方差分析下學(xué)習(xí)教案

1、會(huì)計(jì)學(xué)1方差分析下方差分析下第一頁(yè)，共92頁(yè)。RMRM基本概念基本概念5.1球形檢驗(yàn)球形檢驗(yàn)5.2RM-ANOVARM-ANOVA原理原理5.3結(jié)果分析與表達(dá)結(jié)果分析與表達(dá)5.5數(shù)據(jù)錄入與操作數(shù)據(jù)錄入與操作5.42第1頁(yè)/共93頁(yè)第二頁(yè)，共92頁(yè)。Factorial RM Design ANOVAFactorial RM Design ANOVA5.6Mixed Design ANOVAMixed Design ANOVA5.73第2頁(yè)/共93頁(yè)第三頁(yè)，共92頁(yè)。 Repeated measures Repeated measures（RMRM）是指在實(shí)驗(yàn)過(guò)程中，）是指在實(shí)驗(yàn)過(guò)程中，相同的實(shí)體

2、相同的實(shí)體(sht)(sht)（entities, e.g. entities, e.g. participantsparticipants）參與所有情況下的（實(shí)驗(yàn)控制變量）參與所有情況下的（實(shí)驗(yàn)控制變量的不同水平下的）實(shí)驗(yàn)或者在不同的時(shí)間點(diǎn)下提供的不同水平下的）實(shí)驗(yàn)或者在不同的時(shí)間點(diǎn)下提供數(shù)據(jù)。數(shù)據(jù)。其它的表達(dá)方式：其它的表達(dá)方式：Within-participants design, Related design,Within-participants design, Related design,Within-subjects design Within-subjects design

3、4第3頁(yè)/共93頁(yè)第四頁(yè)，共92頁(yè)。 RM-ANOVA RM-ANOVA，重復(fù)測(cè)量的方差分析適用條件：，重復(fù)測(cè)量的方差分析適用條件：各組樣本數(shù)據(jù)不獨(dú)立各組樣本數(shù)據(jù)不獨(dú)立控制變量的水平控制變量的水平(shupng)(shupng)數(shù)在三個(gè)以上數(shù)在三個(gè)以上滿足球形檢驗(yàn)滿足球形檢驗(yàn)5第4頁(yè)/共93頁(yè)第五頁(yè)，共92頁(yè)。 球形（球形（ sphericity sphericity 表示為表示為）指不同實(shí)）指不同實(shí)驗(yàn)條件（即控制變量的不同水平）下的觀測(cè)驗(yàn)條件（即控制變量的不同水平）下的觀測(cè)變量的變化是相似的。變量的變化是相似的。 球形和方差齊次性相類似，但是方差齊次球形和方差齊次性相類似，但是方差齊次性是同

4、一性是同一(tngy)(tngy)變量在不同觀測(cè)水平下的變量在不同觀測(cè)水平下的方差之間無(wú)顯著性差異；而球形是指不同變方差之間無(wú)顯著性差異；而球形是指不同變量（不同水平下的觀測(cè)變量在量（不同水平下的觀測(cè)變量在RM-ANOVARM-ANOVA中對(duì)中對(duì)應(yīng)于不同的變量）的變化要類似。應(yīng)于不同的變量）的變化要類似。6第5頁(yè)/共93頁(yè)第六頁(yè)，共92頁(yè)。variance A-B variance A-C variance B-C球形檢驗(yàn)(jinyn)通過(guò)的條件為：7第6頁(yè)/共93頁(yè)第七頁(yè)，共92頁(yè)。當(dāng)有兩個(gè)組間差異的方差非常接近時(shí)，數(shù)據(jù)滿足本地(bnd)球形（local sphericity）檢驗(yàn)。在本例中

