. do "C:\Users\hstryhn\AppData\Local\Temp\STD2d2c_000000.tmp"

. * do-file for lecture 13 of VHM 802, Winter 2025
. version 18 /* works also with versions 14-17 */

. set more off

. set scheme stcolor_alt

. cd "r:\"
r:\

.
. * power and sample size calculations are best done from the menu
. * this do-file shows the corresponding commands
.
. * sample size based on precision/ margin of error
. * method has additional probability of achieving target CI width, set at 0.5 for similar results as without it
. * blood pressure example
. ciwidth onemean, probwidth(.8) width(6) sd(10)

Performing iteration ...

Estimated sample size for a one-mean CI

Student's t two-sided CI

Study parameters:

level = 95.00
Pr_width = 0.8000
width = 6.0000
sd = 10.0000

Estimated sample size:

N = 53

. ciwidth onemean, probwidth(.5) width(6) sd(10)

Performing iteration ...

Estimated sample size for a one-mean CI

Student's t two-sided CI

Study parameters:

level = 95.00
Pr_width = 0.5000
width = 6.0000
sd = 10.0000

Estimated sample size:

N = 45

. * VOR example
. ciwidth twomeans, probwidth(.8) width(.5) sd(0.2739)

Performing iteration ...

Estimated sample sizes for a two-means-difference CI

Student's t two-sided CI assuming sd1 = sd2 = sd

Study parameters:

level = 95.00
Pr_width = 0.8000
width = 0.5000
sd = 0.2739

Estimated sample sizes:

N = 26
N per group = 13

. ciwidth twomeans, probwidth(.5) width(.5) sd(0.2739)

Performing iteration ...

Estimated sample sizes for a two-means-difference CI

Student's t two-sided CI assuming sd1 = sd2 = sd

Study parameters:

level = 95.00
Pr_width = 0.5000
width = 0.5000
sd = 0.2739

Estimated sample sizes:

N = 22
N per group = 11

.
. * sample size based on power
. * blood pressure example
. power onemean 0 3, sd(10)

Performing iteration ...

Estimated sample size for a one-sample mean test

t test
H0: m = m0 versus Ha: m != m0

Study parameters:

alpha = 0.0500
power = 0.8000
delta = 0.3000
m0 = 0.0000
ma = 3.0000
sd = 10.0000

Estimated sample size:

N = 90

. * VOR example
. power oneway 2.82 3.89 3.04, varerror(.075) alpha(0.01) npergroup(4)

Estimated power for one-way ANOVA

F test for group effect
H0: delta = 0 versus Ha: delta != 0

Study parameters:

alpha = 0.0100
N = 12
N per group = 4
delta = 1.6847
N_g = 3
m1 = 2.8200
m2 = 3.8900
m3 = 3.0400
Var_m = 0.2129
Var_e = 0.0750

Estimated power:

power = 0.9298

.
. * calcium supplementation example
. * no interaction ~ test by main effect
. power twoway 0 0\ 5 5, varerror(100) factor(row) /* note that mean diff between rows is 5 */

Performing iteration ...

Estimated sample size for two-way ANOVA

F test for row effect
H0: delta = 0 versus Ha: delta != 0

Study parameters:

alpha = 0.0500
power = 0.8000
delta = 0.2500
N_r = 2
N_c = 2
means = <matrix>
Var_r = 6.2500
Var_e = 100.0000

Estimated sample sizes:

N = 128
N per cell = 32

. * interaction
. power twoway 0 0\ 0 5, varerror(100) factor(rowcol) /* note that interaction must be 5 */

Performing iteration ...

Estimated sample size for two-way ANOVA

F test for row-by-column effect
H0: delta = 0 versus Ha: delta != 0

Study parameters:

alpha = 0.0500
power = 0.8000
delta = 0.1250
N_r = 2
N_c = 2
means = <matrix>
Var_rc = 1.5625
Var_e = 100.0000

Estimated sample sizes:

N = 508
N per cell = 127

.
. * cat food example
. import delimited catfood.csv, clear
(encoding automatically selected: ISO-8859-1)
(2 vars, 19 obs)

. ttest protein, by(product) unequal

Two-sample t test with unequal variances

+

Group | Obs Mean Std. err. Std. dev. [95% conf. interval]

+

Discount | 10 33.971 .1836147 .5806408 33.55563 34.38637
Original | 9 34.09222 .0871265 .2613796 33.89131 34.29314

+

Combined | 19 34.02842 .1033143 .4503365 33.81137 34.24548

+

diff | -.1212217 .2032373 -.561058 .3186146

+

diff = mean(Discount) - mean(Original) t = -0.5965
H0: diff = 0 Satterthwaite's degrees of freedom = 12.7802

Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
Pr(T < t) = 0.2806 Pr(|T| > |t|) = 0.5613 Pr(T > t) = 0.7194

. ttest protein, by(product) unequal level(90)

Two-sample t test with unequal variances

+

Group | Obs Mean Std. err. Std. dev. [90% conf. interval]

+

Discount | 10 33.971 .1836147 .5806408 33.63441 34.30759
Original | 9 34.09222 .0871265 .2613796 33.93021 34.25424

+

Combined | 19 34.02842 .1033143 .4503365 33.84927 34.20757

+

diff | -.1212217 .2032373 -.4816154 .239172

+

diff = mean(Discount) - mean(Original) t = -0.5965
H0: diff = 0 Satterthwaite's degrees of freedom = 12.7802

Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
Pr(T < t) = 0.2806 Pr(|T| > |t|) = 0.5613 Pr(T > t) = 0.7194

. * using add-on package tost
. tostt protein, by(product) eqvlevel(.5) unequal

Two-sample unpaired t test for mean equivalence with unequal variances

+

Group | Obs Mean Std. err. Std. dev. [95% conf. interval]

+

| 10 33.971 .1836147 .5806408 33.55563 34.38637
| 9 34.09222 .0871265 .2613796 33.89131 34.29314

+

D-diff | .6212217 .2032373 .1813854 1.061058
diff+D | .3787783 .2032373 -.061058 .8186146

+

diff = mean(protein|product = .) - mean(protein|product = .)
Delta (D) = 0.5000 Delta expressed in same units as protein
df = 12.7802 using Satterthwaite's formula

Ho: |diff| >= Delta:

t1 = 3.057 t2 = 1.864

Ho1: Delta-diff >= 0 Ho2: diff+Delta <= 0
Ha1: Delta-diff < 0 Ha2: diff+Delta > 0
Pr(T > t1) = 0.0047 Pr(T > t2) = 0.0427

. * shows the two one-sided t-tests
.
end of do-file

. exit, clear