Table 6: Median number of iterations needed for Newton’s unidimensional method to converge to four decimal places. In parenthesis is the range of iterations for the 200 simulated contingency tables.

Size of contingency table
True 𝜙 2 × 22 × 32 × 42 × 53 × 33 × 43 × 54 × 44 × 55 × 5

0.002222222222
(1–7)(1–6)(1–9)(1–4)(1–3)(1–4)(1–3)(2-3)(1–3)(1–3)
0.013333333333
(2–14)(2–30)(2–95)(2–14)(2–5)(2-3)(2-3)(2-3)(2-3)(2-3)
0.054444544455
(3–13)(1–7)(2–6)(4–6)(4–6)(4-5)(4-5)(4-5)(4-5)(4–6)
0.105555566667
(3–29)(4–7)(5–8)(5–8)(4–6)(5–7)(5–7)(5–7)(6–8)(6–10)
0.207778889101113
(5–13)(7–12)(7–11)(7–11)(7–10)(7–11)(7–15)(8–13)(9–17)(8–21)
0.3099910101213141723
(3–23)(9–219)(9–128)(9–15)(9–15)(9–17)(10–22)(10–19)(12–27)(15–35)
0.4011111213131619212839
(7–25)(6–16)(11–25)(11–23)(11–22)(12–26)(13–33)(14–47)(16–49)(20–65)
0.5013141516.5172127304468
(4–261)(12–56)(13–28)(14–103)(13–30)(6–47)(18–53)(18–57)(23–80)(24–110)
0.60151618212128374266113
(11–260)(15–32)(16–33)(17–66)(16–47)(18–61)(21–81)(23–98)(30–139)(41–261)
0.701719232827375364101211
(14–737)(17–39)(19–52)(21–67)(19–43)(20–71)(26–150)(30–126)(25–195)(59–560)
0.802024283434497589170359
(8–407)(20–40)(23–58)(25–64)(22–49)(24–140)(32–160)(38–188)(61–352)(102–1026)
0.90242934424367107.5128.5255605
(9–39)(24–46)(27–716)(29–114)(26–101)(32–116)(39–207)(58–332)(62–653)(147–2129)
1.00283242555390145.51723951028
(16–987)(27–83)(17–101)(37–286)(31–122)(42–281)(67–349)(66–480)(99–1173)(3–3243)
1.1032395268.569116211275656.51875.5
(29–863)(4–1983)(38–187)(48–285)(39–181)(45–383)(57–580)(68–590)(151–2370)(8–6656)
1.203647648888157.52853929992725
(28–208)(36–94)(44–180)(51–201)(46–210)(69–579)(94–889)(129–907)(199–3120)(589–12917)
1.30425577109.5109207420.55561571.54730
(29–1239)(33–267)(53–275)(58–265)(52–222)(69–441)(135–1104)(154–1606)(260–4833)(11–23803)
1.40486494143.5135.5284562822.522496224
(23–2288)(45–2781)(58–262)(78–372)(63–431)(88–557)(129–1675)(187–3370)(24–7041)(3–25352)
1.505675114177170369.582712333102.59769
(38–92)(57–216)(74–302)(104–914)(72–624)(103–1071)(189–2641)(305–4608)(22–11773)(9–34759)