Determine the precision of your sample mean relative to the population mean.
Standard Error of the Mean (SEM)0.00
What is Standard Error?
The Standard Error (SE) of a statistic is the standard deviation of its sampling distribution. Most commonly, people refer to the Standard Error of the Mean (SEM), which measures how far the sample mean of the data is likely to be from the true population mean.
SE = σ / √n
Where σ represents the Standard Deviation and n represents the total number of observations (Sample Size).
How to Calculate SE: Step-by-Step
Identify your Standard Deviation: This measures the spread of your data points around your sample mean.
Determine your Sample Size: Count how many individual data points or subjects were included in your study.
Calculate the Square Root: Find the square root of your sample size (√n).
Divide: Divide the Standard Deviation by that square root.
Example Calculation
Imagine you are testing the height of a specific plant species. Your sample has a Standard Deviation of 10 cm and you measured 25 plants.
SD = 10
n = 25
√25 = 5
SE = 10 / 5 = 2.0
The Standard Error is 2.0 cm. This suggests that the sample mean is a relatively precise estimate of the true population mean.
Why is SE Important?
Standard Error is critical in inferential statistics because it helps construct confidence intervals and calculate p-values. A smaller SE indicates that your sample mean is a more accurate reflection of the actual population mean, usually occurring when sample sizes are large or data variability is low.
function calculateSE() {
var sd = document.getElementById("stdDev").value;
var n = document.getElementById("sampleSize").value;
var resultDiv = document.getElementById("seResultArea");
var output = document.getElementById("seOutput");
var interpretation = document.getElementById("seInterpretation");
var sdVal = parseFloat(sd);
var nVal = parseFloat(n);
if (isNaN(sdVal) || isNaN(nVal)) {
alert("Please enter valid numbers for both fields.");
return;
}
if (nVal <= 0) {
alert("Sample size must be greater than zero.");
return;
}
// SE Formula: Standard Deviation / Square Root of Sample Size
var seResult = sdVal / Math.sqrt(nVal);
// Formatting output
output.innerText = seResult.toLocaleString(undefined, {
minimumFractionDigits: 2,
maximumFractionDigits: 4
});
// Interpretation logic
var interText = "This means the sample mean typically deviates from the population mean by " + seResult.toFixed(2) + " units.";
interpretation.innerText = interText;
// Show results
resultDiv.style.display = "block";
}