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首頁精彩閱讀利用統(tǒng)計學知識為android應用的啟動時間做數(shù)據(jù)分析
利用統(tǒng)計學知識為android應用的啟動時間做數(shù)據(jù)分析
2016-01-31
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利用統(tǒng)計學知識為android應用的啟動時間做數(shù)據(jù)分析

一.數(shù)據(jù)說明

啟動時間用同一臺設備，同一個包進行啟動時間的測試，其中三組樣本數(shù)據(jù)（每組100份對比數(shù)據(jù)）如下:

  • 設備pro-5-1 
base_list_1 = [0.944, 0.901, 0.957, 0.911, 1.189, 0.93, 0.94, 0.932, 0.951, 0.911, 0.934, 0.903, 0.922, 0.917, 0.931, 0.962, 0.945, 1.254, 0.918, 0.913, 0.931, 0.935, 0.89, 0.948, 0.932, 0.931, 0.875, 0.96, 1.117, 0.905, 0.955, 0.914, 0.95, 0.933, 0.941, 0.905, 0.919, 1.124, 0.953, 0.918, 0.942, 0.918, 0.914, 0.907, 0.942, 0.907, 0.895, 0.917, 0.927, 0.908, 0.915, 0.914, 0.945, 0.933, 0.894, 0.958, 0.885, 0.971, 0.94, 1.261, 0.949, 0.922, 1.009, 0.941, 0.942, 0.907, 0.913, 0.874, 0.963, 0.951, 0.972, 0.94, 0.952, 0.941, 0.954, 0.914, 0.951, 0.899, 0.908, 0.945, 0.934, 0.922, 0.92, 0.959, 0.946, 0.892, 0.847, 0.96, 0.973, 0.928, 0.913, 0.935, 0.939, 0.967, 0.907, 0.94, 0.927, 0.88, 1.004, 0.986]

cmp_list_1 = [0.931, 0.947, 0.965, 0.912, 0.966, 0.974, 0.97, 0.971, 0.958, 0.938, 0.949, 0.972, 0.946, 0.915, 0.906, 0.926, 0.955, 0.93, 0.931, 0.979, 0.952, 1.062, 0.921, 1.002, 0.927, 0.942, 0.991, 0.898, 1.121, 1.006, 0.941, 0.953, 1.013, 0.979, 0.997, 0.961, 0.947, 0.96, 0.966, 0.917, 1.002, 0.955, 0.946, 0.99, 0.945, 0.911, 0.923, 0.94, 0.933, 0.954, 0.907, 0.961, 0.937, 0.941, 0.897, 0.954, 0.979, 0.927, 0.957, 0.944, 0.961, 0.924, 0.953, 0.954, 0.929, 0.926, 0.965, 0.95, 0.964, 0.895, 0.921, 0.945, 0.955, 0.96, 0.962, 0.907, 0.933, 0.955, 0.921, 0.959, 0.934, 0.973, 0.977, 0.938, 0.945, 0.949, 0.932, 0.976, 0.947, 0.941, 0.898, 0.942, 0.887, 0.963, 0.931, 0.999, 0.915, 0.947, 0.958, 0.988]
  • 設備pro-5-2 
base_list_2 = [0.887, 0.926, 0.931, 0.918, 0.905, 0.896, 0.889, 0.922, 0.923, 0.919, 0.927, 0.904, 0.927, 1.039, 0.933, 1.209, 0.935, 0.882, 0.947, 0.914, 0.871, 0.924, 0.922, 0.943, 0.902, 0.938, 0.896, 0.906, 0.939, 0.899, 0.934, 0.923, 0.927, 0.911, 0.943, 0.886, 0.844, 0.913, 0.907, 0.954, 0.934, 0.854, 0.953, 0.903, 0.931, 0.838, 0.936, 0.955, 0.943, 0.933, 0.901, 1.18, 0.907, 0.883, 0.885, 0.909, 0.94, 0.939, 0.889, 0.917, 0.933, 0.904, 0.888, 0.953, 0.936, 0.947, 0.927, 0.881, 0.914, 0.937, 0.898, 0.914, 0.929, 0.945, 0.935, 0.902, 0.939, 0.925, 0.909, 0.903, 0.92, 0.917, 0.987, 0.911, 0.889, 0.888, 0.91, 0.941, 0.904, 0.911, 0.908, 0.793, 1.113, 0.947, 0.876, 0.908, 0.91, 0.921, 0.941, 0.987]

