calculateIccSampleSize: Function to calculate sample size required for studies where...

In ICC.Sample.Size: Calculation of Sample Size and Power for ICC

Description

Calculates a sample size for given values of p, the null hypothesis p0, number of ratings (k), desired power and alpha. Can also generate sample sizes for different values of p, p0 or combinations of p and p0 from 0-1.

Usage

calculateIccSampleSize(p,p0,k,alpha,tails,power,by,step)

Arguments

p	The hypothesized value of p. Hypothesized based on previous data, or experience. If missing default is 0.
p0	The null hypothesis value of p. If missing default is 0.
k	The number of ratings of each subject. If missing default is 2.
alpha	The desired alpha for hypothesis testing. If missing default is 0.05.
tails	The number of trails for hypothesis test. If missing default is 2.
power	The desired power of the hypothesis test. If missing default is 0.80.
by	Can be used to calculate sample sizes for varied p and/or p0. If by="" Only the sample size for the specified p and p0 will be calculated. If by="p" Calculates sample sizes for all p starting from 0, increasing by step until 1. If by="p0" Calculates sample sizes for all p0 starting from 0, increasing by step until 1. If by="both" Calculates sample sizes for all combinations of p and p0 starting each from 0, increasing by step until 1. Row labels are p and column labels are p0. If missing, default is "".
step	When the function varies p or p0 it calculates sample size for 0, then for 0+step*(i-1) where i is the number of repeats, until p=1

Value

Returns a list with the following items:

resultdf	Data frame with columns N, p, p0, k, alpha, tails, and power.
sampleSize	For by="p" or by="p0" is a data frame with columns of p or p0 respectively and N.
nDataframe	For by="both" is a data frame with rows defined by p and columns defined by p0 representing values of N for each combination.

Author(s)

Alasdair Rathbone, Saurabh Shaw, Dinesh Kumbhare

Maintainer: Alasdair Rathbone <[e-mail]>

References

Zou, G. Y. (2012). Sample size formulas for estimating intraclass correlation coefficients with precision and assurance. Statistics in medicine, 31(29), 3972-3981.

Examples

## Calculate Sample Size for p=0.80, p0=0.60, two ratings, alpha=0.05 with two tails and power=0.80.
calculateIccSampleSize(p=0.80,p0=0.60,k=2,alpha=0.05,tails=2,power=0.80)
## Calculate Sample Size as above, but test varying p from 0 to 1 by steps of 0.05
calculateIccSampleSize(p=0.80,p0=0.60,k=2,alpha=0.05,tails=2,power=0.80,by="p",step=0.05)
## Calculate Sample Size as above, but test varying p0 from 0 to 1 by steps of 0.05
calculateIccSampleSize(p=0.80,p0=0.60,k=2,alpha=0.05,tails=2,power=0.80,by="p0",step=0.05)
## Calculate Sample Size as above, but test varying both p and p0 from 0 to 1 by steps of 0.05
calculateIccSampleSize(p=0.80,p0=0.60,k=2,alpha=0.05,tails=2,power=0.80,by="both",step=0.05)

Example output

[[1]]
   N   p  p0 k alpha tails power
1 49 0.8 0.6 2  0.05     2   0.8

[[1]]
   N   p  p0 k alpha tails power
1 49 0.8 0.6 2  0.05     2   0.8

[[2]]
      p    N
1  0.00   18
2  0.05   20
3  0.10   24
4  0.15   28
5  0.20   34
6  0.25   42
7  0.30   55
8  0.35   75
9  0.40  110
10 0.45  182
11 0.50  381
12 0.55 1406
13 0.60  Inf
14 0.65 1164
15 0.70  260
16 0.75  102
17 0.80   49
18 0.85   26
19 0.90   14
20 0.95    8

[[1]]
   N   p  p0 k alpha tails power
1 49 0.8 0.6 2  0.05     2   0.8

[[2]]
     p0            N
1  0.00 8.000000e+00
2  0.05 9.000000e+00
3  0.10 9.000000e+00
4  0.15 1.000000e+01
5  0.20 1.100000e+01
6  0.25 1.300000e+01
7  0.30 1.400000e+01
8  0.35 1.600000e+01
9  0.40 1.900000e+01
10 0.45 2.200000e+01
11 0.50 2.800000e+01
12 0.55 3.600000e+01
13 0.60 4.900000e+01
14 0.65 7.700000e+01
15 0.70 1.480000e+02
16 0.75 4.990000e+02
17 0.80 5.198178e+31
18 0.85 3.180000e+02
19 0.90 5.800000e+01
20 0.95 1.600000e+01

[[1]]
   N   p  p0 k alpha tails power
1 49 0.8 0.6 2  0.05     2   0.8

[[2]]
        0 0.05  0.1 0.15  0.2 0.25  0.3 0.35  0.4 0.45  0.5 0.55  0.6 0.65 0.7
0     Inf 3136  781  345  192  122   83   60   45   35   28   22   18   15  12
0.05 3136  Inf 3105  769  338  188  118   80   58   43   33   26   20   16  13
0.1   781 3105  Inf 3042  750  328  181  113   77   55   40   31   24   19  15
0.15  345  769 3042  Inf 2950  723  314  172  107   72   51   37   28   22  17
0.2   192  338  750 2950  Inf 2830  690  298  162  100   67   47   34   25  19
0.25  122  188  328  723 2830  Inf 2683  650  279  151   92   61   42   31  22
0.3    83  118  181  314  690 2683  Inf 2511  604  257  138   84   55   38  27
0.35   60   80  113  172  298  650 2511  Inf 2318  553  234  124   75   48  33
0.4    45   58   77  107  162  279  604 2318  Inf 2107  499  208  110   65  41
0.45   35   43   55   72  100  151  257  553 2107  Inf 1882  441  182   94  55
0.5    28   33   40   51   67   92  138  234  499 1882  Inf 1646  381  155  79
0.55   22   26   31   37   47   61   84  124  208  441 1646  Inf 1406  320 128
0.6    18   20   24   28   34   42   55   75  110  182  381 1406  Inf 1164 260
0.65   15   16   19   22   25   31   38   48   65   94  155  320 1164  Inf 929
0.7    12   13   15   17   19   22   27   33   41   55   79  128  260  929 Inf
0.75   10   11   12   13   15   17   19   23   28   34   45   64  102  202 705
0.8     8    9    9   10   11   13   14   16   19   22   28   36   49   77 148
0.85    6    7    7    8    9    9   10   11   13   15   17   21   26   35  53
0.9     5    5    6    6    6    7    7    8    9   10   11   12   14   18  23
0.95    4    4    4    4    4    5    5    5    5    6    6    7    8    9  10
     0.75 0.8 0.85 0.9 0.95
0      10   8    6   5    4
0.05   11   9    7   5    4
0.1    12   9    7   6    4
0.15   13  10    8   6    4
0.2    15  11    9   6    4
0.25   17  13    9   7    5
0.3    19  14   10   7    5
0.35   23  16   11   8    5
0.4    28  19   13   9    5
0.45   34  22   15  10    6
0.5    45  28   17  11    6
0.55   64  36   21  12    7
0.6   102  49   26  14    8
0.65  202  77   35  18    9
0.7   705 148   53  23   10
0.75  Inf 499   99  33   12
0.8   499 Inf  318  58   16
0.85   99 318  Inf 170   25
0.9    33  58  170 Inf   62
0.95   12  16   25  62  Inf

ICC.Sample.Size documentation built on May 2, 2019, 1:27 p.m.