5、A-C差異和B-C差異的方差非常接近，因?yàn)榍蛐螜z驗(yàn)是通過(guò)的。8第7頁(yè)/共93頁(yè)第八頁(yè)，共92頁(yè)。實(shí)際檢驗(yàn)方法：在SPSS中球形檢驗(yàn)可以通過(guò)(tnggu)Mauchlys test進(jìn)行。其零假設(shè)為：實(shí)驗(yàn)不同情況下差異的方差是相等的。若Mauchlys test的檢驗(yàn)結(jié)果不顯著，則球形檢驗(yàn)通過(guò)(tnggu)。9第8頁(yè)/共93頁(yè)第九頁(yè)，共92頁(yè)。 當(dāng)球形檢驗(yàn)沒(méi)通過(guò)時(shí)：當(dāng)球形檢驗(yàn)沒(méi)通過(guò)時(shí)：0.75, 0.75, 采用采用(ciyng)HuynhFeldt (ciyng)HuynhFeldt estimateestimate的結(jié)果的結(jié)果 0.75 0.75或未知，采用或未知，采用(ciyng)Green

6、houseGeisser (ciyng)GreenhouseGeisser 修正結(jié)果修正結(jié)果 球形檢驗(yàn)是否球形檢驗(yàn)是否(sh fu)(sh fu)通過(guò)還影響我們對(duì)置信區(qū)間調(diào)整方法的通過(guò)還影響我們對(duì)置信區(qū)間調(diào)整方法的選擇：選擇：ShpericityShpericity滿足時(shí)，采用滿足時(shí)，采用TukeyTukey（LSDLSD）ShpericityShpericity不滿足時(shí)，采用不滿足時(shí)，采用Bonferroni method Bonferroni method 10第9頁(yè)/共93頁(yè)第十頁(yè)，共92頁(yè)。11第10頁(yè)/共93頁(yè)第十一頁(yè)，共92頁(yè)。12第11頁(yè)/共93頁(yè)第十二頁(yè)，共92頁(yè)。N-1為總離

7、差的自由度，由樣本(yngbn)總量決定13第12頁(yè)/共93頁(yè)第十三頁(yè)，共92頁(yè)。每個(gè)人（participant）的自由度為n-1（n為水平(shupng)數(shù)）SSw的自由度為83=2414第13頁(yè)/共93頁(yè)第十四頁(yè)，共92頁(yè)。dfM = k 1 = 315第14頁(yè)/共93頁(yè)第十五頁(yè)，共92頁(yè)。16第15頁(yè)/共93頁(yè)第十六頁(yè)，共92頁(yè)。17第16頁(yè)/共93頁(yè)第十七頁(yè)，共92頁(yè)。18第17頁(yè)/共93頁(yè)第十八頁(yè)，共92頁(yè)。每一水平下的觀測(cè)(gunc)值單獨(dú)作為一個(gè)變量的值錄入19第18頁(yè)/共93頁(yè)第十九頁(yè)，共92頁(yè)。20第19頁(yè)/共93頁(yè)第二十頁(yè)，共92頁(yè)。添加Within-subject 因素名

8、稱(mngchng)與水平數(shù)21第20頁(yè)/共93頁(yè)第二十一頁(yè)，共92頁(yè)。設(shè)置(shzh)變量22第21頁(yè)/共93頁(yè)第二十二頁(yè)，共92頁(yè)。設(shè)置(shzh)RM模型23第22頁(yè)/共93頁(yè)第二十三頁(yè)，共92頁(yè)。設(shè)置對(duì)比(dub)方法24第23頁(yè)/共93頁(yè)第二十四頁(yè)，共92頁(yè)。設(shè)置繪圖(hu t)模式25第24頁(yè)/共93頁(yè)第二十五頁(yè)，共92頁(yè)。設(shè)置(shzh)置信區(qū)間及其它可選項(xiàng)26第25頁(yè)/共93頁(yè)第二十六頁(yè)，共92頁(yè)。27第26頁(yè)/共93頁(yè)第二十七頁(yè)，共92頁(yè)。28第27頁(yè)/共93頁(yè)第二十八頁(yè)，共92頁(yè)。29第28頁(yè)/共93頁(yè)第二十九頁(yè)，共92頁(yè)。30第29頁(yè)/共93頁(yè)第三十頁(yè)，共92頁(yè)。31第3