cmp_list_1 = [0.929, 0.94, 0.931, 0.978, 0.965, 0.938, 0.941, 0.937, 0.91, 0.92, 0.934, 0.92, 0.981, 0.939, 0.928, 0.95, 0.94, 0.928, 0.925, 0.933, 0.963, 0.954, 0.987, 0.965, 0.96, 0.94, 0.966, 0.96, 0.942, 0.969, 0.978, 0.964, 0.921, 0.964, 0.939, 0.97, 0.961, 0.945, 1.004, 0.951, 0.916, 0.942, 0.955, 0.975, 0.947, 0.917, 0.944, 0.943, 0.905, 0.955, 0.96, 0.994, 0.925, 0.922, 0.958, 0.957, 0.958, 0.907, 0.981, 0.937, 0.959, 0.919, 0.959, 0.932, 0.951, 0.927, 0.949, 0.949, 0.944, 0.913, 0.967, 0.981, 0.942, 0.949, 0.932, 0.933, 0.97, 0.931, 0.918, 0.972, 0.95, 0.962, 0.988, 1.0, 1.003, 0.949, 0.933, 0.955, 0.934, 0.952, 0.937, 0.977, 0.936, 0.991, 0.986, 0.943, 0.997, 0.975, 0.991, 0.984]
  • 設備mx4-pro 
base_list_1 = [1.359, 1.415, 1.395, 1.318, 1.345, 1.417, 1.36, 1.373, 1.337, 1.332, 1.498, 1.318, 1.392, 1.364, 1.397, 1.793, 1.341, 1.364, 1.428, 1.345, 1.418, 1.364, 1.372, 1.541, 1.465, 1.373, 1.337, 1.52, 1.375, 1.367, 1.366, 1.347, 1.334, 1.422, 1.354, 1.369, 1.413, 1.345, 1.373, 1.363, 1.464, 1.344, 1.324, 1.331, 1.405, 1.355, 1.674, 1.38, 1.352, 1.339, 1.326, 1.362, 1.431, 1.774, 1.312, 1.292, 1.384, 1.473, 1.337, 1.406, 1.412, 1.385, 1.292, 1.384, 1.342, 1.333, 1.435, 1.372, 1.42, 1.315, 1.344, 1.414, 1.51, 1.334, 1.308, 1.468, 1.401, 1.316, 1.373, 1.407, 1.474, 1.382, 1.346, 1.373, 1.366, 1.378, 1.315, 1.417, 1.431, 1.379, 1.324, 1.383, 1.349, 1.4, 1.327, 1.734, 1.395, 1.412, 1.438, 1.384]

cmp_list_1 = [1.414, 1.326, 1.421, 1.371, 1.363, 1.36, 1.417, 1.34, 1.357, 1.429, 1.308, 1.324, 1.351, 1.323, 1.367, 1.412, 1.391, 1.661, 1.34, 1.38, 1.528, 1.417, 1.352, 1.569, 1.32, 1.473, 1.531, 1.445, 1.407, 1.529, 1.356, 1.349, 1.362, 1.358, 1.375, 1.365, 1.317, 1.302, 1.342, 1.351, 1.393, 1.473, 1.392, 1.299, 1.367, 1.381, 1.354, 1.374, 1.551, 1.448, 1.387, 1.361, 1.358, 1.362, 1.568, 1.343, 1.334, 1.378, 1.417, 1.382, 1.421, 1.345, 1.336, 1.302, 1.349, 1.381, 1.374, 1.359, 1.38, 1.553, 1.34, 1.269, 1.353, 1.329, 1.649, 1.392, 1.367, 1.377, 1.403, 1.361, 1.352, 1.466, 1.389, 1.346, 1.345, 1.35, 1.383, 1.446, 1.613, 1.395, 1.402, 1.394, 1.348, 1.353, 1.395, 1.345, 1.274, 1.425, 1.351, 1.586]

二.正態(tài)性檢驗（采用spss）

進行正態(tài)性檢驗的目的是為了驗證我們的測試數(shù)據(jù)樣本是不是符合正態(tài)分布（近似），而且下面的統(tǒng)計學利用是需要在正態(tài)分布下進行的，因此，進行正態(tài)性檢驗是必備的。下列圖對應的是區(qū)域內的頻數(shù)統(tǒng)計

因為是同一臺設備的同一個場景，因此可知左右兩邊的分布應該是近似一致的。通過觀察Q-Q圖與Q-Q去勢圖可以斷定，我們的啟動時間是符合正態(tài)分布的。但需要注意的是，base_list_2跟cmp_list_2的分布，方差明顯差很多，可以看出數(shù)據(jù)分布更加零散（基本可以斷定第二組數(shù)據(jù)是不能拿來作為對比的），而其他幾組幾乎是同形狀的分布。

