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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 | <?php/* -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- *//*# ***** BEGIN LICENSE BLOCK *****# This file is part of Plume Framework, a simple PHP Application Framework.# Copyright (C) 2001-2010 Loic d'Anterroches and contributors.## Plume Framework is free software; you can redistribute it and/or modify# it under the terms of the GNU Lesser General Public License as published by# the Free Software Foundation; either version 2.1 of the License, or# (at your option) any later version.## Plume Framework is distributed in the hope that it will be useful,# but WITHOUT ANY WARRANTY; without even the implied warranty of# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the# GNU Lesser General Public License for more details.## You should have received a copy of the GNU Lesser General Public License# along with this program; if not, write to the Free Software# Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA## ***** END LICENSE BLOCK ***** *//** * Core A/B testing component. * * The two importants methods are `test` and `convert`. * * For performance reasons, the A/B testing component requires you to * setup a cache (APC or Memcached) and use the MongoDB database. The * amount of data in the MongoDB should not be that big for most of * the websites and as such it is fine if you are using the 32bit * version of MongoDB. * * For the moment the storage is not abstracted to use another database. * * All the configuration variables for the component start with * `pluf_ab_`. You need to add 'Pluf_AB' to your list of middleware. * */class Pluf_AB{ /** * MongoDB database handler. */ public static $db = null; /** * Returns an alternative for a given test. * * The middleware is already storing the uid of the user and makes * it available as $request->pabuid. * * @param $test string Unique name of the test * @param $request Pluf_HTTP_Request * @param $alts array Alternatives to pick from (array(true,false)) * @param $weights array Weights for the alternatives (null) * @param $desc string Optional description of the test ('') * @return mixed One value from $alts */ public static function test($test, &$request, $alts=array(true,false), $weights=null, $desc='') { if (Pluf::f('pluf_ab_allow_force', false) and isset($request->GET[$test])) { return $alts[$request->GET[$test]]; } $db = self::getDb(); // Get or set test $dtest = $db->tests->findOne(array('_id' => $test), array('_id', 'active', 'winner')); if ($dtest == null) { $dtest = array('_id' => $test, 'creation_dtime' => gmdate('Y-m-d H:i:s', $request->time), 'desc' => $desc, 'alts' => $alts, 'exp' => 0, 'conv' => 0, 'active' => true); for ($i=0;$i<count($alts);$i++) { $dtest['expalt_'.$i] = 0; $dtest['convalt_'.$i] = 0; } $db->tests->update(array('_id'=>$test), $dtest, array('upsert' => true)); } elseif (!$dtest['active']) { // If test closed with given alternative, returns alternative return (isset($dtest['winner'])) ? $alts[$dtest['winner']] : $alts[0]; } if (!isset($request->pabuid)) { $request->pabuid = self::getUid($request); } if ($request->pabuid == 'bot') { return $alts[0]; } // If $request->pabuid in test, returns corresponding alternative $intest = $db->intest->findOne(array('_id' => $test.'##'.$request->pabuid), array('_id', 'alt')); if ($intest) { return $alts[$intest['alt']]; } // Else find alternative, store and return it if ($weights == null) { $weights = array_fill(0, count($alts), 1.0/count($alts)); } $alt = self::weightedRand($weights); $intest = array('_id' => $test.'##'.$request->pabuid, 'test' => $test, 'pabuid' => $request->pabuid, 'first_dtime' => gmdate('Y-m-d H:i:s', $request->time), 'alt' => $alt); $db->intest->update(array('_id' => $test.'