統(tǒng)計學 課件 7-10 假設檢驗 - 匹配樣本總體均值差的假設檢驗

第7講假設檢驗匹配樣本總體均值差的假設檢驗1引例：玩視頻游戲能減肥嗎？有機構認為在傳統(tǒng)運動器械上增加運動視頻游戲有助于減肥.應該如何檢驗該判斷呢？HaddockBL,SiegelSR,WikinLD.Theadditionofavideogametostationarycycling:Theimpactonenergyexpenditureinoverweightchildren[J].Theopensportssciencesjournal,2009,2:42.2引例：玩視頻游戲能減肥嗎？共20名青少年參加運動視頻游戲試驗，所有人騎行兩次，并評估能量消耗.一次有運動視頻游戲設備.一次無運動視頻游戲設備.游戲

A1A2A3A4A5A6A7A8A9A10有5.046.975.524.775.575.675.134.884.558.89無7.273.463.206.722.793.374.724.957.143.11

游戲A11A12A13A14A15A16A17A18A19A20有5.144.627.904.297.986.925.516.417.045.25無6.104.014.495.005.334.323.546.536.666.02Kcal/min3匹配樣本樣本特點同一對象先后測量兩次.

匹配樣本總體均值差的假設檢驗游戲

A1A2A3A4A5A6A7A8A9A10有5.046.975.524.775.575.675.134.884.558.89無7.273.463.206.722.793.374.724.957.143.11

游戲A11A12A13A14A15A16A17A18A19A20有5.144.627.904.297.986.925.516.417.045.25無6.104.014.495.005.334.323.546.536.666.02兩個樣本的樣本量相同.兩個樣本的順序是一一對應的.4匹配樣本總體均值差的假設檢驗假定條件：兩個總體都服從正態(tài)分布.作用：檢驗兩個總體的均值差.假設檢驗的流程1假設研究的問題H0H1提出假設5匹配樣本總體均值差的假設檢驗假設檢驗的流程觀察序號樣本1樣本2差值MMMM

假設的差值

樣本差值均值樣本差值標準差檢驗統(tǒng)計量2345

6例題

Kcal/min游戲

A1A2A3A4A5A6A7A8A9A10有5.046.975.524.775.575.675.134.884.558.89無7.273.463.206.722.793.374.724.957.143.11

游戲A11A12A13A14A15A16A17A18A19A20有5.144.627.904.297.986.925.516.417.045.25無6.104.014.495.005.334.323.546.536.666.027

13

2確定檢驗統(tǒng)計量：0拒絕區(qū)域

8例題計算檢驗統(tǒng)計量的值:4

0拒絕區(qū)域

游戲A1A2A3A4A5A6A7A8A9A10有無

游戲A11A12A13A14A15A16A17A18A19A20有無

9例題

作出統(tǒng)計決策：510例題例題（利用P值進行決策）計算檢驗統(tǒng)計量的值:12

0拒絕區(qū)域

統(tǒng)計決策:P值：原假設為真時，得到樣本觀察結果或者更極端結果的概率.

1.72

11問題拓展：兩種t檢驗是一樣的?[1]Xu,M.,Fralick,D.,Zheng,J.Z.,Wang,B.,Tu,X.M.,&Feng,C.(2017).Thedifferencesandsimilaritiesbetweentwo-samplet-testandpairedt-test.Shanghaiarchivesofpsychiatry,29(3),184-188.

匹配樣本t檢驗

匹配樣本t檢驗

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小結匹配樣本總體均值差的假設檢驗樣本的特點：檢驗統(tǒng)計量：檢驗流程：13同