三.顯著性檢驗

方差齊性檢驗的目的是為了檢驗兩組數(shù)據(jù)兩兩對比的差異，從而判斷兩組數(shù)據(jù)的數(shù)據(jù)來源分布是否一致。能否通過方差齊性檢驗，是我們能否采用這組數(shù)據(jù)作為對比數(shù)據(jù)的前提標準。

判斷腳本如下 

#coding:utf-8
import MySQLdb
import json
import numpy as np
from scipy.stats import levene
import threading
 
import matplotlib.pyplot as plt
import matplotlib.mlab as mlab
 
class DBOperate(object):
    def __init__(self, host, user, db, passwd, port):
        self.host = host
        self.user = user
        self.db = db
        self.passwd = passwd
        self.port = port
        self.conn = MySQLdb.connect(
            host = self.host,
            user = self.user,
            passwd = self.passwd,
            db = self.db,
            port = self.port)
        self.cur = self.conn.cursor()
 
    def execute(self,sql):
        try:
            self.cur.execute(sql)
            self.conn.commit()
            print "======sql執(zhí)行成功: ",sql
        except Exception as e:
            print e
 
    def getData(self,sql):
        try:
            self.cur.execute(sql)
            result = self.cur.fetchall()
            return result
        except Exception as e:
            print e
 
    def close(self):
        self.cur.close()
        self.conn.close()   
 
class MathTools(object):
    def __init__(self,base_data,cmp_data):
        self.base_data = base_data
        self.cmp_data = cmp_data
 
    def testVar(self):
        '''方差齊性檢驗
        '''
        result = levene(self.base_data,self.cmp_data)
        print result
        if float(result[1]) > 0.05:
            print "方差齊性檢驗通過,可以認為方差相等(說明硬件或者執(zhí)行時間不同可能帶來的誤差可以忽略)!"
 
    def getMeanAndVar(self):
        '''獲取樣本均值跟方差
        '''
        for each in [self.base_data,self.cmp_data]:
            mean = np.mean(each)       
            var = np.var(each)
            std = np.std(each)
            print "==================="
            print "均值:",mean
            print "方差:",var
            print "標準差:",std
            print "==================="
        return mean,var,std
 
 
def drawPlot(avg,std):
    x = np.linspace(0.5,1.5,10000)
    plt.plot(x,mlab.normpdf(x,avg,std))
    plt.show()
         
def dataAnalysis(tuple_data):
    avg_list = []
    for each_tuple in tuple_data:
        str_data = each_tuple[0]
        dic_data = json.loads(str_data)
        avg_time = float(dic_data['intervalStartTime'])
        avg_list.append(avg_time)
    return avg_list
 
def outputData(dboperate,task_id_1,task_id_2):
    data_base = dboperate.getData('''SELECT start_time_log from uctc_qms_start_time WHERE task_id=%s'''%task_id_1)
    data_cmp = dboperate.getData('''SELECT start_time_log from uctc_qms_start_time WHERE task_id=%s'''%task_id_2)
    base_list = dataAnalysis(data_base)
    cmp_list = dataAnalysis(data_cmp)
    return base_list,cmp_list
 
    
def main():
    dboperate = DBOperate(
        host="xxxx",
        user="xxxx",
        passwd="xxxx",
        db="xxxx",
        port=3306)
    base_list_1,cmp_list_1 = outputData(dboperate,216674,216675)
    print "base_list_1:\n",base_list_1
    print "cmp_list_1:\n",cmp_list_1
    mt = MathTools(base_list_1,cmp_list_1)
    mt.testVar()
    avg_list = mt.getMeanAndVar()
    base_list_2,cmp_list_2 = outputData(dboperate,216679,216680)
    print "base_list_2:\n",base_list_2
    print "cmp_list_2:\n",cmp_list_2
    mt2 = MathTools(base_list_2,cmp_list_2)
    mt2.testVar()
    mt2.getMeanAndVar()
 
    base_list_3,cmp_list_3 = outputData(dboperate,216677,216682)
    print "base_list_1:\n",base_list_3
    print "cmp_list_1:\n",cmp_list_3
    mt3 = MathTools(base_list_3,cmp_list_3)
    mt3.testVar()
    mt3.getMeanAndVar()    
     
    dboperate.close()
     
    
 
if __name__ == '__main__':
    main()

