方差分析下学习教案

1、会计学1方差分析下方差分析下第一页，共92页。RMRM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5.42第1页/共93页第二页，共92页。Factorial RM Design ANOVAFactorial RM Design ANOVA5.6Mixed Design ANOVAMixed Design ANOVA5.73第2页/共93页第三页，共92页。 Repeated measures Repeated measures（RMRM）是指在实验过程中，）是指在实验过程中，相同的实体

2、相同的实体(sht)(sht)（entities, e.g. entities, e.g. participantsparticipants）参与所有情况下的（实验控制变量）参与所有情况下的（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的不同水平下的）实验或者在不同的时间点下提供数据。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

3、4第3页/共93页第四页，共92页。 RM-ANOVA RM-ANOVA，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：各组样本数据不独立各组样本数据不独立控制变量的水平控制变量的水平(shupng)(shupng)数在三个以上数在三个以上满足球形检验满足球形检验5第4页/共93页第五页，共92页。 球形（球形（ sphericity sphericity 表示为表示为）指不同实）指不同实验条件（即控制变量的不同水平）下的观测验条件（即控制变量的不同水平）下的观测变量的变化是相似的。变量的变化是相似的。 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

4、一性是同一(tngy)(tngy)变量在不同观测水平下的变量在不同观测水平下的方差之间无显著性差异；而球形是指不同变方差之间无显著性差异；而球形是指不同变量（不同水平下的观测变量在量（不同水平下的观测变量在RM-ANOVARM-ANOVA中对中对应于不同的变量）的变化要类似。应于不同的变量）的变化要类似。6第5页/共93页第六页，共92页。variance A-B variance A-C variance B-C球形检验(jinyn)通过的条件为：7第6页/共93页第七页，共92页。当有两个组间差异的方差非常接近时，数据满足本地(bnd)球形（local sphericity）检验。在本例中

5、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第7页/共93页第八页，共92页。实际检验方法：在SPSS中球形检验可以通过(tnggu)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(tnggu)。9第8页/共93页第九页，共92页。 当球形检验没通过时：当球形检验没通过时：0.75, 0.75, 采用采用(ciyng)HuynhFeldt (ciyng)HuynhFeldt estimateestimate的结果的结果 0.75 0.75或未知，采用或未知，采用(ciyng)Green

6、houseGeisser (ciyng)GreenhouseGeisser 修正结果修正结果 球形检验是否球形检验是否(sh fu)(sh fu)通过还影响我们对置信区间调整方法的通过还影响我们对置信区间调整方法的选择：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 Bonferroni method 10第9页/共93页第十页，共92页。11第10页/共93页第十一页，共92页。12第11页/共93页第十二页，共92页。N-1为总离

7、差的自由度，由样本(yngbn)总量决定13第12页/共93页第十三页，共92页。每个人（participant）的自由度为n-1（n为水平(shupng)数）SSw的自由度为83=2414第13页/共93页第十四页，共92页。dfM = k 1 = 315第14页/共93页第十五页，共92页。16第15页/共93页第十六页，共92页。17第16页/共93页第十七页，共92页。18第17页/共93页第十八页，共92页。每一水平下的观测(gunc)值单独作为一个变量的值录入19第18页/共93页第十九页，共92页。20第19页/共93页第二十页，共92页。添加Within-subject 因素名

8、称(mngchng)与水平数21第20页/共93页第二十一页，共92页。设置(shzh)变量22第21页/共93页第二十二页，共92页。设置(shzh)RM模型23第22页/共93页第二十三页，共92页。设置对比(dub)方法24第23页/共93页第二十四页，共92页。设置绘图(hu t)模式25第24页/共93页第二十五页，共92页。设置(shzh)置信区间及其它可选项26第25页/共93页第二十六页，共92页。27第26页/共93页第二十七页，共92页。28第27页/共93页第二十八页，共92页。29第28页/共93页第二十九页，共92页。30第29页/共93页第三十页，共92页。31第3

9、0页/共93页第三十一页，共92页。32第31页/共93页第三十二页，共92页。33第32页/共93页第三十三页，共92页。34第33页/共93页第三十四页，共92页。35第34页/共93页第三十五页，共92页。36第35页/共93页第三十六页，共92页。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页/共93页第三十七页，共92页。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页/共93页第三十八页，共92页。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(yunl)和分析方法与One way RM-ANOVA类似。39第38页/共93页第三十九页，共92页。控制(kngzh)因素：Drink和ImageDrink有三个水平：

