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範例：常態均數的 T-測試
範例：常態均數的 T-測試
檢驗兩個常態總體具有相等均數的假設。
1.
定義要比較的數據集。
<region id="ID0E2W5HB" top="230.4" left="38.4" xml:lang="zh_TW" height="192.99999999999997" width="94.573333333333338" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="87" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve" xml:lang="zh_TW">data1</id> <matrix rows="10" cols="1" xml:lang="zh_TW"> <real xml:lang="zh_TW">22</real> <real xml:lang="zh_TW">48</real> <real xml:lang="zh_TW">88</real> <real xml:lang="zh_TW">35</real> <real xml:lang="zh_TW">7</real> <real xml:lang="zh_TW">98</real> <real xml:lang="zh_TW">57</real> <real xml:lang="zh_TW">39</real> <real xml:lang="zh_TW">76</real> <real xml:lang="zh_TW">81</real> </matrix> </define> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EIX5HB" top="230.4" left="172.8" xml:lang="zh_TW" height="192.99999999999997" width="94.573333333333338" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="89" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve" xml:lang="zh_TW">data2</id> <matrix rows="10" cols="1" xml:lang="zh_TW"> <real xml:lang="zh_TW">55</real> <real xml:lang="zh_TW">22</real> <real xml:lang="zh_TW">67</real> <real xml:lang="zh_TW">12</real> <real xml:lang="zh_TW">45</real> <real xml:lang="zh_TW">21</real> <real xml:lang="zh_TW">67</real> <real xml:lang="zh_TW">78</real> <real xml:lang="zh_TW">83</real> <real xml:lang="zh_TW">92</real> </matrix> </define> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
2.
收集樣本統計。
每個數據集的樣本數
<region id="ID0EY15HB" top="403.20000000000005" left="38.400000000000006" xml:lang="zh_TW" height="25.6" width="137.98000000000002" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="91" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve" xml:lang="zh_TW">n1</id> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">length</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">data1</id> </apply> </define> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EF25HB" top="441.60000000000008" left="38.400000000000006" xml:lang="zh_TW" height="25.6" width="137.98000000000002" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="95" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve" xml:lang="zh_TW">n2</id> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">length</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">data2</id> </apply> </define> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0E525HB" top="403.20000000000005" left="384.00000000000006" xml:lang="zh_TW" height="25.6" width="65.516666666666666" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="93" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">n1</id> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EQ35HB" top="441.60000000000008" left="384.00000000000006" xml:lang="zh_TW" height="25.6" width="65.516666666666666" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="97" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">n2</id> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
取樣均數
<region id="ID0EZ45HB" top="480.00000000000006" left="38.400000000000006" xml:lang="zh_TW" height="25.6" width="136.66000000000003" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="99" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve" xml:lang="zh_TW">m1</id> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">mean</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">data1</id> </apply> </define> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EL55HB" top="518.40000000000009" left="38.400000000000006" xml:lang="zh_TW" height="25.6" width="136.66000000000003" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="103" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve" xml:lang="zh_TW">m2</id> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">mean</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">data2</id> </apply> </define> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EE65HB" top="480.00000000000006" left="384.00000000000006" xml:lang="zh_TW" height="25.6" width="82.250000000000014" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="101" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">m1</id> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EW65HB" top="518.40000000000009" left="384.00000000000006" xml:lang="zh_TW" height="25.6" width="82.250000000000014" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="105" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">m2</id> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
取樣標準差
