Differentially Private Randomized Response Design
Calculation Mode
Choose what you want to calculate. See below for details.
Sample Size (\(n\)) and Design Parameter (\(p\))
Optimal Design Parameter (\(p\))
Sample Size (\(n\)) and Design Parameter (\(p\)):
Calculate the design parameter and minimum sample size required to achieve desired statistical power and privacy budget.
Optimal Design Parameter (\(p\)):
Determine the optimal design parameter for randomized response designs, considering either the privacy budget or statistical power. Specifically, when the privacy budget is fixed, it yields the design parameter that maximizes the statistical power, whereas when the power is fixed, it identifies the design parameter that mnimizes the differential privacy budget.
🔧 Calculate Optimal Design Parameter Considering
Differential Privacy Budget
Statistical Power
Design Parameters
Design Type
Warner
Two Step
Unrelated Question
Forced Response
Kuk's Design
Null Hypothesis, \(\pi_0\)
Alternative Hypothesis, \(\pi_1\)
Significance Level, \(\alpha\)
Target Power
Privacy Budget, \(\varepsilon\)
Proportion of the Unrelated Question Group, \(\pi_Y\)
Calculate Sample Size
Design Parameters
Design Type
Warner
Unrelated Question Design
Two Step Design
Forced Response Design
Kuk's Design
Privacy Budget, \(\varepsilon\)
Proportion under Null Hypothesis, \(\pi_0\)
Proportion under Alternative Hypothesis, \(\pi_1\)
Sample Size, \(n\)
Significance Level, \(\alpha\)
Proportion of the Unrelated Question Group, \(\pi_Y\)
Compute Design Parameter
Desired Power
Null Hypothesis, \(\pi_0\)
Alternative Hypothesis, \(\pi_1\)
Significance Level, \(\alpha\)
Sample Size, \(n\)
Proportion of the Unrelated Question Group, \(\pi_Y\)
Compute Design Parameter
Calculated Results
Design Parameter(s) vs Differential Privacy Budget
Design Parameter(s) vs Power
Note: All results are rounded to three decimal places for consistency.