第六講方差分析(下)

1、第5章方差分析（下）Repeated-measure & Mixed design ANOVA1RMRM基本概念基本概念5.1球形檢驗球形檢驗5.2RM-ANOVARM-ANOVA原理原理5.3結(jié)果分析與表達結(jié)果分析與表達5.5數(shù)據(jù)錄入與操作數(shù)據(jù)錄入與操作5.42Factorial RM Design ANOVAFactorial RM Design ANOVA5.6Mixed Design ANOVAMixed Design ANOVA5.73 Repeated measuresRepeated measures（RMRM）是指在實驗過程中，）是指在實驗過程中，相同的實體（相同的實體

2、（entities, e.g. participantsentities, e.g. participants）參）參與所有情況下的（實驗控制變量的不同水平下的）與所有情況下的（實驗控制變量的不同水平下的）實驗或者在不同的時間點下提供數(shù)據(jù)。實驗或者在不同的時間點下提供數(shù)據(jù)。其它的表達方式：其它的表達方式：Within-participants design, Related design,Within-participants design, Related design,Within-subjects design Within-subjects design 4 RM-ANOVARM-AN

3、OVA，重復測量的方差分析適用條件：，重復測量的方差分析適用條件：o 各組樣本數(shù)據(jù)不獨立各組樣本數(shù)據(jù)不獨立o 控制變量的水平數(shù)在三個以上控制變量的水平數(shù)在三個以上o 滿足球形檢驗滿足球形檢驗5 球形（球形（ sphericity 表示為表示為）指不同實驗）指不同實驗條件（即控制變量的不同水平）下的觀測變量條件（即控制變量的不同水平）下的觀測變量的變化是相似的。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一變量在不同觀測水平下的方差之間無性是同一變量在不同觀測水平下的方差之間無顯著性差異；而球形是指不同變量（不同水平顯著性差異；而球形是指不同變

4、量（不同水平下的觀測變量在下的觀測變量在RM-ANOVARM-ANOVA中對應(yīng)于不同的變中對應(yīng)于不同的變量）的變化要類似。量）的變化要類似。6variance A-B variance A-C variance B-C球形檢驗通過的條件為：7當有兩個組間差異的方差非常接近時，數(shù)據(jù)滿足本地球形（local sphericity）檢驗。在本例中A-C差異和B-C差異的方差非常接近，因為球形檢驗是通過的。8實際檢驗方法： 在SPSS中球形檢驗可以通過Mauchlys test進行。 其零假設(shè)為：實驗不同情況下差異的方差是相等的。 若Mauchlys test的檢驗結(jié)果不顯著，則球形檢驗通過。9 當球

5、形檢驗沒通過時：當球形檢驗沒通過時： 0.75, 0.75, 采用采用HuynhFeldt estimateHuynhFeldt estimate的結(jié)的結(jié)果果 0.750.75或未知，采用或未知，采用GreenhouseGeisserGreenhouseGeisser 修正結(jié)果修正結(jié)果 球形檢驗是否通過還影響我們對置信區(qū)間調(diào)整方法的選擇：球形檢驗是否通過還影響我們對置信區(qū)間調(diào)整方法的選擇： ShpericityShpericity滿足時，采用滿足時，采用TukeyTukey（LSDLSD） ShpericityShpericity不滿足時，采用不滿足時，采用Bonferroni method

6、Bonferroni method 101112N-1為總離差的自由度，由樣本總量決定13每個人（participant）的自由度為n-1（n為水平數(shù)）SSw的自由度為83=2414dfM = k 1 = 315161718每一水平下的觀測值單獨作為一個變量的值錄入1920添加Within-subject 因素名稱與水平數(shù)21設(shè)置變量22設(shè)置RM模型23設(shè)置對比方法24設(shè)置繪圖模式25設(shè)置置信區(qū)間及其它可選項2627282930313233343536Mauchlys test indicated that the assumption of sphericity had been viola

7、ted, 2(5) = 11.41, p = .047, therefore GreenhouseGeisser corrected tests are reported ( = .53). The 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 = .063.37Mauchlys test indicated that the assumption of sphericity had been vio

8、lated, 2(5) = 11.41, p = .047, therefore multivariate tests are reported ( = .53). 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指在RM design中有兩個以上的控制因素。對應(yīng)的方差分析稱為 Factorial RM-ANOVA。基本的原理和分析方法與One way RM-ANOVA類似。39

9、控制因素：Drink和ImageDrink有三個水平：Beer、Wine、Water。Image有三個水平：Positive、Neutral、Negative。40每個控制要素中作為基準或參考水平的數(shù)據(jù)放在第一位或者最后一位。4142設(shè)置Within-Subject Factor： 定義因素的順序要和控制要素順序及數(shù)據(jù)錄入的順序相一致。4344按順序添加Within-Subjects Variables45根據(jù)問題的實際性質(zhì)設(shè)置對比方式46設(shè)置Profile Plots47設(shè)置Options4849球形檢驗結(jié)果：兩個主因素效果Significant 交互因素效果non-significant5