##'.$request->pabuid), $intest, array('upsert' => true)); // Update the counts of the test $db->tests->update(array('_id' => $test), array('$inc' => array('exp' => 1, 'expalt_'.$alt => 1))); return $alts[$alt]; } /** * Mark a test as converted. * * A user which was not exposed to the test or a bot is not marked * as converted as it is not significant. * * @param $test string Test * @param $request Pluf_HTTP_Request */ public static function convert($test, $request) { if (!isset($request->pabuid) or $request->pabuid == 'bot') { return; } $db = self::getDb(); $id = $test.'##'.$request->pabuid; $intest = $db->intest->findOne(array('_id' => $id), array('_id', 'alt')); if (!$intest) { // Not tested return; } $conv = $db->convert->findOne(array('_id' => $id)); if ($conv) { // Already converted return; } $dtest = $db->tests->findOne(array('_id' => $test)); if (!$dtest or !$dtest['active']) { return; } $conv = array( '_id' => $id, 'test' => $test, ); $db->convert->update(array('_id' => $id), $conv, array('upsert' => true)); // increment the test counters $db->tests->update(array('_id' => $test), array('$inc' => array('conv' => 1, 'convalt_'.$intest['alt'] => 1))); } /** * Register a property set for the user. * * This allows you to segment your users with these properties. * * @param $request Pluf_HTTP_Request * @param $props array Properties */ public static function register(&$request, $props) { $pabuid = (isset($request->pabuid)) ? $request->pabuid : self::getUid($request); if ($pabuid == 'bot') { return; } $request->pabuid = $pabuid; $request->pabprops = array_merge($request->pabprops, $props); } /** * Track a funnel. * * The array of properties can be used to track different A/B * testing cases. * * The list of properties must be the same at all the steps of the * funnel, you cannot pass array('gender' => 'M') at step 1 and * array('age' => 32) at step 2. You need to pass both of them at * all steps. * * @param $funnel string Name of the funnel * @param $step int Step in the funnel, from 1 to n * @param $stepname string Readable name for the step * @param $request Pluf_HTTP_Request Request object * @param $props array Array of properties associated with the funnel (array()) */ public static function trackFunnel($funnel, $step, $stepname, $request, $props=array()) { $pabuid = (isset($request->pabuid)) ? $request->pabuid : self::getUid($request); if ($pabuid == 'bot') { return; } $request->pabuid = $pabuid; $cache = Pluf_Cache::factory(); $key = 'pluf_ab_funnel_'.crc32($funnel.'#'.$step.'#'.$pabuid); if ($cache->get($key, false)) { return; // The key is valid 60s not to track 2 steps within 60s } $cache->set($key, '1', 60); $what = array( 'f' => $funnel, 's' => $step, 'sn' => $stepname, 't' => (int) gmdate('Ymd', $request->time), 'u' => $pabuid, 'p' => array_merge($request->pabprops, $props), ); $db = self::getDb(); $db->funnellogs->insert($what); } /** * Process the response of a view. * * If the request has no cookie and the request has a pabuid, set * the cookie in the response. * * @param Pluf_HTTP_Request The request * @param Pluf_HTTP_Response The response * @return Pluf_HTTP_Response The response */ function process_response($request, $response) { if (!isset($request->COOKIE['pabuid']) and isset($request->pabuid) and $request->pabuid != 'bot') { $response->cookies['pabuid'] = $request->pabuid; } if (isset($request->pabprops) and count($request->pabprops) and $request->pabuid != 'bot') { $response->cookies['pabprops'] = Pluf_Sign::dumps($request->pabprops, null, true); } return $response; } /** * Process the request. * * If the request has the A/B test cookie, set $request->pabuid. * * @param Pluf_HTTP_Request The