Calculateur de test de Friedman
Le test de Friedman est l’alternative non paramétrique à l’ANOVA unidirectionnelle avec mesures répétées. Il est utilisé pour tester les différences entre les groupes lorsque la variable dépendante est ordinale.
Pour effectuer un test de Friedman pour un ensemble de données donné, entrez simplement les valeurs d’un maximum de cinq échantillons dans les cellules ci-dessous, puis appuyez sur le bouton « Calculer ».
La calculatrice affichera la statistique de test Q, la valeur p du test et les calculs utilisés pour dériver la statistique de test Q.
Groupe 1 | Groupe 2 | Groupe 3 | Groupe 4 | Groupe 5 |
---|---|---|---|---|
Statistique de test Q :
Valeur p :
Solution
Q =
Q =
Q =
//create function that performs calculations function calc() {
//define addition function function add(a, b) { return a + b; }
//define function that can flatten a multi-dimensional array function flatten(arr) { return arr.reduce(function (flat, toFlatten) { return flat.concat(Array.isArray(toFlatten) ? flatten(toFlatten) : toFlatten); }, []); }
//get total number of rows var row_input = document.getElementsByClassName('table_span_a'); var row_array = []; for (var i = 0; i < row_input.length; i++) { row_array[i] = row_input[i].innerText; } values_row = row_array.filter(n => n); var n = values_row.length;
//create massive for loop that gets ranks for every single row all_data = [];
for (var i = 0; i < n; i++) { var p = "p" var p_number = i-(-1); var str = p.concat(p_number); str = str.replace(/ +/g, ""); //get row data var p1_input = document.getElementsByClassName(str); var p1_array = []; for (var j = 0; j < p1_input.length; j++) { p1_array[j] = p1_input[j].innerText; } values_p1 = p1_array.filter(n => n); var p1 = values_p1.map(Number);
//sort row data var sorted = p1.slice().sort(function(a,b){return a-b}) var reversed = sorted.slice(0).reverse(); var frac_rank = p1.slice().map(function(n) { return ( (sorted.indexOf(n) + 1) + (reversed.length - reversed.indexOf(n)) ) / 2 });
//push sorted row data to total data array all_data.push(frac_rank);
} //end massive for loop that ranks every row
//find total treatments var k = all_data[0].length;
//flatten multi-dimensional array into one long array flat_data = flatten(all_data);
//find sum of ranks for each treatment var a = [], b = [], c = [], d = [], e = [], total_squared_ranks;
if (k == 2) { for (i = 0; i < flat_data.length; i+= k) { a.push(flat_data[i]); } for (i = 1; i < flat_data.length; i+= k) { b.push(flat_data[i]); } var sum_a_squared = Math.pow(a.reduce(add, 0), 2); var sum_b_squared = Math.pow(b.reduce(add, 0), 2); total_squared_ranks = [sum_a_squared, sum_b_squared].reduce(add, 0); } if (k == 3) { for (i = 0; i < flat_data.length; i+= k) { a.push(flat_data[i]); } for (i = 1; i < flat_data.length; i+= k) { b.push(flat_data[i]); } for (i = 2; i < flat_data.length; i+= k) { c.push(flat_data[i]); } var sum_a_squared = Math.pow(a.reduce(add, 0), 2); var sum_b_squared = Math.pow(b.reduce(add, 0), 2); var sum_c_squared = Math.pow(c.reduce(add, 0), 2); total_squared_ranks = [sum_a_squared, sum_b_squared, sum_c_squared].reduce(add, 0); } if (k == 4) { for (i = 0; i < flat_data.length; i+= k) { a.push(flat_data[i]); } for (i = 1; i < flat_data.length; i+= k) { b.push(flat_data[i]); } for (i = 2; i < flat_data.length; i+= k) { c.push(flat_data[i]); } for (i = 3; i < flat_data.length; i+= k) { d.push(flat_data[i]); } var sum_a_squared = Math.pow(a.reduce(add, 0), 2); var sum_b_squared = Math.pow(b.reduce(add, 0), 2); var sum_c_squared = Math.pow(c.reduce(add, 0), 2); var sum_d_squared = Math.pow(d.reduce(add, 0), 2); total_squared_ranks = [sum_a_squared, sum_b_squared, sum_c_squared, sum_d_squared].reduce(add, 0); } if (k == 5) { for (i = 0; i < flat_data.length; i+= k) { a.push(flat_data[i]); } for (i = 1; i < flat_data.length; i+= k) { b.push(flat_data[i]); } for (i = 2; i < flat_data.length; i+= k) { c.push(flat_data[i]); } for (i = 3; i < flat_data.length; i+= k) { d.push(flat_data[i]); } for (i = 4; i < flat_data.length; i+= k) { e.push(flat_data[i]); } var sum_a_squared = Math.pow(a.reduce(add, 0), 2); var sum_b_squared = Math.pow(b.reduce(add, 0), 2); var sum_c_squared = Math.pow(c.reduce(add, 0), 2); var sum_d_squared = Math.pow(d.reduce(add, 0), 2); var sum_e_squared = Math.pow(e.reduce(add, 0), 2); total_squared_ranks = [sum_a_squared, sum_b_squared, sum_c_squared, sum_d_squared, sum_e_squared].reduce(add, 0); } //final calculations for critical value and p value q_term1 = 12 / (n*k*(k-(-1))); q_term3 = 3*n*(k-(-1)); q = (q_term1 * total_squared_ranks) - q_term3; p = 1 - jStat.chisquare.cdf(q, k-1); //output results document.getElementById('q').innerHTML = q.toFixed(5); document.getElementById('p').innerHTML = p.toFixed(5); document.getElementById('solution1').innerHTML = "(12/(nk(k+1)) * (∑R2) - 3n(k+1)"; document.getElementById('solution2').innerHTML = q_term1 + " * " + total_squared_ranks.toFixed(1) + " - " + q_term3; document.getElementById('solution3').innerHTML = q.toFixed(5); } //end calc() function