10、0 51自由度的計算：dfD-M=KD-1 =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自由度的計算：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 drinks

11、） =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 of re

12、sidual interaction effects for drinks*Imagery ） =80-4 =7653dfGG-D=dfDGG =20.577=1.154dfR-GG-D=dfR-DGG=380.577=21.926調(diào)整F檢驗中的其余各項自由度計算方法相同。545556不一致！5758當Post hoc和Contracts的結(jié)果不一致時，以后者為準。596061Mauchlys test indicated that the assumption of sphericity had been violated for the main effects of drink, 2(2

13、) = 23.75, p .001, and imagery, 2(2) = 7.42, p = .024. Therefore degrees of freedom were corrected using GreenhouseGeisser estimates of sphericity ( = .58 for the main effect of drink and .75 for the main effect of imagery).Report the results:62Report the results:There was a significant main effect

14、of the type of drink on ratings of the drink, F(1.15, 21.93) = 5.11, p = .011.Contrasts 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,

15、 F(1.50, 28.40) = 122.57.63Contrasts revealed that ratings 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:64There was a

16、 significant interaction effect between 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

17、 to their baseline (water) and all imagery 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:

18、65Looking at the interaction 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 ter

19、m when comparing positive 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:66Mixed design是指在實驗過程中有多個控制因素，其中有些因素（within-subje

20、cts factor）的不同水平為所有的實驗實體（Entity，如subjects）都參與測試，而另外一部分的因素(between-subjects factor)的不同水平則由不同的實驗實體參與測試。67組內(nèi)因素（within-subjects factor)的每個水平都按照單獨的變量進行數(shù)據(jù)錄入，一個組間因素（between-subjects factor)的作為一個單獨的變量進行數(shù)據(jù)錄入。錄入組內(nèi)因素的不同水平時，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或最后一位。若某因素的各個水平之間地位對等，則在排列時

21、沒有特殊要求，在對比時一般采用repeated 方式進行對比。68問題：測試長相（looks）和個性魅力(personality)對快速約會效果的影響。控制因素：長相（3個水平）個性魅力（3個水平）性別（2個水平）測試值：愿意和同一個人再次約會的意愿。69按照實驗測試的順序（該順序和數(shù)據(jù)錄入順序相一致），添加組內(nèi)因素名稱及各因素水平數(shù)。70映射組內(nèi)因素變量指定組間因素71設(shè)置各因素的對比方式72設(shè)置繪圖方式73設(shè)置可選項因有組間因素，所以需要進行方差齊次性檢驗74因素摘要表75描述性統(tǒng)計76檢查組間因素方差分析的條件是否滿足v 方差齊次性檢驗77檢查組內(nèi)因素方差分析的條件是否滿足v 球形檢驗7

22、8組間因素效果79組間因素效果對比80Main effect- Gender81Main effect- Looks82Interaction-Looks83All effects are reported as significant at p .001 unless otherwise stated. There was a significant main effect of the attractiveness of the date on interest expressed by participant, F(2, 36) = 423.73. Contrasts revealed

23、that attractive dates were significantly more desirable than average-looking ones, F(1, 18) = 226.99, and ugly dates were significantly less desirable than average-looking ones, F(1, 18) = 160.07.84There was also a significant main effect of the amount of charisma the date possessed on the interest

24、expressed in dating them, F(2, 36) = 328.25. Contrasts revealed that dates with high charisma were significantly more desirable than dates with some charisma, F(1, 18) = 109.94, anddullards were significantly less desirable than dates with some charisma, F(1, 18) = 227.94.85There was no significant

25、effect of gender, indicating that ratings from male and female participants were similar, F(1, 18) = 0.005, p =.946. There 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 d

26、ates of different levels of attractiveness differed in men and women.86To break down this interaction, 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 att

27、ractive dates compared to average looking dates, F(1, 18) = 43.26, and to ugly dates compared to average-looking dates, F(1, 18) = 30.23.87The interaction graph shows that although both males and females interest decreased as attractiveness decreased, this decrease was more pronounced for men, sugge

28、sting that when charisma is ignored, mens interest in dating a person was more influenced by their looks than womens.88There 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 o

29、f different levels of charisma differed in men and women. Contrasts 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 charismat

30、ic dates compared to dates with some charisma, F(1, 18) = 27.20, and to dullards compared to dates with some charisma F(1, 18) = 33.69.89The interaction graph reveals that both males and females interest decreased as charisma decreased, but this decrease was more pronounced for females, suggesting w

31、omens interest in dating a person was more influenced by their charisma than mens.90There 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 perf

32、ormed 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 when the date had high charisma compared to some charisma, F(1, 18) = 21.94, and tells us that as dates became less attractive there was a greater decline in interest when ch