request * @return bool False */ function process_request($request) { if (isset($request->COOKIE['pabuid']) and self::check_uid($request->COOKIE['pabuid'])) { $request->pabuid = $request->COOKIE['pabuid']; } $request->pabprops = array(); if (isset($request->COOKIE['pabprops'])) { try { $request->pabprops = Pluf_Sign::loads($request->COOKIE['pabprops']); } catch (Exception $e) { } } return false; } /** * Get a MongoDB database handle. * * It opens only one connection per request and tries to keep a * persistent connection between the requests. * * The configuration keys used are: * * `pluf_ab_mongo_server`: 'mongodb://localhost:27017' * `pluf_ab_mongo_options`: array('connect' => true, * 'persist' => 'pluf_ab_mongo') * `pluf_ab_mongo_db`: 'pluf_ab' * * If you have a default installation of MongoDB, it should work * out of the box. * */ public static function getDb() { if (self::$db !== null) { return self::$db; } $options = Pluf::f('pluf_ab_mongo_options', array('connect' => true, 'persist' => 'pluf_ab_mongo')); $conn = new Mongo($server, $options); self::$db = $conn->selectDB(Pluf::f('pluf_ab_mongo_db', 'pluf_ab')); return self::$db; } /** * Get the uid of a given request. * * @param $request Pluf_HTTP_Request */ public static function getUid($request) { if (isset($request->COOKIE['pabuid']) and self::check_uid($request->COOKIE['pabuid'])) { return $request->COOKIE['pabuid']; } if (!isset($request->SERVER['HTTP_USER_AGENT']) or self::isBot($request->SERVER['HTTP_USER_AGENT'])) { return 'bot'; } // Here we need to make an uid, first check if a user with // same ip/agent exists and was last seen within the last 1h. // We get that from MemcacheDB $cache = Pluf_Cache::factory(); $key = 'pluf_ab_'.crc32($request->remote_addr.'#'.$request->SERVER['HTTP_USER_AGENT']); if ($uid=$cache->get($key, null)) { $cache->set($key, $uid, 3600); return $uid; } $uid = self::make_uid($request); $cache->set($key, $uid, 3600); return $uid; } /** * Check if a given user agent is a bot. * * @param $user_agent string User agent string * @return bool True if the user agent is a bot */ public static function isBot($user_agent) { static $bots = array('robot', 'checker', 'crawl', 'discovery', 'hunter', 'scanner', 'spider', 'sucker', 'larbin', 'slurp', 'libwww', 'lwp', 'yandex', 'netcraft', 'wget', 'twiceler'); static $pbots = array('/bot[\s_+:,\.\;\/\\\-]/i', '/[\s_+:,\.\;\/\\\-]bot/i'); foreach ($bots as $r) { if (false !== stristr($user_agent, $r)) { return true; } } foreach ($pbots as $p) { if (preg_match($p, $user_agent)) { return true; } } if (false === strpos($user_agent, '(')) { return true; } return false; } /** * Returns a random weighted alternative. * * Given a series of weighted alternative in the format: * * <pre> * array('alt1' => 0.2, * 'alt2' => 0.3, * 'alt3' => 0.5); * </pre> * * Returns the key of the selected alternative. In the following * example, the alternative 3 (alt3) has a 50% chance to be * selected, if the selected the results would be 'alt3'. * * @param $weights array Weighted alternatives * @return mixed Key of the selected $weights array */ public static function weightedRand($weights) { $r = mt_rand(1,10000); $offset = 0; foreach ($weights as $k => $w) { $offset += $w*10000; if ($r <= $offset) { return $k; } } } /** * Given a request, make a corresponding A/B test UID. * * The UID is based on the time, the remote address, a random * component and is hashed to ensure the integrity and avoid the * need of a database hit when controlled. * * @param $request Pluf_HTTP_Request * @return string UID */ public static function make_uid($request) { $base = sprintf('%08X%08X%08X', $request->time, sprintf('%u', crc32($request->remote_addr)), rand()); return