分別對三組數(shù)據(jù)做方差齊性檢驗發(fā)現(xiàn)第二組數(shù)據(jù)沒有通過方差齊性檢驗，第二組數(shù)據(jù)中base_list_2跟cmp_list_2存在顯著性差異，由于我們的測試是用了同一設備的同一個包進行同一種測試，因此可以斷定第二組數(shù)據(jù)必須過濾掉。 


base_list_1:
[0.944, 0.901, 0.957, 0.911, 1.189, 0.93, 0.94, 0.932, 0.951, 0.911, 0.934, 0.903, 0.922, 0.917, 0.931, 0.962, 0.945, 1.254, 0.918, 0.913, 0.931, 0.935, 0.89, 0.948, 0.932, 0.931, 0.875, 0.96, 1.117, 0.905, 0.955, 0.914, 0.95, 0.933, 0.941, 0.905, 0.919, 1.124, 0.953, 0.918, 0.942, 0.918, 0.914, 0.907, 0.942, 0.907, 0.895, 0.917, 0.927, 0.908, 0.915, 0.914, 0.945, 0.933, 0.894, 0.958, 0.885, 0.971, 0.94, 1.261, 0.949, 0.922, 1.009, 0.941, 0.942, 0.907, 0.913, 0.874, 0.963, 0.951, 0.972, 0.94, 0.952, 0.941, 0.954, 0.914, 0.951, 0.899, 0.908, 0.945, 0.934, 0.922, 0.92, 0.959, 0.946, 0.892, 0.847, 0.96, 0.973, 0.928, 0.913, 0.935, 0.939, 0.967, 0.907, 0.94, 0.927, 0.88, 1.004, 0.986]
cmp_list_1:
[0.931, 0.947, 0.965, 0.912, 0.966, 0.974, 0.97, 0.971, 0.958, 0.938, 0.949, 0.972, 0.946, 0.915, 0.906, 0.926, 0.955, 0.93, 0.931, 0.979, 0.952, 1.062, 0.921, 1.002, 0.927, 0.942, 0.991, 0.898, 1.121, 1.006, 0.941, 0.953, 1.013, 0.979, 0.997, 0.961, 0.947, 0.96, 0.966, 0.917, 1.002, 0.955, 0.946, 0.99, 0.945, 0.911, 0.923, 0.94, 0.933, 0.954, 0.907, 0.961, 0.937, 0.941, 0.897, 0.954, 0.979, 0.927, 0.957, 0.944, 0.961, 0.924, 0.953, 0.954, 0.929, 0.926, 0.965, 0.95, 0.964, 0.895, 0.921, 0.945, 0.955, 0.96, 0.962, 0.907, 0.933, 0.955, 0.921, 0.959, 0.934, 0.973, 0.977, 0.938, 0.945, 0.949, 0.932, 0.976, 0.947, 0.941, 0.898, 0.942, 0.887, 0.963, 0.931, 0.999, 0.915, 0.947, 0.958, 0.988]
(2.585452271112739, 0.10944298973519527)
方差齊性檢驗通過,可以認為方差相等(說明硬件或者執(zhí)行時間不同可能帶來的誤差可以忽略)!
===================
均值: 0.9432
方差: 0.00405766
標準差: 0.0636997645208
===================
===================
均值: 0.95079
方差: 0.0011006859
標準差: 0.0331765866237
===================
base_list_2:
[0.887, 0.926, 0.931, 0.918, 0.905, 0.896, 0.889, 0.922, 0.923, 0.919, 0.927, 0.904, 0.927, 1.039, 0.933, 1.209, 0.935, 0.882, 0.947, 0.914, 0.871, 0.924, 0.922, 0.943, 0.902, 0.938, 0.896, 0.906, 0.939, 0.899, 0.934, 0.923, 0.927, 0.911, 0.943, 0.886, 0.844, 0.913, 0.907, 0.954, 0.934, 0.854, 0.953, 0.903, 0.931, 0.838, 0.936, 0.955, 0.943, 0.933, 0.901, 1.18, 0.907, 0.883, 0.885, 0.909, 0.94, 0.939, 0.889, 0.917, 0.933, 0.904, 0.888, 0.953, 0.936, 0.947, 0.927, 0.881, 0.914, 0.937, 0.898, 0.914, 0.929, 0.945, 0.935, 0.902, 0.939, 0.925, 0.909, 0.903, 0.92, 0.917, 0.987, 0.911, 0.889, 0.888, 0.91, 0.941, 0.904, 0.911, 0.908, 0.793, 1.113, 0.947, 0.876, 0.908, 0.91, 0.921, 0.941, 0.987]
cmp_list_2:
[0.929, 0.94, 0.931, 0.978, 0.965, 0.938, 0.941, 0.937, 0.91, 0.92, 0.934, 0.92, 0.981, 0.939, 0.928, 0.95, 0.94, 0.928, 0.925, 0.933, 0.963, 0.954, 0.987, 0.965, 0.96, 0.94, 0.966, 0.96, 0.942, 0.969, 0.978, 0.964, 0.921, 0.964, 0.939, 0.97, 0.961, 0.945, 1.004, 0.951, 0.916, 0.942, 0.955, 0.975, 0.947, 0.917, 0.944, 0.943, 0.905, 0.955, 0.96, 0.994, 0.925, 0.922, 0.958, 0.957, 0.958, 0.907, 0.981, 0.937, 0.959, 0.919, 0.959, 0.932, 0.951, 0.927, 0.949, 0.949, 0.944, 0.913, 0.967, 0.981, 0.942, 0.949, 0.932, 0.933, 0.97, 0.931, 0.918, 0.972, 0.95, 0.962, 0.988, 1.0, 1.003, 0.949, 0.933, 0.955, 0.934, 0.952, 0.937, 0.977, 0.936, 0.991, 0.986, 0.943, 0.997, 0.975, 0.991, 0.984]
(4.5987224867656273, 0.0332145312054625)
===================
均值: 0.92446
方差: 0.0028034084
標準差: 0.0529472227789
===================
===================
均值: 0.95108
方差: 0.0005381736
標準差: 0.0231985689214
 
