function calculateDixonQ() {
var input = document.getElementById("dataPoints").value;
var cl = document.getElementById("confidenceLevel").value;
var resultDiv = document.getElementById("dixonResult");
// Clean and parse input
var data = input.split(',').map(function(item) {
return parseFloat(item.trim());
}).filter(function(item) {
return !isNaN(item);
});
if (data.length < 3) {
resultDiv.style.display = "block";
resultDiv.style.backgroundColor = "#fdeaea";
resultDiv.style.color = "#c0392b";
resultDiv.innerHTML = "Error: Please enter at least 3 numerical data points.";
return;
}
if (data.length > 30) {
resultDiv.style.display = "block";
resultDiv.style.backgroundColor = "#fdeaea";
resultDiv.style.color = "#c0392b";
resultDiv.innerHTML = "Error: Dixon's Q test is intended for small datasets (n ≤ 30).";
return;
}
// Sort data ascending
data.sort(function(a, b) { return a – b; });
var n = data.length;
var range = data[n – 1] – data[0];
if (range === 0) {
resultDiv.style.display = "block";
resultDiv.style.backgroundColor = "#fdeaea";
resultDiv.style.color = "#c0392b";
resultDiv.innerHTML = "Error: Range is zero. All data points are identical.";
return;
}
// Suspect the value furthest from its neighbor
var gapLow = data[1] – data[0];
var gapHigh = data[n – 1] – data[n – 2];
var qExp, outlierValue;
if (gapLow > gapHigh) {
qExp = gapLow / range;
outlierValue = data[0];
} else {
qExp = gapHigh / range;
outlierValue = data[n – 1];
}
// Critical values table (n=3 to 15, common for chemistry/physics)
var qTable = {
90: {3:0.941, 4:0.765, 5:0.642, 6:0.560, 7:0.507, 8:0.468, 9:0.437, 10:0.412, 11:0.392, 12:0.376, 13:0.361, 14:0.349, 15:0.338},
95: {3:0.970, 4:0.829, 5:0.710, 6:0.625, 7:0.568, 8:0.526, 9:0.493, 10:0.466, 11:0.444, 12:0.426, 13:0.410, 14:0.396, 15:0.384},
99: {3:0.994, 4:0.926, 5:0.821, 6:0.740, 7:0.680, 8:0.634, 9:0.598, 10:0.568, 11:0.542, 12:0.522, 13:0.503, 14:0.488, 15:0.475}
};
var qCrit = qTable[cl][n] || qTable[cl][15]; // Default to 15 if larger for this simple demo
var status = qExp > qCrit ? "REJECT" : "KEEP";
var statusColor = qExp > qCrit ? "#e74c3c" : "#27ae60";
resultDiv.style.display = "block";
resultDiv.style.backgroundColor = "#f4f7f6";
resultDiv.style.color = "#2c3e50";
resultDiv.style.borderLeft = "6px solid " + statusColor;
var htmlResult = '
Result: ' + status + ' Outlier
';
htmlResult += '
';
htmlResult += '
Suspected Outlier:
' + outlierValue + '
';
htmlResult += '
Experimental Q (Qexp):
' + qExp.toFixed(4) + '
';
htmlResult += '
Critical Q (Qcrit):
' + qCrit.toFixed(3) + '
';
htmlResult += '
Sample Size (n):
' + n + '
';
htmlResult += '
';
if (qExp > qCrit) {
htmlResult += 'Since Qexp > Qcrit, the value ' + outlierValue + ' is statistically likely to be an outlier at the ' + cl + '% confidence level and should be rejected.';
} else {
htmlResult += 'Since Qexp ≤ Qcrit, there is no statistical evidence to reject ' + outlierValue + ' at the ' + cl + '% confidence level.';
}
resultDiv.innerHTML = htmlResult;
}
Understanding the Dixon Q Test
The Dixon's Q test, or simply the Q test, is a statistical method used to identify and reject outliers in small data sets. This test is particularly popular in analytical chemistry and experimental physics where sample sizes are typically small (usually between $n=3$ and $n=10$).
The Mathematical Formula
The calculation of the experimental Q-value ($Q_{exp}$) is based on the relationship between the "gap" and the "range" of the dataset:
Q = Gap / Range
Gap: The absolute difference between the suspected outlier and its nearest numerical neighbor.
Range: The difference between the highest value and the lowest value in the entire set.
Step-by-Step Calculation Example
Imagine a chemist performing a titration five times. The volumes recorded are: 12.5, 12.8, 12.4, 15.1, and 12.6 mL.
Sort the data: 12.4, 12.5, 12.6, 12.8, 15.1
Identify the suspect: 15.1 appears much higher than the rest.
Calculate Range: $15.1 – 12.4 = 2.7$
Calculate Gap: $15.1 – 12.8 = 2.3$
Calculate Qexp: $2.3 / 2.7 = 0.8519$
Compare: At 95% confidence for $n=5$, $Q_{crit}$ is 0.710. Since $0.8519 > 0.710$, we reject 15.1.
When to use the Q Test
The Dixon Q Test should only be applied once to a dataset. Repeatedly using the test to prune a dataset can lead to biased results. It is most effective for small samples. For larger datasets ($n > 30$), other tests like the Grubbs' test or the Peirce's criterion are generally preferred.
SEO Tip: When reporting analytical results, always specify the confidence level used (e.g., 95% CL) and whether an outlier was removed using the Dixon Q Test to maintain scientific transparency.