9、0頁(yè)/共93頁(yè)第三十一頁(yè)，共92頁(yè)。32第31頁(yè)/共93頁(yè)第三十二頁(yè)，共92頁(yè)。33第32頁(yè)/共93頁(yè)第三十三頁(yè)，共92頁(yè)。34第33頁(yè)/共93頁(yè)第三十四頁(yè)，共92頁(yè)。35第34頁(yè)/共93頁(yè)第三十五頁(yè)，共92頁(yè)。36第35頁(yè)/共93頁(yè)第三十六頁(yè)，共92頁(yè)。Mauchlys test indicated that the assumption of sphericity had been violated, 2(5) = 11.41, p = .047, therefore GreenhouseGeisser corrected tests are reported ( = .53). The

10、results show that the time to retch was not significantly affected by the type of animal eaten, F(1.60, 11.19) = 3.79, p = .063.37第36頁(yè)/共93頁(yè)第三十七頁(yè)，共92頁(yè)。Mauchlys test indicated that the assumption of sphericity had been violated, 2(5) = 11.41, p = .047, therefore multivariate tests are reported ( = .53

11、). The results show that the time to retch was significantly affected by the type of animal eaten, V = 0.94, F(3, 5) = 26.96, p = .00238第37頁(yè)/共93頁(yè)第三十八頁(yè)，共92頁(yè)。指在RM design中有兩個(gè)以上的控制因素。對(duì)應(yīng)的方差分析稱為 Factorial RM-ANOVA?；镜脑?yunl)和分析方法與One way RM-ANOVA類似。39第38頁(yè)/共93頁(yè)第三十九頁(yè)，共92頁(yè)。控制(kngzh)因素：Drink和ImageDrink有三個(gè)水平：

12、Beer、Wine、Water。Image有三個(gè)水平：Positive、Neutral、Negative。40第39頁(yè)/共93頁(yè)第四十頁(yè)，共92頁(yè)。每個(gè)控制要素中作為基準(zhǔn)或參考水平的數(shù)據(jù)(shj)放在第一位或者最后一位。41第40頁(yè)/共93頁(yè)第四十一頁(yè)，共92頁(yè)。42第41頁(yè)/共93頁(yè)第四十二頁(yè)，共92頁(yè)。設(shè)置Within-Subject Factor： 定義因素的順序(shnx)要和控制要素順序(shnx)及數(shù)據(jù)錄入的順序(shnx)相一致。43第42頁(yè)/共93頁(yè)第四十三頁(yè)，共92頁(yè)。44第43頁(yè)/共93頁(yè)第四十四頁(yè)，共92頁(yè)。按順序(shnx)添加Within-Subjects Varia

13、bles45第44頁(yè)/共93頁(yè)第四十五頁(yè)，共92頁(yè)。根據(jù)問(wèn)題的實(shí)際性質(zhì)設(shè)置(shzh)對(duì)比方式46第45頁(yè)/共93頁(yè)第四十六頁(yè)，共92頁(yè)。設(shè)置(shzh)Profile Plots47第46頁(yè)/共93頁(yè)第四十七頁(yè)，共92頁(yè)。設(shè)置(shzh)Options48第47頁(yè)/共93頁(yè)第四十八頁(yè)，共92頁(yè)。49第48頁(yè)/共93頁(yè)第四十九頁(yè)，共92頁(yè)。球形檢驗(yàn)結(jié)果：兩個(gè)主因素效果(xiogu)Significant 交互因素效果(xiogu)non-significant50第49頁(yè)/共93頁(yè)第五十頁(yè)，共92頁(yè)。51第50頁(yè)/共93頁(yè)第五十一頁(yè)，共92頁(yè)。自由度的計(jì)算(j sun)：dfD-M=KD-1