===================
base_list_3:
[1.359, 1.415, 1.395, 1.318, 1.345, 1.417, 1.36, 1.373, 1.337, 1.332, 1.498, 1.318, 1.392, 1.364, 1.397, 1.793, 1.341, 1.364, 1.428, 1.345, 1.418, 1.364, 1.372, 1.541, 1.465, 1.373, 1.337, 1.52, 1.375, 1.367, 1.366, 1.347, 1.334, 1.422, 1.354, 1.369, 1.413, 1.345, 1.373, 1.363, 1.464, 1.344, 1.324, 1.331, 1.405, 1.355, 1.674, 1.38, 1.352, 1.339, 1.326, 1.362, 1.431, 1.774, 1.312, 1.292, 1.384, 1.473, 1.337, 1.406, 1.412, 1.385, 1.292, 1.384, 1.342, 1.333, 1.435, 1.372, 1.42, 1.315, 1.344, 1.414, 1.51, 1.334, 1.308, 1.468, 1.401, 1.316, 1.373, 1.407, 1.474, 1.382, 1.346, 1.373, 1.366, 1.378, 1.315, 1.417, 1.431, 1.379, 1.324, 1.383, 1.349, 1.4, 1.327, 1.734, 1.395, 1.412, 1.438, 1.384]
cmp_list_3:
[1.414, 1.326, 1.421, 1.371, 1.363, 1.36, 1.417, 1.34, 1.357, 1.429, 1.308, 1.324, 1.351, 1.323, 1.367, 1.412, 1.391, 1.661, 1.34, 1.38, 1.528, 1.417, 1.352, 1.569, 1.32, 1.473, 1.531, 1.445, 1.407, 1.529, 1.356, 1.349, 1.362, 1.358, 1.375, 1.365, 1.317, 1.302, 1.342, 1.351, 1.393, 1.473, 1.392, 1.299, 1.367, 1.381, 1.354, 1.374, 1.551, 1.448, 1.387, 1.361, 1.358, 1.362, 1.568, 1.343, 1.334, 1.378, 1.417, 1.382, 1.421, 1.345, 1.336, 1.302, 1.349, 1.381, 1.374, 1.359, 1.38, 1.553, 1.34, 1.269, 1.353, 1.329, 1.649, 1.392, 1.367, 1.377, 1.403, 1.361, 1.352, 1.466, 1.389, 1.346, 1.345, 1.35, 1.383, 1.446, 1.613, 1.395, 1.402, 1.394, 1.348, 1.353, 1.395, 1.345, 1.274, 1.425, 1.351, 1.586]
(0.0077692351582683648, 0.92985189389348166)
方差齊性檢驗通過,可以認為方差相等(說明硬件或者執(zhí)行時間不同可能帶來的誤差可以忽略)!
===================
均值: 1.39346
方差: 0.0075982484
標準差: 0.0871679321769
===================
===================
均值: 1.39223
方差: 0.0058431971
標準差: 0.0764408078189
===================

2.T檢驗

如果均值的誤差重疊，則認為軟件迭代對性能沒有影響。顯著性檢驗是為了檢查兩組樣本有沒有顯著性差異，通過校驗可以說明這兩組數(shù)據(jù)的可信度。

其實T檢驗更適合服從正態(tài)分布的小樣本判斷，大樣本應采用z檢驗。但由于我對小樣本跟大樣本都有對應測試，得到了同樣的結論（ps:具體t值不同），故這里暫時先用原來的大樣本來處理。

