我的得分算法有问题吗？

Question

我要找的是那些平均收视率最高的俱乐部，根据票数和明显的最高收视率。

我所做的是：

• 计算整个人口的差异(所有选票和所有俱乐部)
• 根据人口差异确定各俱乐部的标准偏差
• 一种新的club weighted median计算方法:对低票数的杂草俱乐部减去一个标准差

问题是我无法确定为什么我的数据没有正确显示。我想我的算盘有问题。当我从0-5得到一个数值时，我得到的是10的数字，并且是负值(就像评分一样)。。

我不太清楚我的逻辑哪里失败了。

下面是我的评级代码逻辑：

    $sql="SELECT SUM(rating) AS sumrating,COUNT(reviews.rating) AS countrating FROM reviews";   
    $rs=mysqli_fetch_array(mysqli_query($scx_dbh,$sql));    

    // get the total summation of ratings against all reviews
    $ratingssum=(int)$rs['sumrating'];

    // get the total number of ratings against all reviews
    $ratingscount=(int)$rs['countrating'];  

    // get the population mediam
    $mean = $ratingssum / $ratingscount;    

    // determine the variance of the population
    $variance = 0;
    $sql="SELECT rating AS score FROM reviews";
    $rs=mysqli_query($scx_dbh,$sql);
    while($row=mysqli_fetch_array($rs)){        
        $score = (int)$row['score'];        
        $variance += pow(($score-$mean),2);                     
    }
    $variance = $variance/$ratingscount;

    // loop through all clubs and implement new rating
    $scores=array();
    $sql="SELECT locid,COUNT(reviewid) AS locationrecordcount,AVG(rating) AS locationmedian FROM reviews GROUP BY locid";
    $rs=mysqli_query($scx_dbh,$sql);

    /// begin loop
    while($row=mysqli_fetch_array($rs)){

        // get the number of review votes for this club
        $numvotes=(int)$row['locationrecordcount'];

        // get the location id 
        $locId = (int)$row['locid'];

        // find the standard deviation for this club (total variance * numclubvotes)
        $standarddev=sqrt($variance*$numvotes);

        // create the new rating for this club with 1 standard deviation less
        $oldRating=$row['locationmedian'];          
        $newRating=$oldRating-$standarddev;
        $scores[$locId] = array(            
          'numvotes'=>$numvotes,
          'standard-deviation'=>$standarddev,
          'original-rating'=> $oldRating,
          'weighted-rating'=>$newRating
       );
    }

    usort($scores,function($a,$b){
        return $a['weighted-rating']-$b['weighted-rating'];
    });

以下是我的研究结果：

前10名

 [0] => Array
        (
            [numvotes] => 1121
            [standard-deviation] => 68.898321138853
            [original-rating] => 4.415700267618207
            [weighted-rating] => -64.482620871235
        )

    [1] => Array
        (
            [numvotes] => 909
            [standard-deviation] => 62.042283630954
            [original-rating] => 3.1290979097910174
            [weighted-rating] => -58.913185721163
        )

    [2] => Array
        (
            [numvotes] => 594
            [standard-deviation] => 50.153247058093
            [original-rating] => 4.414225589225589
            [weighted-rating] => -45.739021468868
        )

    [3] => Array
        (
            [numvotes] => 505
            [standard-deviation] => 46.243587892712
            [original-rating] => 4.090099009900985
            [weighted-rating] => -42.153488882811
        )

    [4] => Array
        (
            [numvotes] => 517
            [standard-deviation] => 46.78979093937
            [original-rating] => 4.661025145067699
            [weighted-rating] => -42.128765794302
        )

    [5] => Array
        (
            [numvotes] => 505
            [standard-deviation] => 46.243587892712
            [original-rating] => 3.2117821782178173
            [weighted-rating] => -43.031805714494
        )

    [6] => Array
        (
            [numvotes] => 398
            [standard-deviation] => 41.053233483774
            [original-rating] => 4.231155778894469
            [weighted-rating] => -36.822077704879
        )

    [7] => Array
        (
            [numvotes] => 340
            [standard-deviation] => 37.944190471069
            [original-rating] => 3.9102941176470547
            [weighted-rating] => -34.033896353422
        )

    [8] => Array
        (
            [numvotes] => 323
            [standard-deviation] => 36.983422110177
            [original-rating] => 3.261145510835913
            [weighted-rating] => -33.722276599341
        )

    [9] => Array
        (
            [numvotes] => 280
            [standard-deviation] => 34.433791770728
            [original-rating] => 3.36767857142857
            [weighted-rating] => -31.066113199299
        )

