APPENDIX A Tables and Formulas 747 Ch. 14: Control Charts R chart: Plot sample ranges UCL: D4R Centerline: R LCL: D3R x chart: Plot sample means UCL: x + A2R Centerline: x LCL: x - A2R p chart: Plot sample proportions UCL: p + 3 Bp q n Centerline: p LCL: p - 3 Bp q n Ch. 13: Nonparametric Tests z = 1x + 0.52 - 1n>22 1 n 2 Sign test for n 7 25 z = T - n 1n + 12>4 Bn 1n + 1212n + 12 24 Formulas by Mario F. Triola Copyright 2022 Pearson Education, Inc. Wilcoxon signed ranks (matched pairs and n 7 30) z = R - mR sR = R - n11n1 + n2 + 12 2 Bn1n21n1 + n2 + 12 12 Wilcoxon rank-sum (two independent samples) H = 12 N1N + 12 a R2 1 n1 + R2 2 n2 + g+ R2 k nk b - 31N + 12 Kruskal-Wallis (chi-square df = k - 1) rs = 1 - 6Σd2 n1n2 - 12 Rank correlation acritical values for n 7 30: { z 1 n - 1b z = G - mG sG = G - a 2n1n2 n1 + n2 + 1b B12n1n2212n1n2 - n1 - n22 1n1 + n22 21n 1 + n2 - 12 Runs test for n 7 20 Control Chart Constants Subgroup Size n D3 D4 A2 2 0.000 3.267 1.880 3 0.000 2.574 1.023 4 0.000 2.282 0.729 5 0.000 2.114 0.577 6 0.000 2.004 0.483 7 0.076 1.924 0.419 Inferences about M: choosing between t and normal distributions t distribution: s not known and normally distributed population or s not known and n 7 30 Normal distribution: s known and normally distributed population or s known and n 7 30 Nonparametric method or bootstrapping: Population not normally distributed and n … 30
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