14、=3-1=2dfD-W=ndfD-M =202 =40 dfR-D=dfD-W-dfD-M =40-2 =38dfDI-M=dfD-MdfI-M =22 =4dfDI-W=ndfDI-M =204 =80dfR-DI=dfDI-W-dfDI-M =80-4 =7652第51頁(yè)/共93頁(yè)第五十二頁(yè)，共92頁(yè)。自由度的計(jì)算(j sun)：dfD-M=KD-1 （ dfD-M freedom degrees, df, of model effects for drinks ） =3-1=2dfD-W=ndfD-M （ dfD-w df of within-subject effects for dr

15、inks ） =202 =40 dfR-D=dfD-W-dfD-M （ dfR-D df of residual effects for drinks ） =40-2 =38dfDI-M=dfD-MdfI-M （ dfDI-M df of model interaction effects for drinks*Imagery ） =22 =4dfDI-W=ndfDI-M （ dfDI-W df of within-subject interaction effects for drinks*Imagery ） =204 =80dfR-DI=dfDI-W-dfDI-M （ dfDI-W df

16、of residual interaction effects for drinks*Imagery ） =80-4 =7653第52頁(yè)/共93頁(yè)第五十三頁(yè)，共92頁(yè)。dfGG-D=dfDGG =20.577=1.154dfR-GG-D=dfR-DGG=380.577=21.926調(diào)整F檢驗(yàn)(jinyn)中的其余各項(xiàng)自由度計(jì)算方法相同。54第53頁(yè)/共93頁(yè)第五十四頁(yè)，共92頁(yè)。55第54頁(yè)/共93頁(yè)第五十五頁(yè)，共92頁(yè)。56第55頁(yè)/共93頁(yè)第五十六頁(yè)，共92頁(yè)。不一致(yzh)！57第56頁(yè)/共93頁(yè)第五十七頁(yè)，共92頁(yè)。58第57頁(yè)/共93頁(yè)第五十八頁(yè)，共92頁(yè)。當(dāng)Post hoc和Co

17、ntracts的結(jié)果不一致(yzh)時(shí)，以后者為準(zhǔn)。59第58頁(yè)/共93頁(yè)第五十九頁(yè)，共92頁(yè)。60第59頁(yè)/共93頁(yè)第六十頁(yè)，共92頁(yè)。61第60頁(yè)/共93頁(yè)第六十一頁(yè)，共92頁(yè)。Mauchlys test indicated that the assumption of sphericity had been violated for the main effects of drink, 2(2) = 23.75, p .001, and imagery, 2(2) = 7.42, p = .024. Therefore degrees of freedom were corrected

18、using GreenhouseGeisser estimates of sphericity ( = .58 for the main effect of drink and .75 for the main effect of imagery).Report the results:62第61頁(yè)/共93頁(yè)第六十二頁(yè)，共92頁(yè)。Report the results:There was a significant main effect of the type of drink on ratings of the drink, F(1.15, 21.93) = 5.11, p = .011.C

19、ontrasts revealed that ratings of beer, F(1, 19) = 6.22, p = .022, and wine, F(1, 19) = 18.61, were significantly higher than water.There was also a significant main effect of the type of imagery on ratings of the drinks, F(1.50, 28.40) = 122.57.63第62頁(yè)/共93頁(yè)第六十三頁(yè)，共92頁(yè)。Contrasts revealed that ratings

20、after positive imagery were significantly higher than after neutral imagery, F(1, 19) = 142.19. Conversely, ratings after negative imagery were significantly lower than after neutral imagery, F(1, 19) = 47.07.Report the results:64第63頁(yè)/共93頁(yè)第六十四頁(yè)，共92頁(yè)。There was a significant interaction effect between

21、 the type of drink and the type of imagery used, F(4, 76) = 17.16. This indicates that imagery had different effects on peoples ratings depending on which type of drink was used. To break down this interaction, contrasts were performed comparing all drink types to their baseline (water) and all imag

22、ery types to their baseline (neutral imagery). These revealed significant interactions when comparing negative imagery to neutral imagery both for beer compared to water, F(1, 19) = 6.75, p = .018, and wine compared to water, F(1,19) = 26.91.Report the results:65第64頁(yè)/共93頁(yè)第六十五頁(yè)，共92頁(yè)。Looking at the in