<region id="ID0E6A6HB" top="614.40000000000009" left="38.400000000000006" xml:lang="zh_TW" height="50.065333527326587" width="197.0459999702374" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="111" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve" xml:lang="zh_TW">s1</id> <apply xml:lang="zh_TW"> <mult xml:lang="zh_TW" /> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">stdev</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">data1</id> </apply> <apply xml:lang="zh_TW"> <nthRoot xml:lang="zh_TW" /> <placeholder xml:lang="zh_TW" /> <apply xml:lang="zh_TW"> <div xml:lang="zh_TW" /> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">n1</id> <apply xml:lang="zh_TW"> <minus xml:lang="zh_TW" /> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">n1</id> <real xml:lang="zh_TW">1</real> </apply> </apply> </apply> </apply> </define> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0ERB6HB" top="672.00000000000011" left="38.400000000000006" xml:lang="zh_TW" height="50.065333527326587" width="197.0459999702374" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="115" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve" xml:lang="zh_TW">s2</id> <apply xml:lang="zh_TW"> <mult xml:lang="zh_TW" /> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">stdev</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">data2</id> </apply> <apply xml:lang="zh_TW"> <nthRoot xml:lang="zh_TW" /> <placeholder xml:lang="zh_TW" /> <apply xml:lang="zh_TW"> <div xml:lang="zh_TW" /> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">n2</id> <apply xml:lang="zh_TW"> <minus xml:lang="zh_TW" /> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">n2</id> <real xml:lang="zh_TW">1</real> </apply> </apply> </apply> </apply> </define> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EKC6HB" top="614.40000000000009" left="384.00000000000006" xml:lang="zh_TW" height="25.6" width="90.876666666666679" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="113" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">s1</id> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0E3C6HB" top="672.00000000000011" left="384.00000000000006" xml:lang="zh_TW" height="25.6" width="90.876666666666679" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="117" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">s2</id> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
合併兩個均數時的自由度
<region id="ID0EFE6HB" top="556.80000000000007" left="38.400000000000006" xml:lang="zh_TW" height="25.6" width="105.12666666666667" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="107" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve" xml:lang="zh_TW">ν</id> <apply xml:lang="zh_TW"> <minus xml:lang="zh_TW" /> <apply xml:lang="zh_TW"> <plus xml:lang="zh_TW" /> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">n1</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">n2</id> </apply> <real xml:lang="zh_TW">2</real> </apply> </define> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0E5E6HB" top="556.80000000000007" left="384.00000000000006" xml:lang="zh_TW" height="25.6" width="56.493333333333339" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="109" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">ν</id> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
數據集中差分的標準誤差
<region id="ID0EFG6HB" top="729.60000000000014" left="38.400000000000006" xml:lang="zh_TW" height="52.217333527326588" width="313.71933330357075" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="119" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve" xml:lang="zh_TW">s</id> <apply xml:lang="zh_TW"> <nthRoot xml:lang="zh_TW" /> <placeholder xml:lang="zh_TW" /> <apply xml:lang="zh_TW"> <mult xml:lang="zh_TW" /> <apply xml:lang="zh_TW"> <div xml:lang="zh_TW" /> <apply xml:lang="zh_TW"> <plus xml:lang="zh_TW" /> <apply xml:lang="zh_TW"> <mult xml:lang="zh_TW" /> <parens xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <minus xml:lang="zh_TW" /> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">n1</id> <real xml:lang="zh_TW">1</real> </apply> </parens> <apply xml:lang="zh_TW"> <pow xml:lang="zh_TW" /> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">s1</id> <real xml:lang="zh_TW">2</real> </apply> </apply> <apply xml:lang="zh_TW"> <mult xml:lang="zh_TW" /> <parens xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <minus xml:lang="zh_TW" /> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">n2</id> <real xml:lang="zh_TW">1</real> </apply> </parens> <apply xml:lang="zh_TW"> <pow xml:lang="zh_TW" /> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">s2</id> <real xml:lang="zh_TW">2</real> </apply> </apply> </apply> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">ν</id> </apply> <parens xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <plus xml:lang="zh_TW" /> <apply xml:lang="zh_TW"> <div xml:lang="zh_TW" /> <real xml:lang="zh_TW">1</real> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">n1</id> </apply> <apply xml:lang="zh_TW"> <div xml:lang="zh_TW" /> <real xml:lang="zh_TW">1</real> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">n2</id> </apply> </apply> </parens> </apply> </apply> </define> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0E4G6HB" top="729.60000000000014" left="384.00000000000006" xml:lang="zh_TW" height="25.6" width="82.896666666666675" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="121" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">s</id> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
3.
