University:
York University
Course:
AP/ADMS 2320 | Business Statistics
Academic year:

2022
Views:

310

Pages:

3
Author:

Niklas

Scenario 1= the means are very different Scenario 2= the means are slightly different Scenario 3= the means are the same The spreading out of data helps us find the differing means. spreading out is measured by the sample variance value Mean square between (MSB) ① find mean of sample means = overall sample mean (x̄) ② find sums of squares between treatments (SSB) SSB = (x̄₁ - x̄)² + (x̄₂ - x̄)² + (x̄₃ - x̄)² Mean of each sample then find MSB = SSB / (3-1) mean of the means a low MSB means the means are very close Using the sample variances (s1, s2, s3) Sum of square due to error: SSE = s1^2 + s2^2 + s3^2 mean square error: MSE = SSE / (N-3) -> no. of groups hypothesis testing uses F distribution F(d1, d2) -> d1 and d2 are degrees of freedom F = MSB / MSE anova table Source of variation | SS | df | MS | F | F critical between groups | SSB | g-1 | MSB | MSB/MSE | Fc error | SSE | N-g | MSE | | total | SST | N-1 | | | total sum of square (SST) -> sum of square difference between all observation and overall mean SST=(x1-x̄)²+(x2-x̄)²+(x3-x̄)²+... relationships: dfSST = dfsso + dfsse -> N-1=(g-1) + (N-g) SST= SSB+ SSE e.g. don't know SSB or g, but do know SST=168252, SSE=124740, N= 63, dfsse=60. How to calculate SSB and g: 168252= SSB + 124740 dfSSB= dfSST-dfsse = g-1 = (N-1)-(N-g) = 62-60=2 dfssB=3 SSB=SST-SSE = 168252-124740=43512