第六讲方差分析(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球形检验球形检验5.2RM-ANOVARM-ANOVA原理原理5.3结果分析与表达结果分析与表达5.5数据录入与操作数据录入与操作5.42Factorial RM Design ANOVAFactorial RM Design ANOVA5.6Mixed Design ANOVAMixed Design ANOVA5.73 Repeated measuresRepeated measures（RMRM）是指在实验过程中，）是指在实验过程中，相同的实体（相同的实体（ent

2、ities, e.g. participantsentities, e.g. participants）参）参与所有情况下的（实验控制变量的不同水平下的）与所有情况下的（实验控制变量的不同水平下的）实验或者在不同的时间点下提供数据。实验或者在不同的时间点下提供数据。其它的表达方式：其它的表达方式：Within-participants design, Related design,Within-participants design, Related design,Within-subjects design Within-subjects design 4 RM-ANOVARM-ANOVA，

3、重复测量的方差分析适用条件：，重复测量的方差分析适用条件：o 各组样本数据不独立各组样本数据不独立o 控制变量的水平数在三个以上控制变量的水平数在三个以上o 满足球形检验满足球形检验5 球形（球形（ sphericity 表示为表示为）指不同实验）指不同实验条件（即控制变量的不同水平）下的观测变量条件（即控制变量的不同水平）下的观测变量的变化是相似的。的变化是相似的。 球形和方差齐次性相类似，但是方差齐次球形和方差齐次性相类似，但是方差齐次性是同一变量在不同观测水平下的方差之间无性是同一变量在不同观测水平下的方差之间无显著性差异；而球形是指不同变量（不同水平显著性差异；而球形是指不同变量（不同

4、水平下的观测变量在下的观测变量在RM-ANOVARM-ANOVA中对应于不同的变中对应于不同的变量）的变化要类似。量）的变化要类似。6variance A-B variance A-C variance B-C球形检验通过的条件为：7当有两个组间差异的方差非常接近时，数据满足本地球形（local sphericity）检验。在本例中A-C差异和B-C差异的方差非常接近，因为球形检验是通过的。8实际检验方法： 在SPSS中球形检验可以通过Mauchlys test进行。 其零假设为：实验不同情况下差异的方差是相等的。 若Mauchlys test的检验结果不显著，则球形检验通过。9 当球形检验没

5、通过时：当球形检验没通过时： 0.75, 0.75, 采用采用HuynhFeldt estimateHuynhFeldt estimate的结的结果果 0.750.75或未知，采用或未知，采用GreenhouseGeisserGreenhouseGeisser 修正结果修正结果 球形检验是否通过还影响我们对置信区间调整方法的选择：球形检验是否通过还影响我们对置信区间调整方法的选择： ShpericityShpericity满足时，采用满足时，采用TukeyTukey（LSDLSD） ShpericityShpericity不满足时，采用不满足时，采用Bonferroni method Bonf

6、erroni method 101112N-1为总离差的自由度，由样本总量决定13每个人（participant）的自由度为n-1（n为水平数）SSw的自由度为83=2414dfM = k 1 = 315161718每一水平下的观测值单独作为一个变量的值录入1920添加Within-subject 因素名称与水平数21设置变量22设置RM模型23设置对比方法24设置绘图模式25设置置信区间及其它可选项2627282930313233343536Mauchlys test indicated that the assumption of sphericity had been violated,

7、 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 violate

8、d, 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中有两个以上的控制因素。对应的方差分析称为 Factorial RM-ANOVA。基本的原理和分析方法与One way RM-ANOVA类似。39控制因素

9、：Drink和ImageDrink有三个水平：Beer、Wine、Water。Image有三个水平：Positive、Neutral、Negative。40每个控制要素中作为基准或参考水平的数据放在第一位或者最后一位。4142设置Within-Subject Factor： 定义因素的顺序要和控制要素顺序及数据录入的顺序相一致。4344按顺序添加Within-Subjects Variables45根据问题的实际性质设置对比方式46设置Profile Plots47设置Options4849球形检验结果：两个主因素效果Significant 交互因素效果non-significant50 51

10、自由度的计算：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自由度的计算：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 ） =2

11、02 =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 residu

12、al interaction effects for drinks*Imagery ） =80-4 =7653dfGG-D=dfDGG =20.577=1.154dfR-GG-D=dfR-DGG=380.577=21.926调整F检验中的其余各项自由度计算方法相同。545556不一致！5758当Post hoc和Contracts的结果不一致时，以后者为准。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 of t

14、he 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, F(1

15、.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 sig

16、nificant 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 to

17、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:65Lo

18、oking 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 term wh

19、en 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是指在实验过程中有多个控制因素，其中有些因素（within-subjects

20、factor）的不同水平为所有的实验实体（Entity，如subjects）都参与测试，而另外一部分的因素(between-subjects factor)的不同水平则由不同的实验实体参与测试。67组内因素（within-subjects factor)的每个水平都按照单独的变量进行数据录入，一个组间因素（between-subjects factor)的作为一个单独的变量进行数据录入。录入组内因素的不同水平时，需要考虑不同水平的次序关系，把参考水平（reference level or baseline）排在该因素不同水平的第一位或最后一位。若某因素的各个水平之间地位对等，则在排列时没有特殊

21、要求，在对比时一般采用repeated 方式进行对比。68问题：测试长相（looks）和个性魅力(personality)对快速约会效果的影响。控制因素：长相（3个水平）个性魅力（3个水平）性别（2个水平）测试值：愿意和同一个人再次约会的意愿。69按照实验测试的顺序（该顺序和数据录入顺序相一致），添加组内因素名称及各因素水平数。70映射组内因素变量指定组间因素71设置各因素的对比方式72设置绘图方式73设置可选项因有组间因素，所以需要进行方差齐次性检验74因素摘要表75描述性统计76检查组间因素方差分析的条件是否满足v 方差齐次性检验77检查组内因素方差分析的条件是否满足v 球形检验78组间因

22、素效果79组间因素效果对比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 that

23、 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 expr

24、essed 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 effe

25、ct 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 dates

26、 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 attract

27、ive 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, suggestin

28、g 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 of di

29、fferent 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 charismatic d

30、ates 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 women

31、s 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 performe

32、d 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