Power calculations

Abstract

Power calculations for our updated sample sizes for different comparisons

Below are some power calculation results with the following assumptions:

• \(\alpha = 0.05\)
• Power = 0.8
• Standardized Outcome variable (\(N(0, 1)\))
• Standard Deviation of outcomes across all groups are identical

Stable v Predictable / Stable v Control

```{stata}
power twomeans 0, n1(400) n2(400) power(`power_val') alpha(`alpha_val')
```

Performing iteration ...

Estimated experimental-group mean for a two-sample means test
t test assuming sd1 = sd2 = sd
H0: m2 = m1  versus  Ha: m2 != m1; m2 > m1

Study parameters:

        alpha =    0.0500
        power =    0.8000
            N =       800
           N1 =       400
           N2 =       400
           m1 =    0.0000
           sd =    1.0000

Estimated effect size and experimental-group mean:

        delta =    0.1983
           m2 =    0.1983

Treated v Control

```{stata}
power twomeans 0, n1(400) n2(1867) power(`power_val') alpha(`alpha_val')
```

Performing iteration ...

Estimated experimental-group mean for a two-sample means test
t test assuming sd1 = sd2 = sd
H0: m2 = m1  versus  Ha: m2 != m1; m2 > m1

Study parameters:

        alpha =    0.0500
        power =    0.8000
            N =     2,267
           N1 =       400
           N2 =     1,867
        N2/N1 =    4.6675
           m1 =    0.0000
           sd =    1.0000

Estimated effect size and experimental-group mean:

        delta =    0.1544
           m2 =    0.1544

Predictable (or Stable / Control) v Risky

```{stata}
power twomeans 0, n1(400) n2(1067) power(`power_val') alpha(`alpha_val')
```

Performing iteration ...

Estimated experimental-group mean for a two-sample means test
t test assuming sd1 = sd2 = sd
H0: m2 = m1  versus  Ha: m2 != m1; m2 > m1

Study parameters:

        alpha =    0.0500
        power =    0.8000
            N =     1,467
           N1 =       400
           N2 =     1,067
        N2/N1 =    2.6675
           m1 =    0.0000
           sd =    1.0000

Estimated effect size and experimental-group mean:

        delta =    0.1644
           m2 =    0.1644

Predictable v Risky (Income Equated)

In expectation, about \(\frac{20}{64} = 31.25\% = 333\) risky participants will have an income equal to the stable and predictable arm

```{stata}
power twomeans 0, n1(400) n2(333) power(`power_val') alpha(`alpha_val')
```

Performing iteration ...

Estimated experimental-group mean for a two-sample means test
t test assuming sd1 = sd2 = sd
H0: m2 = m1  versus  Ha: m2 != m1; m2 > m1

Study parameters:

        alpha =    0.0500
        power =    0.8000
            N =       733
           N1 =       400
           N2 =       333
        N2/N1 =    0.8325
           m1 =    0.0000
           sd =    1.0000

Estimated effect size and experimental-group mean:

        delta =    0.2081
           m2 =    0.2081

Stable and Predictable v Risky (Income Equated)

```{stata}
power twomeans 0, n1(800) n2(333) power(`power_val') alpha(`alpha_val')
```

Performing iteration ...

Estimated experimental-group mean for a two-sample means test
t test assuming sd1 = sd2 = sd
H0: m2 = m1  versus  Ha: m2 != m1; m2 > m1

Study parameters:

        alpha =    0.0500
        power =    0.8000
            N =     1,133
           N1 =       800
           N2 =       333
        N2/N1 =    0.4163
           m1 =    0.0000
           sd =    1.0000

Estimated effect size and experimental-group mean:

        delta =    0.1829
           m2 =    0.1829