    [10] => Array
        (
            [numvotes] => 254
            [standard-deviation] => 32.796136967109
            [original-rating] => 3.1411417322834665
            [weighted-rating] => -29.654995234825
        )

最差10

[232] => Array
    (
        [numvotes] => 2
        [standard-deviation] => 2.9101865621466
        [original-rating] => 4.95
        [weighted-rating] => 2.0398134378534
    )

[233] => Array
    (
        [numvotes] => 2
        [standard-deviation] => 2.9101865621466
        [original-rating] => 5
        [weighted-rating] => 2.0898134378534
    )

[234] => Array
    (
        [numvotes] => 1
        [standard-deviation] => 2.0578126526118
        [original-rating] => 4
        [weighted-rating] => 1.9421873473882
    )

[235] => Array
    (
        [numvotes] => 2
        [standard-deviation] => 2.9101865621466
        [original-rating] => 4.8
        [weighted-rating] => 1.8898134378534
    )

[236] => Array
    (
        [numvotes] => 1
        [standard-deviation] => 2.0578126526118
        [original-rating] => 3.25
        [weighted-rating] => 1.1921873473882
    )

[237] => Array
    (
        [numvotes] => 1
        [standard-deviation] => 2.0578126526118
        [original-rating] => 5
        [weighted-rating] => 2.9421873473882
    )

[238] => Array
    (
        [numvotes] => 1
        [standard-deviation] => 2.0578126526118
        [original-rating] => 5
        [weighted-rating] => 2.9421873473882
    )

[239] => Array
    (
        [numvotes] => 1
        [standard-deviation] => 2.0578126526118
        [original-rating] => 4.1
        [weighted-rating] => 2.0421873473882
    )

[240] => Array
    (
        [numvotes] => 1
        [standard-deviation] => 2.0578126526118
        [original-rating] => 5
        [weighted-rating] => 2.9421873473882
    )

[241] => Array
    (
        [numvotes] => 2
        [standard-deviation] => 2.9101865621466
        [original-rating] => 5
        [weighted-rating] => 2.0898134378534
    )

)

更新

好的，我重新计算了standard deviation对整个种群的影响。是2.0578126526118。

以下是我的当前代码：

    $sql="SELECT SUM(reviews.rating) AS sumrating,COUNT(reviews.rating) AS countrating FROM reviews";   
    $rs=mysqli_fetch_array(mysqli_query($scx_dbh,$sql));    
    $ratingssum=(int)$rs['sumrating'];
    $ratingscount=(int)$rs['countrating'];  
    $mean = $ratingssum / $ratingscount;    
    $variance = 0;
    $sql="SELECT rating AS score FROM reviews";
    $rs=mysqli_query($scx_dbh,$sql);
    while($row=mysqli_fetch_array($rs)){        
        $score = (int)$row['score'];        
        $variance += pow(($score-$mean),2);                     
    }
    $variance = $variance/$ratingscount;
    $standarddev=sqrt($variance);
    $scores=array();
    $sql="SELECT locid,COUNT(reviewid) AS locationrecordcount,AVG(rating) AS locationmedian FROM reviews GROUP BY locid";
    $rs=mysqli_query($scx_dbh,$sql);
    while($row=mysqli_fetch_array($rs)){
        $numvotes=(int)$row['locationrecordcount'];
        $locId = (int)$row['locid'];        
        $oldRating=$row['locationmedian'];
        $newRating=$oldRating-$standarddev;
        $scores[$locId] = array(            
            'numvotes'=>$numvotes,
            'standard-deviation'=>$standarddev,
            'original-rating'=> $oldRating,
            'weighted-rating'=>$newRating
        );
    }   
    usort($scores,function($a,$b){
        return (int)($a['weighted-rating']-$b['weighted-rating']);
    });

1./我认为我的排序功能不正确。在使用我的排序函数进行排序之后，以下是前5位：

     [0] => Array
            (
                [numvotes] => 1
                [standard-deviation] => 2.0578126526118
                [original-rating] => 0.2
                [weighted-rating] => -1.8578126526118
            )

        [1] => Array
            (
                [numvotes] => 1
                [standard-deviation] => 2.0578126526118
                [original-rating] => 0.05
                [weighted-rating] => -2.0078126526118
            )

        [2] => Array
            (
                [numvotes] => 4
                [standard-deviation] => 2.0578126526118
                [original-rating] => 0.7625
                [weighted-rating] => -1.2953126526118
            )