顯著性檢驗腳本： 

#!/usr/bin/python  
import string  
import math  
import sys  
   
from scipy.stats import  t  
import matplotlib.pyplot as plt  
import numpy as np  
   
##############  
# Parameters #  
##############  
ver = 1 
verbose = 0 
alpha = 0.05 
   
def usage():  
    print """ 
    usage: ./program data_file(one sample in one line) 
    """ 
   
def main():  
   
    sample1 = [1.15, 1.119, 1.098, 1.147, 1.092, 1.131, 1.17, 1.138, 1.115, 1.143, 1.126, 1.182, 1.124, 1.145, 1.093, 1.131, 1.102, 1.191, 1.093, 1.089, 1.115, 1.128, 1.119, 1.163, 1.143, 1.114, 1.098, 1.142, 1.126, 1.213, 1.279, 1.125, 1.174, 1.103, 1.13, 1.089, 1.164, 1.106, 1.155, 1.085, 1.186, 1.155, 1.207, 1.081, 1.122, 1.112, 1.137, 1.096, 1.078, 1.122, 1.11, 1.095, 1.132, 1.134, 1.118, 1.117, 1.116, 1.116, 1.108, 1.14, 1.099, 1.124, 1.113, 1.203, 1.135, 1.124, 1.098, 1.105, 1.082, 1.107, 1.155, 1.164, 1.096, 1.175, 1.17, 1.161, 1.093, 1.152, 1.085, 0.969, 1.068, 0.95, 1.077, 0.999, 1.147, 1.144, 1.097, 1.119, 1.126, 1.148, 1.083, 1.106, 1.107, 1.094, 1.121, 1.136, 1.086, 1.141, 1.119, 1.153]
    sample2 = [1.154, 1.094, 1.131, 1.087, 1.148, 1.046, 1.228, 1.142, 0.931, 1.063, 1.12, 1.08, 1.129, 1.073, 1.116, 1.081, 1.177, 1.081, 1.133, 1.093, 1.13, 1.085, 1.125, 1.062, 1.133, 1.062, 0.927, 1.055, 1.202, 1.162, 1.102, 1.098, 1.126, 1.144, 1.088, 1.131, 1.105, 1.094, 1.099, 1.112, 1.158, 1.181, 1.107, 0.937, 1.082, 1.1, 1.06, 1.114, 1.088, 1.141, 1.085, 1.232, 1.131, 1.155, 1.069, 1.149, 1.088, 1.125, 1.074, 1.13, 1.053, 1.102, 1.128, 1.166, 1.101, 1.192, 1.073, 1.131, 1.057, 1.098, 1.077, 1.119, 1.084, 1.164, 1.114, 1.148, 1.063, 1.113, 1.084, 1.063, 1.05, 1.078, 1.112, 1.181, 1.109, 1.087, 1.075, 1.078, 1.109, 1.081, 1.104, 1.059, 1.099, 1.142, 1.084, 1.084, 1.09, 1.089, 1.14, 1.105]
     
    sample_len = len(sample1)
    sample_diff = []  
   
    for i in range(sample_len):  
        sample_diff.append(sample1[i] - sample2[i])  
   
    if (verbose):  
        print("sample_diff = ", sample_diff)  
   
   
    ######################  
    # Hypothesis testing #  
    ######################  
    sample = sample_diff  
   
    numargs = t.numargs  
    [ df ] = [sample_len - 1,] * numargs  
    if (verbose):  
        print("df(degree of freedom, student's t distribution parameter) = ", df)  
   
    sample_mean = np.mean(sample)  
    sample_std = np.std(sample, dtype=np.float64, ddof=1)  
    if (verbose):  
        print("mean = %f, std = %f" % (sample_mean, sample_std))  
   
    abs_t = math.fabs( sample_mean / (sample_std / math.sqrt(sample_len)) )  
    if (verbose):  
        print("t = ", abs_t)  
   
    t_alpha_percentile = t.ppf(1 - alpha / 2, df)  
   
    if (verbose):  
        print("abs_t = ", abs_t)  
        print("t_alpha_percentile = ", t_alpha_percentile)  
   
    if (abs_t >= t_alpha_percentile):  
        print "REJECT the null hypothesis" 
    else:  
        print "ACCEPT the null hypothesis" 
   