23、teraction graph, these effects reflect that negative imagery (compared to neutral) lowered scores significantly more in water than it did for beer, and lowered scores significantly more for wine than it did for water. The remaining contrasts revealed no significant interaction term when comparing po

24、sitive imagery to neutral imagery both for beer compared to water, F(1, 19) = 1.58, p = .225, and wine compared to water, F(1, 19) = 0.24, p = .633. However, these contrasts did yield small to medium effect sizes.Report the results:66第65頁(yè)/共93頁(yè)第六十六頁(yè)，共92頁(yè)。Mixed design是指在實(shí)驗(yàn)過(guò)程中有多個(gè)控制因素，其中有些因素（within-subj

25、ects factor）的不同水平為所有(suyu)的實(shí)驗(yàn)實(shí)體（Entity，如subjects）都參與測(cè)試，而另外一部分的因素(between-subjects factor)的不同水平則由不同的實(shí)驗(yàn)實(shí)體參與測(cè)試。67第66頁(yè)/共93頁(yè)第六十七頁(yè)，共92頁(yè)。組內(nèi)因素（within-subjects factor)的每個(gè)水平都按照單獨(dú)的變量進(jìn)行數(shù)據(jù)錄入，一個(gè)組間因素（between-subjects factor)的作為一個(gè)單獨(dú)的變量進(jìn)行數(shù)據(jù)錄入。錄入組內(nèi)因素的不同水平時(shí)，需要考慮不同水平的次序關(guān)系，把參考水平（reference level or baseline）排在該因素不同水平的第一位

26、或最后一位。若某因素的各個(gè)水平之間地位對(duì)等，則在排列時(shí)沒(méi)有特殊要求，在對(duì)比(dub)時(shí)一般采用repeated 方式進(jìn)行對(duì)比(dub)。68第67頁(yè)/共93頁(yè)第六十八頁(yè)，共92頁(yè)。問(wèn)題：測(cè)試長(zhǎng)相（looks）和個(gè)性魅力(personality)對(duì)快速約會(huì)(yu hu)效果的影響?？刂埔蛩兀洪L(zhǎng)相（3個(gè)水平）個(gè)性魅力（3個(gè)水平）性別（2個(gè)水平）測(cè)試值：愿意和同一個(gè)人再次約會(huì)(yu hu)的意愿。69第68頁(yè)/共93頁(yè)第六十九頁(yè)，共92頁(yè)。按照實(shí)驗(yàn)測(cè)試的順序（該順序和數(shù)據(jù)錄入順序相一致），添加組內(nèi)因素名稱(mngchng)及各因素水平數(shù)。70第69頁(yè)/共93頁(yè)第七十頁(yè)，共92頁(yè)。 映射組內(nèi)因素變量(

27、binling) 指定組間因素71第70頁(yè)/共93頁(yè)第七十一頁(yè)，共92頁(yè)。設(shè)置(shzh)各因素的對(duì)比方式72第71頁(yè)/共93頁(yè)第七十二頁(yè)，共92頁(yè)。設(shè)置繪圖(hu t)方式73第72頁(yè)/共93頁(yè)第七十三頁(yè)，共92頁(yè)。設(shè)置可選項(xiàng)因有組間因素，所以(suy)需要進(jìn)行方差齊次性檢驗(yàn)74第73頁(yè)/共93頁(yè)第七十四頁(yè)，共92頁(yè)。因素(yn s)摘要表75第74頁(yè)/共93頁(yè)第七十五頁(yè)，共92頁(yè)。描述性統(tǒng)計(jì)(tngj)76第75頁(yè)/共93頁(yè)第七十六頁(yè)，共92頁(yè)。檢查組間因素方差分析的條件是否(sh fu)滿足方差齊次性檢驗(yàn)77第76頁(yè)/共93頁(yè)第七十七頁(yè)，共92頁(yè)。檢查組內(nèi)因素方差分析的條件是否(sh f