定義顯著程度。
<region id="ID0ESI6HB" top="921.60000000000014" left="38.400000000000006" xml:lang="zh_TW" height="25.6" width="62.676666666666669" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="123" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve" xml:lang="zh_TW">α</id> <real xml:lang="zh_TW">0.01</real> </define> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
4.
計算測試統計。
<region id="ID0EHK6HB" top="1017.6000000000001" left="38.400000000000006" xml:lang="zh_TW" height="47.2" width="93.573333333333352" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="125" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve" xml:lang="zh_TW">t</id> <apply xml:lang="zh_TW"> <div xml:lang="zh_TW" /> <apply xml:lang="zh_TW"> <minus xml:lang="zh_TW" /> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">m1</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">m2</id> </apply> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">s</id> </apply> </define> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EZK6HB" top="1056.0000000000002" left="38.400000000000006" xml:lang="zh_TW" height="25.6" width="74.433333333333337" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="127" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">t</id> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
5.
指定虛無假設與對立假設。
H0: m1
≤
m2
H1: m1
>
m2
6.
計算 p 值並測試假設。在此範例中，當虛無假設為真 (不拒絕
H0
) 時，所有布林運算式的計算結果為 1。
<region id="ID0EYO6HB" top="1248.0000000000002" left="38.400000000000006" xml:lang="zh_TW" height="25.6" width="146.95000000000002" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="129" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve" xml:lang="zh_TW">P</id> <apply xml:lang="zh_TW"> <mult xml:lang="zh_TW" /> <real xml:lang="zh_TW">2</real> <parens xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <minus xml:lang="zh_TW" /> <real xml:lang="zh_TW">1</real> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">pt</id> <sequence xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <absval xml:lang="zh_TW" /> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">t</id> </apply> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">ν</id> </sequence> </apply> </apply> </parens> </apply> </define> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EKP6HB" top="1286.4" left="38.400000000000006" xml:lang="zh_TW" height="25.6" width="78.876666666666665" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="131" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">P</id> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0E3P6HB" top="1324.8000000000002" left="38.400000000000006" xml:lang="zh_TW" height="25.6" width="74.763333333333335" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="133" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <apply xml:lang="zh_TW"> <lessOrEqual xml:lang="zh_TW" /> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">P</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">α</id> </apply> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
假設虛無假設為真，則檢驗統計有 0.946 的機率會大於所觀察到的結果。p 值與顯著程度的比較，無法證實對立假設為真。
7.
計算臨界區域的限制，並測試假設。
<region id="ID0EWR6HB" top="1574.4000000000003" left="38.400000000000006" xml:lang="zh_TW" height="47.2" width="117.79" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="135" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve" xml:lang="zh_TW">crit</id> <apply xml:lang="zh_TW"> <absval xml:lang="zh_TW" /> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">qt</id> <sequence xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <div xml:lang="zh_TW" /> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">α</id> <real xml:lang="zh_TW">2</real> </apply> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">ν</id> </sequence> </apply> </apply> </define> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EIS6HB" top="1632.0000000000002" left="38.400000000000006" xml:lang="zh_TW" height="25.6" width="93.396666666666675" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="137" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">crit</id> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0E1S6HB" top="1670.4000000000003" left="38.400000000000006" xml:lang="zh_TW" height="25.6" width="94.473333333333329" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="139" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <apply xml:lang="zh_TW"> <greaterThan xml:lang="zh_TW" /> <apply xml:lang="zh_TW"> <absval xml:lang="zh_TW" /> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">t</id> </apply> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">crit</id> </apply> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
接受虛無假設。無證據顯示
m1
大於
m2
。
8.