12、Beer、Wine、Water。Image有三个水平：Positive、Neutral、Negative。40第39页/共93页第四十页，共92页。每个控制要素中作为基准或参考水平的数据(shj)放在第一位或者最后一位。41第40页/共93页第四十一页，共92页。42第41页/共93页第四十二页，共92页。设置Within-Subject Factor： 定义因素的顺序(shnx)要和控制要素顺序(shnx)及数据录入的顺序(shnx)相一致。43第42页/共93页第四十三页，共92页。44第43页/共93页第四十四页，共92页。按顺序(shnx)添加Within-Subjects Varia

13、bles45第44页/共93页第四十五页，共92页。根据问题的实际性质设置(shzh)对比方式46第45页/共93页第四十六页，共92页。设置(shzh)Profile Plots47第46页/共93页第四十七页，共92页。设置(shzh)Options48第47页/共93页第四十八页，共92页。49第48页/共93页第四十九页，共92页。球形检验结果：两个主因素效果(xiogu)Significant 交互因素效果(xiogu)non-significant50第49页/共93页第五十页，共92页。51第50页/共93页第五十一页，共92页。自由度的计算(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页/共93页第五十二页，共92页。自由度的计算(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页/共93页第五十三页，共92页。dfGG-D=dfDGG =20.577=1.154dfR-GG-D=dfR-DGG=380.577=21.926调整F检验(jinyn)中的其余各项自由度计算方法相同。54第53页/共93页第五十四页，共92页。55第54页/共93页第五十五页，共92页。56第55页/共93页第五十六页，共92页。不一致(yzh)！57第56页/共93页第五十七页，共92页。58第57页/共93页第五十八页，共92页。当Post hoc和Co

17、ntracts的结果不一致(yzh)时，以后者为准。59第58页/共93页第五十九页，共92页。60第59页/共93页第六十页，共92页。61第60页/共93页第六十一页，共92页。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页/共93页第六十二页，共92页。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页/共93页第六十三页，共92页。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页/共93页第六十四页，共92页。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页/共93页第六十五页，共92页。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页/共93页第六十六页，共92页。Mixed design是指在实验过程中有多个控制因素，其中有些因素（within-subj

25、ects factor）的不同水平为所有(suyu)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第66页/共93页第六十七页，共92页。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

26、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要求，在对比(dub)时一般采用repeated 方式进行对比(dub)。68第67页/共93页第六十八页，共92页。问题：测试长相（looks）和个性魅力(personality)对快速约会(yu hu)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(yu hu)的意愿。69第68页/共93页第六十九页，共92页。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(mngchng)及各因素水平数。70第69页/共93页第七十页，共92页。 映射组内因素变量(

27、binling) 指定组间因素71第70页/共93页第七十一页，共92页。设置(shzh)各因素的对比方式72第71页/共93页第七十二页，共92页。设置绘图(hu t)方式73第72页/共93页第七十三页，共92页。设置可选项因有组间因素，所以(suy)需要进行方差齐次性检验74第73页/共93页第七十四页，共92页。因素(yn s)摘要表75第74页/共93页第七十五页，共92页。描述性统计(tngj)76第75页/共93页第七十六页，共92页。检查组间因素方差分析的条件是否(sh fu)满足方差齐次性检验77第76页/共93页第七十七页，共92页。检查组内因素方差分析的条件是否(sh f

28、u)满足球形检验78第77页/共93页第七十八页，共92页。组间因素(yn s)效果79第78页/共93页第七十九页，共92页。组间因素(yn s)效果对比80第79页/共93页第八十页，共92页。Main effect- Gender81第80页/共93页第八十一页，共92页。Main effect- Looks82第81页/共93页第八十二页，共92页。Interaction-Looks83第82页/共93页第八十三页，共92页。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页/共93页第八十四页，共92页。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页/共93页第八十五页，共92页。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页/共93页第八十六页，共92页。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页/共93页第八十七页，共92页。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页/共93页第八十八页，共92页。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页/共93页第八十九页，共92页。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页/共93页第九十页，共92页。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