSE n I Total n l SST n 211 m Total number of observation Example PlantGrowth data set librarylattice librarylSwR strPlantGrowth fit1lt aovweight groupdataPlantGrowth summaryfit1 Df Sum Sq Mean Sq F value PrgtF group 2 37663 18832 48461 001591 Residuals 27 104921 03886 VVVVV attachPlantGrowth meanweight y1lt weight110 y2lt weight1120 y3lt weight2130 SSB 10meany1 meanweight 2meany2 meanweight 2meany3 meanweight 2 yidotlt repcmeany1meany2meany3c101010 yidot SSE sumy yidot 2 SST Sumymeanweight 2 1 1425843 gt 1 pf48461227 1 001590982 gt TukeyHSDfit1 VVVVVVVVVVVVV 12 Two Way ANOVA There are two factors Many time7 one is block factor7 one is treatment factor We are only interest in the difference of the different treatments Modelno replication yijMOti8j6ij7 I7j17277J Decomposition wjyx7y04jiyuluiyriyjyj Relation among sum of square SST SS7 5 SSE Suppose a is block effect We are interested in B The test is 61 g 8J 0 ANOVA Table Source df SS MS F p value block I1 SSb SSbIl MSbMSe PFgtMSbMSe treatment J l SSt SSt J l MStMSe P FgtMSbMSe residual 1 1 J l SSe SSeI 1J 1
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