sprintf('%s%08X', $base, sprintf('%u', crc32($base.md5(Pluf::f('secret_key'))))); } /** * Validate the uid in the cookie. * * @see self::make_uid * * @param $uid string The UID * @return bool True if the UID is valid */ public static function check_uid($uid) { if (strlen($uid) != 32) { return false; } $check = sprintf('%08X', sprintf('%u', crc32(substr($uid, 0, 24).md5(Pluf::f('secret_key'))))); return ($check == substr($uid, -8)); } /* ------------------------------------------------------------ * * Statistics Functions * * Note: I am not a statistician, use at your own risk! * * ------------------------------------------------------------ */ /** * Given a conversion rate calculate the recommended sample sizes. * * The sample sizes is calculated to be significant at 95% in the * case of a variation of conversion with respect to the other * alternative of 25%, 15% and 5%. * * @param $conv Conversion rate ]0.0;1.0] * @return array The 3 sample sizes for 25%, 15% and 5% */ public static function ssize($conv) { $a = 3.84145882689; // $a = pow(inverse_ncdf(1-(1-0.95)/2),2) $res = array(); $bs = array(0.0625, 0.0225, 0.0025); foreach ($bs as $b) { $res[] = (int) ((1-$conv)*$a/($b*$conv)); } return $res; } /** * Given a test, returns the corresponding stats. * * @param $test array Test definition and results * @return array Statistics for the test */ public static function getTestStats($test) { $stats = array(); // Will store the stats $n = count($test['alts']); $aconvr = array(); // All the conversion rates to sort the alternatives for ($i=0;$i<$n;$i++) { $conv = (isset($test['convalt_'.$i])) ? $test['convalt_'.$i] : 0; $exp = (isset($test['expalt_'.$i])) ? $test['expalt_'.$i] : 0; $convr = self::cr(array($exp, $conv)); $nconvr = ($convr !== null) ? sprintf('%01.2f%%', $convr*100.0) : 'N/A'; $ssize = ($convr !== null and $convr > 0) ? self::ssize($convr) : array(); $stats[] = array('alt' => $i, 'convr' => $convr, 'conv' => $conv, 'exp' => $exp, 'nconvr' => $nconvr, 'ssize' => $ssize); $aconvr[] = ($convr === null) ? 0 : $convr; } array_multisort($aconvr, SORT_DESC, $stats); // We want the best to be significantly better than the second best. for ($i=0;$i<$n;$i++) { $convr = $stats[$i]['convr']; $exp = $stats[$i]['exp']; $conv = $stats[$i]['conv']; $comp = false; $zscore = false; $conf = false; $better = false; if ($i != 1 and $stats[1]['convr'] > 0) { // Compare with base case and get confidence/Z-score $comp = 100.0 * (float) ($convr - $stats[1]['convr'])/ (float) ($stats[1]['convr']); if ($comp > 0) $better = true; $comp = sprintf('%01.2f%%', $comp); $zscore = self::zscore(array($stats[1]['exp'], $stats[1]['conv']), array($exp, $conv)); $conf = sprintf('%01.2f%%', self::cumnormdist($zscore)*100.0); $zscore = sprintf('%01.2f', $zscore); } $stats[$i]['comp'] = $comp; $stats[$i]['zscore'] = $zscore; $stats[$i]['conf'] = $conf; $stats[$i]['better'] = $better; } return $stats; } public static function cr($t) { if ($t[1] < 0) return null; if ($t[0] <= 0) return null; return $t[1]/$t[0]; } public static function zscore($c, $t) { $z = self::cr($t)-self::cr($c); $s = (self::cr($t)*(1-self::cr($t)))/$t[0] + (self::cr($c)*(1-self::cr($c)))/$c[0]; return $z/sqrt($s); } /** * Approximation of the cumulative normal distribution. */ public static function cumnormdist($x) { $b1 = 0.319381530; $b2 = -0.356563782; $b3 = 1.781477937; $b4 = -1.821255978; $b5 = 1.330274429; $p = 0.2316419; $c = 0.39894228; if($x >= 0.0) { $t = 1.0 / ( 1.0 + $p * $x ); return (1.0 - $c * exp( -$x * $x / 2.0 ) * $t * ( $t *( $t * ( $t * ( $t * $b5 + $b4 ) + $b3 ) + $b2 ) + $b1 )); } else { $t = 1.0 / ( 1.0 - $p * $x ); return ( $c * exp( -$x * $x / 2.0 ) * $t * ( $t *( $t * ( $t * ( $t * $b5 + $b4 ) + $b3 ) + $b2 ) + $b1 )); } }} |
