How to Calculate Sample Deviation Rate

Sample Deviation Rate Calculator

function calculateSampleDeviationRate() { // Get input values var sampleSizeInput = document.getElementById('sdr_sample_size').value; var deviationCountInput = document.getElementById('sdr_deviation_count').value; var populationSizeInput = document.getElementById('sdr_population_size').value; // Parse values var n = parseFloat(sampleSizeInput); var d = parseFloat(deviationCountInput); var N = parseFloat(populationSizeInput); // Validation if (isNaN(n) || n <= 0) { alert("Please enter a valid Sample Size greater than 0."); return; } if (isNaN(d) || d n) { alert("Number of Deviations cannot exceed the Sample Size."); return; } // Calculate Rate var rate = (d / n) * 100; // Display Logic document.getElementById('sdr_results_area').style.display = 'block'; document.getElementById('sdr_output_rate').innerHTML = rate.toFixed(2) + '%'; document.getElementById('sdr_output_deviations').innerHTML = d; // Calculate Projection if Population Size is provided if (!isNaN(N) && N > 0) { var projection = (rate / 100) * N; // Round projection to nearest whole number as you can't have half a deviation in reality usually var roundedProjection = Math.round(projection); document.getElementById('sdr_projection_row').style.display = 'flex'; document.getElementById('sdr_output_projection').innerHTML = roundedProjection.toLocaleString(); } else { document.getElementById('sdr_projection_row').style.display = 'none'; } }

How to Calculate Sample Deviation Rate

In the fields of auditing, quality control, and statistical analysis, the Sample Deviation Rate is a critical metric used to estimate the percentage of error or non-compliance within a larger population based on a smaller, representative sample.

Whether you are an internal auditor checking invoices for authorized signatures or a quality assurance manager inspecting products on an assembly line, calculating this rate helps you assess whether the population as a whole meets your standards without having to inspect every single item.

The Formula

The calculation for the sample deviation rate is straightforward. It represents the proportion of items in the sample that contain a deviation (error, defect, or exception).

Formula:
Sample Deviation Rate = (Number of Deviations Found ÷ Sample Size) × 100

Where:

• Sample Size (n): The total number of items selected for testing.
• Number of Deviations (d): The count of items within that sample that failed to meet the specific criteria (e.g., missing signature, wrong color, calculation error).

Step-by-Step Calculation Example

Let's assume you are auditing a company's expense reports. There are 5,000 total reports (Population) for the year. You cannot check them all, so you select a random sample of 60 reports.

1. Define the Sample: You inspect the 60 reports.
2. Identify Deviations: You find that 3 reports are missing the required manager approval.
3. Apply the Formula: 3 ÷ 60 = 0.05
4. Convert to Percentage: 0.05 × 100 = 5%

In this scenario, your Sample Deviation Rate is 5%. This implies that, based on your sample, approximately 5% of all expense reports in the population might be non-compliant.

Projecting Errors to the Population

Once you have the deviation rate, you can project the total number of errors in the entire population. This is useful for estimating the total magnitude of a problem.

Using the example above:

• Population Size: 5,000 reports
• Deviation Rate: 5%
• Projected Total Errors: 5,000 × 0.05 = 250 reports

You can estimate that roughly 250 reports in the total population are likely missing approvals.

Interpreting the Results

In auditing standards (such as AICPA or ISA), the calculated deviation rate is compared against a Tolerable Deviation Rate.

• If Sample Rate < Tolerable Rate: The control is generally considered effective.
• If Sample Rate > Tolerable Rate: The control may be ineffective, and the auditor may need to increase the sample size or rely less on that specific control.

Common Use Cases

• Financial Auditing: Checking for compliance with accounting procedures.
• Manufacturing: Estimating the defect rate in a production batch.
• Healthcare: Reviewing patient records for required documentation.
• Inventory Management: Verifying accuracy of stock counts.