Online Poll Bias Estimator

Online Poll Bias Estimator calculates bias score, reliability, and margin of error from sample size, response rate, and platform for accurate poll analysis.

Sample Size (people):

Response Rate (%):

Selection Bias Factor (%):

Platform Type:

Formulas Used in Online Poll Bias Estimator

The calculator uses the following formulas to estimate poll bias:

Bias Score:

\\[ B_s = \min\left(100 \cdot \frac{S_b}{R \cdot M_p}, 100\right) \\]

Sample Reliability:

\\[ R_s = \min\left(100 \cdot \frac{N \cdot R}{N_{\text{max}}}, 100\right) \\]

Margin of Error:

\\[ M_e = \frac{1.96}{\sqrt{N \cdot R}} \cdot 100 \\]

Where:

\\( B_s \\): Bias score (%)
\\( S_b \\): Selection bias factor (decimal)
\\( R \\): Response rate (decimal)
\\( M_p \\): Platform type multiplier (Social Media: 1.2, Email: 1.0, Website: 0.8)
\\( R_s \\): Sample reliability (%)
\\( N \\): Sample size (people)
\\( N_{\text{max}} \\): Maximum reference sample size (10000)
\\( M_e \\): Margin of error (%)

Example Calculations

Example 1: Small Poll, High Bias, Social Media

Input: Sample Size = 100, Response Rate = 20%, Selection Bias Factor = 30%, Platform Type = Social Media

\\[ B_s = \min\left(100 \cdot \frac{S_b}{R \cdot M_p}, 100\right) = \min\left(100 \cdot \frac{0.3}{0.2 \cdot 1.2}, 100\right) = 100 \ \% \\] \\[ R_s = \min\left(100 \cdot \frac{N \cdot R}{N_{\text{max}}}, 100\right) = \min\left(100 \cdot \frac{100 \cdot 0.2}{10000}, 100\right) = 0.2 \ \% \\] \\[ M_e = \frac{1.96}{\sqrt{N \cdot R}} \cdot 100 = \frac{1.96}{\sqrt{100 \cdot 0.2}} \cdot 100 = 43.84 \ \% \\]

Result: Bias Score: 100%, Sample Reliability: 0.2%, Margin of Error: 43.84%

Example 2: Medium Poll, Moderate Bias, Email

Input: Sample Size = 500, Response Rate = 40%, Selection Bias Factor = 15%, Platform Type = Email

\\[ B_s = \min\left(100 \cdot \frac{S_b}{R \cdot M_p}, 100\right) = \min\left(100 \cdot \frac{0.15}{0.4 \cdot 1.0}, 100\right) = 37.5 \ \% \\] \\[ R_s = \min\left(100 \cdot \frac{N \cdot R}{N_{\text{max}}}, 100\right) = \min\left(100 \cdot \frac{500 \cdot 0.4}{10000}, 100\right) = 2 \ \% \\] \\[ M_e = \frac{1.96}{\sqrt{N \cdot R}} \cdot 100 = \frac{1.96}{\sqrt{500 \cdot 0.4}} \cdot 100 = 13.86 \ \% \\]

Result: Bias Score: 37.5%, Sample Reliability: 2%, Margin of Error: 13.86%

Example 3: Large Poll, Low Bias, Website

Input: Sample Size = 2000, Response Rate = 60%, Selection Bias Factor = 5%, Platform Type = Website

\\[ B_s = \min\left(100 \cdot \frac{S_b}{R \cdot M_p}, 100\right) = \min\left(100 \cdot \frac{0.05}{0.6 \cdot 0.8}, 100\right) = 10.42 \ \% \\] \\[ R_s = \min\left(100 \cdot \frac{N \cdot R}{N_{\text{max}}}, 100\right) = \min\left(100 \cdot \frac{2000 \cdot 0.6}{10000}, 100\right) = 12 \ \% \\] \\[ M_e = \frac{1.96}{\sqrt{N \cdot R}} \cdot 100 = \frac{1.96}{\sqrt{2000 \cdot 0.6}} \cdot 100 = 5.66 \ \% \\]

Result: Bias Score: 10.42%, Sample Reliability: 12%, Margin of Error: 5.66%

Formulas Used in Online Poll Bias Estimator

Example Calculations

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