散布圖相關(guān)系數(shù)判定

實(shí)例－鋼的淬火溫度與硬度的相關(guān)關(guān)系判斷序號(hào)淬火溫度（C0）x硬度（HRC）Y序號(hào)淬火溫度（C0）x硬度（HRC）Y18104716820482890561786055385048188705548404519830495850542082044689059218104478705022850538860512388054981042248805708205325840501184052268805412870532783046138305128860521483045298605015820463084049對(duì)照典型圖例判斷法81042444648505254565860820830840850860870880890●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

○硬度（HRC）淬火溫度（℃）象限判斷法象限判斷法又叫中值判斷法、符號(hào)檢定判斷法。使用此法的步驟如下：⒈在散布圖上畫(huà)一條與Y軸平行的中值線f，使f線的左、右兩邊的點(diǎn)子數(shù)大致相等；⒉在散布圖上畫(huà)一條與X軸平行的中值線g，使g線的上、下兩邊的點(diǎn)子數(shù)大致相等；⒊f、g兩條線把散布圖分成4個(gè)象限區(qū)域I、II、III、IV。分別統(tǒng)計(jì)落入各象限區(qū)域內(nèi)的點(diǎn)子數(shù)；⒋分別計(jì)算對(duì)角象限區(qū)內(nèi)的點(diǎn)子數(shù)；⒌判斷規(guī)則；若nI＋nIII＞nII＋nIV，則判為正相關(guān)若nI＋nIII＜nII＋nIV，則判為負(fù)相關(guān)象限判斷法(續(xù))8104244464850525456586082083084085086087088089081042444648505254565860820830840850860870880890●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

○81042444648505254565860820830840850860870880890●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

○硬度（HRC）淬火溫度（℃）gfⅠ

Ⅱ

ⅢⅣ相關(guān)系數(shù)判斷法相關(guān)系數(shù)判斷法的應(yīng)用步驟：簡(jiǎn)化X、Y數(shù)據(jù)。計(jì)算X’2，Y’2，X’Y’、（X’＋Y’）和（

X’＋Y’）2。計(jì)算∑

X’、∑

Y’、∑

X’Y’、∑X’2、∑Y’2、∑（X’＋Y’）和∑（

X’＋Y’）2。計(jì)算LX’X’

、LY’Y’

、LX’Y’

。LX’X’=∑

X’2－（∑X’）

2NLY’Y’

=∑

Y’2－（∑Y’）

2NLX’Y’

=∑

X’Y’

－（∑X’）（∑Y’）N相關(guān)系數(shù)判斷法(續(xù))計(jì)算相關(guān)數(shù)據(jù)（γ）。γ＝

LX’Y’LX’X’LY’Y’查出臨界相關(guān)數(shù)據(jù)（γα

）。γα

可根據(jù)N－2和顯著性水平α查表求得。判斷。判斷規(guī)則：若∣

γ

∣

＞

γα

，則X與Y相關(guān)若∣

γ

∣

＜

γα

，則X與Y不相關(guān)相關(guān)系數(shù)判斷法(續(xù))NOX’Y’X’2Y’2X’Y’X’＋Y’（

X’＋Y’）2117149786429168125614425625358256440131694451625209815514251967019361691981361171287847710491007017289861136121661728991214239102134169261522511412161444816256127134916991204001331191213314196143592515864152643612864相關(guān)系數(shù)判斷法(續(xù))NOX’Y’X’2Y’2X’Y’X’＋Y’（

X’＋Y’）2162846416101001761536225902144118715492251052248419399812712144202441686362114116452522513251696518324238146419611222484248176428913625625254101610040141962681464196112224842736936189812861236144721832429610361006016256304916813613169合計(jì)141312839377817164538049相關(guān)系數(shù)判斷法(續(xù))注：①表中X’值是（X－800）1/10的簡(jiǎn)化值；Y’值是（Y－40）×1的簡(jiǎn)化值。

②表中X’＋Y’、（X’＋Y’）2欄是校對(duì)欄，以免X’、Y’、X’2、Y’2、X’Y’各欄計(jì)算錯(cuò)誤，導(dǎo)致相關(guān)性結(jié)論錯(cuò)誤。校核公式是：

∑（

X’＋Y’）＝∑X’＋∑Y’

∑（X’＋Y’）2＝∑X’2＋2∑（X’＋Y’）＋∑Y’2計(jì)算LX’X’

、LY’Y’

、LX’Y’

。LX’X’=∑

X’2－（∑X’）

2NLY’Y’

=∑

Y’2－（∑Y’）

2NLX’Y’

=∑

X’Y’

－（∑X’）（∑Y’）＝839

－

（141）

230＝176.3＝3778－

（312）

230＝533.2＝1716－

30＝249.6141×312N相關(guān)系數(shù)判斷法(續(xù))計(jì)算相關(guān)系數(shù)（γ）。γ＝

LX’Y’LX’X’LY’Y’＝176.3533.2249.6＝0.814判斷。判斷規(guī)則：查出臨界相關(guān)數(shù)據(jù)（γα

）。根據(jù)N－2和顯著性水平α查表求得γα＝0.361（α＝0.05）γ＝

0.814

>γα＝0.361，所以鋼的硬度與淬火溫度呈強(qiáng)正相關(guān)。后附相關(guān)系數(shù)檢查表以上三種判斷方法對(duì)同一實(shí)例進(jìn)行分析判斷的結(jié)論是一致的。相關(guān)系數(shù)檢查表0.050.010.050.0110.9971.000110.5530.68420.9500.990120.5320.66130.8780.959130.5140.64140.8110.917140.4970.62350.7540.874150.4820.60660.7070.834160.4680.59070.6660.798170.4560.57580.6320.765180.4440.56190.6020.735190.4330.549100.6750.708200.4230.537α

N－2

α

N－2

相關(guān)系數(shù)檢查表0.050.010.050.01210.4130.526350.3250.418220.4040.515400.3040.393230.3960.505450.2880.372240.3880.496500.2730.354250.3810.487600.2500.325260.3740.478700.2320.302270.3670.470800.2170.283280.3610.463900.2050.267290.3550.4561000.1950.25