    ########  
    # Plot #  
    ########  
    rv = t(df)  
    limit = np.minimum(rv.dist.b, 5)  
    x = np.linspace(-1 * limit, limit)  
    h = plt.plot(x, rv.pdf(x))  
    plt.xlabel('x')  
    plt.ylabel('t(x)')  
    plt.title('Difference significance test')  
    plt.grid(True)  
    plt.axvline(x = t_alpha_percentile, ymin = 0, ymax = 0.095,   
            linewidth=2, color='r')  
    plt.axvline(x = abs_t, ymin = 0, ymax = 0.6,   
            linewidth=2, color='g')  
   
    plt.annotate(r'(1 - $\alpha$ / 2) percentile', xy = (t_alpha_percentile, 0.05),  
            xytext=(t_alpha_percentile + 0.5, 0.09), arrowprops=dict(facecolor = 'black', shrink = 0.05),)  
    plt.annotate('t value', xy = (abs_t, 0.26),  
            xytext=(abs_t + 0.5, 0.30), arrowprops=dict(facecolor = 'black', shrink = 0.05),)  
   
    leg = plt.legend(('Student\'s t distribution', r'(1 - $\alpha$ / 2) percentile', 't value'),   
            'upper left', shadow = True)  
    frame = leg.get_frame()  
    frame.set_facecolor('0.80')  
    for i in leg.get_texts():  
        i.set_fontsize('small')  
   
    for l in leg.get_lines():  
        l.set_linewidth(1.5)  
   
    normalized_sample = [0] * sample_len   
    for i in range(0, sample_len):  
        normalized_sample[i] = (sample[i] - sample_mean) / (sample_std / math.sqrt(sample_len))  
    plt.plot(normalized_sample, [0] * len(normalized_sample), 'ro')  
    plt.show()  
   
if __name__ == "__main__":  
    main()

輪流替換sample里的值。為了保證結果是可行的，先用numpy生成了兩組服從標準正態(tài)分布的測試數(shù)據(jù)來說明。

檢驗結果如下：

輸出為：ACCEPT the null hypothesis。

意思是這兩組數(shù)據(jù)沒有顯著性差異（均值）

另外對我們云測設備的數(shù)據(jù)進行測試。

  1. 第一組測試：

輸出：REJECT the null hypothesis（代表我們數(shù)據(jù)存在顯著性差異）

2.第二組測試：

輸出：REJECT the null hypothesis（代表我們數(shù)據(jù)存在顯著性差異）

3.第三組測試：

輸出：ACCEPT the null hypothesis（代表我們的數(shù)據(jù)沒有顯著性差異）

四.總結

1.通過正態(tài)性檢驗－方差齊性檢驗－t檢驗后，真正能用的數(shù)據(jù)就只剩下第三組。 

base_list_3:
[1.359, 1.415, 1.395, 1.318, 1.345, 1.417, 1.36, 1.373, 1.337, 1.332, 1.498, 1.318, 1.392, 1.364, 1.397, 1.793, 1.341, 1.364, 1.428, 1.345, 1.418, 1.364, 1.372, 1.541, 1.465, 1.373, 1.337, 1.52, 1.375, 1.367, 1.366, 1.347, 1.334, 1.422, 1.354, 1.369, 1.413, 1.345, 1.373, 1.363, 1.464, 1.344, 1.324, 1.331, 1.405, 1.355, 1.674, 1.38, 1.352, 1.339, 1.326, 1.362, 1.431, 1.774, 1.312, 1.292, 1.384, 1.473, 1.337, 1.406, 1.412, 1.385, 1.292, 1.384, 1.342, 1.333, 1.435, 1.372, 1.42, 1.315, 1.344, 1.414, 1.51, 1.334, 1.308, 1.468, 1.401, 1.316, 1.373, 1.407, 1.474, 1.382, 1.346, 1.373, 1.366, 1.378, 1.315, 1.417, 1.431, 1.379, 1.324, 1.383, 1.349, 1.4, 1.327, 1.734, 1.395, 1.412, 1.438, 1.384]
cmp_list_3:
[1.414, 1.326, 1.421, 1.371, 1.363, 1.36, 1.417, 1.34, 1.357, 1.429, 1.308, 1.324, 1.351, 1.323, 1.367, 1.412, 1.391, 1.661, 1.34, 1.38, 1.528, 1.417, 1.352, 1.569, 1.32, 1.473, 1.531, 1.445, 1.407, 1.529, 1.356, 1.349, 1.362, 1.358, 1.375, 1.365, 1.317, 1.302, 1.342, 1.351, 1.393, 1.473, 1.392, 1.299, 1.367, 1.381, 1.354, 1.374, 1.551, 1.448, 1.387, 1.361, 1.358, 1.362, 1.568, 1.343, 1.334, 1.378, 1.417, 1.382, 1.421, 1.345, 1.336, 1.302, 1.349, 1.381, 1.374, 1.359, 1.38, 1.553, 1.34, 1.269, 1.353, 1.329, 1.649, 1.392, 1.367, 1.377, 1.403, 1.361, 1.352, 1.466, 1.389, 1.346, 1.345, 1.35, 1.383, 1.446, 1.613, 1.395, 1.402, 1.394, 1.348, 1.353, 1.395, 1.345, 1.274, 1.425, 1.351, 1.586]
(0.0077692351582683648, 0.92985189389348166)
方差齊性檢驗通過,可以認為方差相等(說明硬件或者執(zhí)行時間不同可能帶來的誤差可以忽略)!
===================
均值: 1.39346
方差: 0.0075982484
標準差: 0.0871679321769
===================
===================
均值: 1.39223
方差: 0.0058431971
標準差: 0.0764408078189
===================