繪製 T-測試 (藍色)、臨界區域的邊界 (綠色) 及測試統計 (紅色)。
<region id="ID0E6U6HB" top="1804.8000000000002" left="38.400000000000006" xml:lang="zh_TW" height="211.19999999999996" width="580" xmlns="http://schemas.mathsoft.com/worksheet50"> <plot background-type="white" origin-positioning="true" xml:lang="zh_TW"> <xyPlot xml:lang="zh_TW"> <title class="- topic/title " xml:lang="zh_TW" toc="yes" wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" /> <legend xml:lang="zh_TW" /> <traces xml:lang="zh_TW"> <trace resultRef="141" xml:lang="zh_TW" num-of-points="500"> <traceStyle color="#FF00008B" symbol="none" line-weight="1" line-style="Solid" xml:lang="zh_TW">線條</traceStyle> </trace> </traces> <axes xml:lang="zh_TW"> <xAxis rank="1" legend-position="PlotBoundaryBottom" start="-4" end="4" xml:lang="zh_TW"> <axisLine position="origin" positionticmark="0" legendWidth="60.93" xml:lang="zh_TW" /> <axisGrid xml:lang="zh_TW"> <gridFrequency xml:lang="zh_TW">9</gridFrequency> <gridLabels display="true" xml:lang="zh_TW" /> <gridLines xml:lang="zh_TW" /> <tickMarks display="true" xml:lang="zh_TW" /> </axisGrid> <axisLabel xml:lang="zh_TW" /> <markers xml:lang="zh_TW"> <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">crit</id> <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">t</id> </markers> <numberFormat xml:lang="zh_TW"> <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" xml:lang="zh_TW" /> </numberFormat> <plotEquations xml:lang="zh_TW"> <plotEquation xml:lang="zh_TW"> <math resultRef="152" xml:lang="zh_TW"> <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">x</id> </math> <math resultRef="153" xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> </plotEquations> <xyDomain scale-type="linear" auto-scale="true" xml:lang="zh_TW"> <startValue xml:lang="zh_TW" resultRef="147"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">-4</real> </startValue> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">-3</real> <endValue xml:lang="zh_TW" resultRef="151"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">4</real> </endValue> </xyDomain> </xAxis> <yAxis rank="1" legend-position="PlotBoundaryLeft" start="0" end="0.4" xml:lang="zh_TW"> <axisLine position="origin" positionticmark="4" legendWidth="106.173333333333" xml:lang="zh_TW" /> <axisGrid xml:lang="zh_TW"> <gridFrequency xml:lang="zh_TW">5</gridFrequency> <gridLabels display="true" xml:lang="zh_TW" /> <gridLines xml:lang="zh_TW" /> <tickMarks display="true" xml:lang="zh_TW" /> </axisGrid> <axisLabel xml:lang="zh_TW" /> <markers xml:lang="zh_TW" /> <numberFormat xml:lang="zh_TW"> <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" xml:lang="zh_TW" /> </numberFormat> <plotEquations xml:lang="zh_TW"> <plotEquation xml:lang="zh_TW"> <math resultRef="160" xml:lang="zh_TW"> <apply xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id xml:space="preserve" xml:lang="zh_TW">dt</id> <sequence xml:lang="zh_TW"> <id xml:space="preserve" xml:lang="zh_TW">x</id> <id xml:space="preserve" xml:lang="zh_TW">ν</id> </sequence> </apply> </math> <math resultRef="161" xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> </plotEquations> <xyDomain scale-type="linear" auto-scale="true" xml:lang="zh_TW"> <startValue xml:lang="zh_TW" resultRef="155"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">0</real> </startValue> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">0.1</real> <endValue xml:lang="zh_TW" resultRef="159"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">0.4</real> </endValue> </xyDomain> </yAxis> </axes> </xyPlot> </plot> </region>
複製運算式
