effectSizeCI function

effectSizeCI

95

The procedure is based on finding the upper and lower 0.025 bounds for the related t-variable. The t-variable needs to be adjusted for bias by multiplying by c The upper and lower bounds on the t-variable are then used to calculate to upper and lower bounds on the repeated measures effect size (d_RM) by multiplying the upper and lower bound of the t-variable by sqrt((n1+n2)/(2*(n1*n2))). Upper and lower bounds on the equivalent independent groups effect size (d_IG) are found by multiplying the upper and lower bounds on d_RM by sqrt(1-r).

effectSizeCI(
  expDesign,
  t,
  n1,
  n2,
  r = 0,
  epsilon = 1e-10,
  maxsteps = 1000,
  stepsize = 3
)

Arguments

• expDesign: Experimental design: 1) crossover repeated measures ('CrossOverRM'), 2) before-after repeated measures (expDesign=='BeforeAfterRM'), 3) independent groups ('IG)
• t: t-statistics (t must be less than or equal to 37.62, the limit from the R function documentation)
• n1: The number of observations in sequence group 1 (expDesign=='CrossOverRM'), the number of observations in group 1 (expDesign=='IG'), or the total number of observations (expDesign=='BeforeAfterRM')
• n2: The number of observations in sequence group 2 (expDesign=='CrossOverRM') or the number of observations in group 2 (expDesign=='IG')
• r: The correlation between outcomes for individual subject (the within subject correlation)
• epsilon: The precision of the iterative procedure
• maxsteps: The maximum number of steps of the iterative procedure (the procedure terminates at maxsteps or earlier if CI with enough precision have been calculated)
• stepsize: The size of steps (influences the convergence of the calculations, i.e., the number of steps required to obtain the final result of precision defined by the epsilon)

Returns

A list of Confidence Intervals for: t-statistic (t_LB and t_UB), repeated-measures effect size d_RM (d_RM_LB, d_RM_UB), independent groups effect size (d_IG_LB, d_IG_UB)

Examples

effectSizeCI(expDesign = "CrossOverRM", t = 14.4, n1 = 15, n2 = 15, r = 0.6401)
effectSizeCI(expDesign = "BeforeAfterRM", t = 14.16536, n1 = 15, n2 = 0, r = 0.6146771)
effectSizeCI(expDesign = "IG", t = -6.344175, n1 = 15, n2 = 15)
effectSizeCI(expDesign = "CrossOverRM", t = 0.5581, n1 = 6, n2 = 6, r = 0.36135)
effectSizeCI(expDesign = "CrossOverRM", r = 0.855, t = 4.33, n1 = 7, n2 = 6)

Author(s)

Lech Madeyski and Barbara Kitchenham