        [3] => Array
            (
                [numvotes] => 1
                [standard-deviation] => 2.0578126526118
                [original-rating] => 0.1
                [weighted-rating] => -1.9578126526118
            )

        [4] => Array
            (
                [numvotes] => 1
                [standard-deviation] => 2.0578126526118
                [original-rating] => 0.4
                [weighted-rating] => -1.6578126526118
            )

可以看到，除了产生负数外，位置1(索引0)的weighted-average是-1.85，位置2(索引1)是-2.00。我想，我的算法或我的代码or else why are there negative numbers being sorted as first中的排序函数都有问题。

而且，当俱乐部有1票的时候，我会让他们站在第1位。这个算法的目的是清除这些俱乐部，这样我就可以专注于拥有1000张选票的俱乐部。

以下是倒数第五位：

       [237] => Array
            (
                [numvotes] => 29
                [standard-deviation] => 2.0578126526118
                [original-rating] => 4.112068965517241
                [weighted-rating] => 2.0542563129054
            )

        [238] => Array
            (
                [numvotes] => 5
                [standard-deviation] => 2.0578126526118
                [original-rating] => 3.8800000000000003
                [weighted-rating] => 1.8221873473882
            )

        [239] => Array
            (
                [numvotes] => 31
                [standard-deviation] => 2.0578126526118
                [original-rating] => 3.7499999999999996
                [weighted-rating] => 1.6921873473882
            )

        [240] => Array
            (
                [numvotes] => 1
                [standard-deviation] => 2.0578126526118
                [original-rating] => 5
                [weighted-rating] => 2.9421873473882
            )

        [241] => Array
            (
                [numvotes] => 1
                [standard-deviation] => 2.0578126526118
                [original-rating] => 4.45
                [weighted-rating] => 2.3921873473882
            )

同样的行为出现在底部5。位置5(指数241)为weighted-average of 2.39，位置4(索引240)为weighted-average 2.94。

Answer 1

标准差是按变化的平方根计算的，而不是用变化的平方根乘以人口(数字)计算的：

// find the standard deviation for this club (total variance)
$standarddev=sqrt($variance);

如果你想自己衡量每个俱乐部，那么你需要计算每个俱乐部的变化(和标准差)。要做到这一点，你需要的只是每个俱乐部的票数之和，而不是所有的选票，然后计算变化和标准差。那么，所有选票的变异和标准差似乎都是不必要的。

更新：

你想要完成的事情(用很少的选票淘汰俱乐部)不能用标准差(σ)来完成。

接待员：

• 一个俱乐部有1: 5的票数，σ是0。5/1=5, (5-5)^2 / 1=0, sqrt(0)=0
• 一家俱乐部有1票:1。σ又是0。1/1=1, (1-1)^2 / 1=0, sqrt(0)=0
• 一家俱乐部有2票: 5票，5票。σ又是0票。10/2=5, ((5-5)^2 + (5-5)^2) / 2=0, sqrt(0)=0

现在你会认为你可以用低σ来清除那些俱乐部。

• 俱乐部有2票: 1票，5票。σ现在是2.83票。6/2=3, ((1-3)^2 + (5-3)^2) / 2=8, sqrt(8)=2.83

正如你所看到的，这里没有说“嘿，这个俱乐部获得了很多选票”。σ说的唯一一件事是选票的差距有多大。如果没有或小的传播(变化)，那么σ将是0或小，反之亦然。

你可以尝试的是看看俱乐部σ(Cσ)和总σ(Tσ)之间的区别。如果这个值接近0(我们假设为0.1)，那么你就会知道，俱乐部和整个人群都有类似的变化。但这仍不能保证至少有x票。这种计算方式类似于abs(Cσ - Tσ) < 0.1。

关于您的排序功能：

usort期望返回的整数为-1、0或1才能正常工作。当你开始减去负数时，你会得到相当奇怪的结果。正确的排序函数应该如下所示：

usort($scores, function cmp($a, $b)
{
  if ($a['weighted-rating'] == $b['weighted-rating']) {
    return 0;
  }
  return ($a['weighted-rating'] < $b['weighted-rating']) ? -1 : 1;
}

Answer 2

$standarddev=sqrt($variance*$numvotes);

应该是

$standarddev=sqrt($variance);

编辑

你的问题是在你的逻辑中找不到错误。原因是你有一个很大的复杂函数。您应该研究测试驱动的开发，并将您的代码分成小的、易于测试的工作单元。对于每个工作单元，您可以测试不同输入值的预期输出。这样，就可以更容易地排除代码的部分，例如stdCalculator，因为该部分包含在一系列测试用例中。