可以看到這兩組數(shù)據(jù)的均值跟方差均比較接近，也是比較符合我們經驗結果的測試數(shù)據(jù)。

2.同一個包，同一臺設備的啟動時間測試結論如下

（1）.三組測試數(shù)據(jù)失敗兩組，足以說明我們的測試很不穩(wěn)定。（需要找目前測試不穩(wěn)定的原因，主要是目前引入的變量）

（2）.兩組樣本通過方差齊性檢驗，說明我們不需要引入新的測試變量，如cpu,內存變化,以及硬件等對啟動時間的影響。

（3）.通過控制t分布的置信區(qū)間，可以動態(tài)調整對應的數(shù)據(jù)均值范圍。

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') } function initGt() { var handler = function (captchaObj) { captchaObj.appendTo('#captcha'); captchaObj.onReady(function () { $("#wait").hide(); }).onSuccess(function(){ $('.getcheckcode').removeClass('dis'); $('.getcheckcode').trigger('click'); }); window.captchaObj = captchaObj; }; $('#captcha').show(); $.ajax({ url: "/login/gtstart?t=" + (new Date()).getTime(), // 加隨機數(shù)防止緩存 type: "get", dataType: "json", success: function (data) { $('#text').hide(); $('#wait').show(); // 調用 initGeetest 進行初始化 // 參數(shù)1：配置參數(shù) // 參數(shù)2：回調，回調的第一個參數(shù)驗證碼對象，之后可以使用它調用相應的接口 initGeetest({ // 以下 4 個配置參數(shù)為必須，不能缺少 gt: data.gt, challenge: data.challenge, offline: !data.success, // 表示用戶后臺檢測極驗服務器是否宕機 new_captcha: data.new_captcha, // 用于宕機時表示是新驗證碼的宕機 product: "float", // 產品形式，包括：float，popup width: "280px", https: true // 更多配置參數(shù)說明請參見：http://docs.geetest.com/install/client/web-front/ }, handler); } }); } function codeCutdown() { if(_wait == 0){ //倒計時完成 $(".getcheckcode").removeClass('dis').html("重新獲取"); }else{ $(".getcheckcode").addClass('dis').html("重新獲取("+_wait+"s)"); _wait--; setTimeout(function () { codeCutdown(); },1000); } } function inputValidate(ele,telInput) { var oInput = ele; var inputVal = oInput.val(); var oType = ele.attr('data-type'); var oEtag = $('#etag').val(); var oErr = oInput.closest('.form_box').next('.err_txt'); var empTxt = '請輸入'+oInput.attr('placeholder')+'！'; var errTxt = '請輸入正確的'+oInput.attr('placeholder')+'！'; var pattern; if(inputVal==""){ if(!telInput){ errFun(oErr,empTxt); } return false; }else { switch (oType){ case 'login_mobile': pattern = /^1[3456789]\d{9}$/; if(inputVal.length==11) { $.ajax({ url: '/login/checkmobile', type: "post", dataType: "json", data: { mobile: inputVal, etag: oEtag, page_ur: window.location.href, page_referer: document.referrer }, success: function (data) { } }); } break; case 'login_yzm': pattern = /^\d{6}$/; break; } if(oType=='login_mobile'){ } if(!!validateFun(pattern,inputVal)){ errFun(oErr,'') if(telInput){ $('.getcheckcode').removeClass('dis'); } }else { if(!telInput) { errFun(oErr, errTxt); }else { $('.getcheckcode').addClass('dis'); } return false; } } return true; } function errFun(obj,msg) { obj.html(msg); if(msg==''){ $('.login_submit').removeClass('dis'); }else { $('.login_submit').addClass('dis'); } } function validateFun(pat,val) { return pat.test(val); }