|
public static twoWay ( variadic |
||
| $data | variadic |
Samples to analyze [ // Factor A₁ [ [4, 6, 8] // Factor B₁ [6, 6, 9] // Factor B₂ ⋮ ], // Factor A₂ [ [4, 8, 9] // Factor B₁ [7, 10, 13] // Factor B₂ ⋮ ], ... ] |
| Результат | array | [ ANOVA => [ factorA => [SS, df, MS, F, P], factorB => [SS, df, MS, F, P], factorAB => [SS, df, MS, F, P], error => [SS, df, MS], total => [SS, df], ], total_summary => [n, sum, mean, SS, variance, sd, sem], summary_factorA => [ 0 => [n, sum, mean, SS, variance, sd, sem], 1 => [n, sum, mean, SS, variance, sd, sem], ... ], summary_factorB => [ 0 => [n, sum, mean, SS, variance, sd, sem], 1 => [n, sum, mean, SS, variance, sd, sem], ... ], summary_factorAB => [ 0 => [n, sum, mean, SS, variance, sd, sem], 1 => [n, sum, mean, SS, variance, sd, sem], ... ] ] |
public static function twoWay(array ...$data)
{
// Must have at least two rows (two types of factor A)
$r = count($data);
if ($r < 2) {
throw new Exception\BadDataException('Must have at least two rows (two types of factor A)');
}
// All samples must have the same number the second factor B
$c = count($data[0]);
for ($i = 1; $i < $r; $i++) {
if (count($data[$i]) !== $c) {
throw new Exception\BadDataException('All samples must have the same number of the second factor B');
}
}
// Each AB factor interaction must have the same number of values
$v = count($data[0][0]);
for ($i = 0; $i < $r; $i++) {
for ($j = 0; $j < $c; $j++) {
if (count($data[$i][$j]) !== $v) {
throw new Exception\BadDataException('Each AB factor interaction must have the same number of values');
}
}
}
// Aggregates for all elements, rows (factor A), and columns (factor B)
$all_elements = [];
$A_elements = [];
$B_elements = [];
// Summaries for factor A, factor B, AB, and total
$summary_A = [];
$summary_B = [];
$summary_AB = [];
$summary_total = [];
// Summary data for each AB
// And aggregate all elements and elements for factor A
foreach ($data as $A => $Bs) {
$A_elements[$A] = [];
foreach ($Bs as $B => $values) {
// Aggregates
$all_elements = array_merge($all_elements, $values);
$A_elements[$A] = array_merge($A_elements[$A], $values);
// AB summary
$summary_AB[$A][$B] = [];
$summary_AB[$A][$B]['n'] = $c;
$summary_AB[$A][$B]['sum'] = array_sum($values);
$summary_AB[$A][$B]['mean'] = Average::mean($values);
$summary_AB[$A][$B]['SS'] = RandomVariable::sumOfSquares($values);
$summary_AB[$A][$B]['variance'] = Descriptive::sampleVariance($values);
$summary_AB[$A][$B]['sd'] = Descriptive::sd($values);
$summary_AB[$A][$B]['sem'] = RandomVariable::standardErrorOfTheMean($values);
}
}
// Aggregate elements for factor B
for ($B = 0; $B < $c; $B++) {
$B_elements[$B] = [];
foreach ($data as $factor1s) {
$B_elements[$B] = array_merge($B_elements[$B], $factor1s[$B]);
}
}
// Factor A summary
foreach ($A_elements as $A => $elements) {
$summary_A[$A] = [];
$summary_A[$A]['n'] = count($elements);
$summary_A[$A]['sum'] = array_sum($elements);
$summary_A[$A]['mean'] = Average::mean($elements);
$summary_A[$A]['SS'] = RandomVariable::sumOfSquares($elements);
$summary_A[$A]['variance'] = Descriptive::sampleVariance($elements);
$summary_A[$A]['sd'] = Descriptive::sd($elements);
$summary_A[$A]['sem'] = RandomVariable::standardErrorOfTheMean($elements);
}
// Factor B summary
foreach ($B_elements as $B => $elements) {
$summary_B[$B] = [];
$summary_B[$B]['n'] = count($elements);
$summary_B[$B]['sum'] = array_sum($elements);
$summary_B[$B]['mean'] = Average::mean($elements);
$summary_B[$B]['SS'] = RandomVariable::sumOfSquares($elements);
$summary_B[$B]['variance'] = Descriptive::sampleVariance($elements);
$summary_B[$B]['sd'] = Descriptive::sd($elements);
$summary_B[$B]['sem'] = RandomVariable::standardErrorOfTheMean($elements);
}
// Totals summary
$μ = Average::mean($all_elements);
$summary_total = ['n' => count($all_elements), 'sum' => array_sum($all_elements), 'mean' => $μ, 'SS' => RandomVariable::sumOfSquares($all_elements), 'variance' => Descriptive::sampleVariance($all_elements), 'sd' => Descriptive::sd($all_elements), 'sem' => RandomVariable::standardErrorOfTheMean($all_elements)];
// Sum of squares factor A
$SSA = array_sum(array_map(function ($f1) use($μ) {
return $f1['n'] * ($f1['mean'] - $μ) ** 2;
}, $summary_A));
// Sum of squares factor B
$SSB = array_sum(array_map(function ($B) use($μ) {
return $B['n'] * ($B['mean'] - $μ) ** 2;
}, $summary_B));
// Sum of squares within (error)
$SSW = 0;
foreach ($data as $A => $Bs) {
foreach ($Bs as $B => $values) {
foreach ($values as $value) {
$SSW += ($value - $summary_AB[$A][$B]['mean']) ** 2;
}
}
}
// Sum of squares total
$SST = 0;
foreach ($data as $A => $Bs) {
foreach ($Bs as $B => $values) {
foreach ($values as $value) {
$SST += ($value - $μ) ** 2;
}
}
}
// Sum of squares AB interaction
$SSAB = $SST - $SSA - $SSB - $SSW;
// Degrees of freedom
$dfA = $r - 1;
$dfB = $c - 1;
$dfAB = ($r - 1) * ($c - 1);
$dfW = $summary_total['n'] - $r * $c;
$dfT = $summary_total['n'] - 1;
// Mean squares
$MSA = $SSA / $dfA;
$MSB = $SSB / $dfB;
$MSAB = $SSAB / $dfAB;
$MSW = $SSW / $dfW;
// F test statistics
$FA = $MSA / $MSW;
$FB = $MSB / $MSW;
$FAB = $MSAB / $MSW;
// P values
$PA = F::above($FA, $dfA, $dfW);
$PB = F::above($FB, $dfB, $dfW);
$PAB = F::above($FAB, $dfAB, $dfW);
// Return ANOVA report
return ['ANOVA' => ['factorA' => ['SS' => $SSA, 'df' => $dfA, 'MS' => $MSA, 'F' => $FA, 'P' => $PA], 'factorB' => ['SS' => $SSB, 'df' => $dfB, 'MS' => $MSB, 'F' => $FB, 'P' => $PB], 'interaction' => ['SS' => $SSAB, 'df' => $dfAB, 'MS' => $MSAB, 'F' => $FAB, 'P' => $PAB], 'error' => ['SS' => $SSW, 'df' => $dfW, 'MS' => $MSW], 'total' => ['SS' => $SST, 'df' => $dfT]], 'total_summary' => $summary_total, 'summary_factorA' => $summary_A, 'summary_factorB' => $summary_B, 'summary_interaction' => $summary_AB];
}