28、u)滿足球形檢驗(yàn)78第77頁(yè)/共93頁(yè)第七十八頁(yè)，共92頁(yè)。組間因素(yn s)效果79第78頁(yè)/共93頁(yè)第七十九頁(yè)，共92頁(yè)。組間因素(yn s)效果對(duì)比80第79頁(yè)/共93頁(yè)第八十頁(yè)，共92頁(yè)。Main effect- Gender81第80頁(yè)/共93頁(yè)第八十一頁(yè)，共92頁(yè)。Main effect- Looks82第81頁(yè)/共93頁(yè)第八十二頁(yè)，共92頁(yè)。Interaction-Looks83第82頁(yè)/共93頁(yè)第八十三頁(yè)，共92頁(yè)。All effects are reported as significant at p .001 unless otherwise stated. There

29、was a significant main effect of the attractiveness of the date on interest expressed by participant, F(2, 36) = 423.73. Contrasts revealed that attractive dates were significantly more desirable than average-looking ones, F(1, 18) = 226.99, and ugly dates were significantly less desirable than aver

30、age-looking ones, F(1, 18) = 160.07.84第83頁(yè)/共93頁(yè)第八十四頁(yè)，共92頁(yè)。There was also a significant main effect of the amount of charisma the date possessed on the interest expressed in dating them, F(2, 36) = 328.25. Contrasts revealed that dates with high charisma were significantly more desirable than dates w

31、ith some charisma, F(1, 18) = 109.94, anddullards were significantly less desirable than dates with some charisma, F(1, 18) = 227.94.85第84頁(yè)/共93頁(yè)第八十五頁(yè)，共92頁(yè)。There was no significant effect of gender, indicating that ratings from male and female participants were similar, F(1, 18) = 0.005, p =.946. The

32、re was a significant interaction effect between the attractiveness of the date and the gender of the participant, F(2, 36) = 80.43. This effect indicates that the desirability of dates of different levels of attractiveness differed in men and women.86第85頁(yè)/共93頁(yè)第八十六頁(yè)，共92頁(yè)。To break down this interactio

33、n, contrasts compared each level of attractiveness to average looks, across male and female participants. These contrasts revealed significant interactions when comparing male and female scores to attractive dates compared to average looking dates, F(1, 18) = 43.26, and to ugly dates compared to ave

34、rage-looking dates, F(1, 18) = 30.23.87第86頁(yè)/共93頁(yè)第八十七頁(yè)，共92頁(yè)。The interaction graph shows that although both males and females interest decreased as attractiveness decreased, this decrease was more pronounced for men, suggesting that when charisma is ignored, mens interest in dating a person was more i

35、nfluenced by their looks than womens.88第87頁(yè)/共93頁(yè)第八十八頁(yè)，共92頁(yè)。There was a significant interaction effect between the level of charisma of the date and the gender of the participant, F(2, 36) = 62.45, indicating that the desirability of dates of different levels of charisma differed in men and women. Co

36、ntrasts were performed comparing each level of charisma to the middle category of some charisma across male and female participants. These contrasts revealed significant interactions when comparing male and female scores to highly charismatic dates compared to dates with some charisma, F(1, 18) = 27

37、.20, and to dullards compared to dates with some charisma F(1, 18) = 33.69.89第88頁(yè)/共93頁(yè)第八十九頁(yè)，共92頁(yè)。The interaction graph reveals that both males and females interest decreased as charisma decreased, but this decrease was more pronounced for females, suggesting womens interest in dating a person was mo

38、re influenced by their charisma than mens.90第89頁(yè)/共93頁(yè)第九十頁(yè)，共92頁(yè)。There was a significant charisma attractiveness interaction, F(4, 72) = 36.63, indicating that the desirability of dates of different levels of charisma differed according to their attractiveness. Contrasts were performed comparing each level of charisma to the middle category of some charisma across each level of attractiveness compared to the category of average attractiveness. The first contrast revealed a significant interaction when comparing attractive dates to average-looking dates