Lab3: writing up results and ANOVAs with within and between factors 1

Should be able to answer: What are the independent and dependent variables? Are the conditions of application met? – Compound symmetry? – Sphericity? 2

Conditions of application Normality: – fully balanced design, all subjects in all conditions, all cells filled so probably safe Compound symmetry: – Smallest covariance:.147, Largest covariance: 39 Sphericity: – p>.05, fail to reject hypothesis that pairwise variances differ 3

Should be able to answer: Are there main effects? – Contrasts: to learn about others, p

Summary of results A significant main effect of coil was observed, suggesting that the fMRI signal varies for coils with different numbers of channels (F 1,11 )=37, p<.001), while collapsing across (or irrespective to) acceleration level. Means reveal that signal was greater for the 32 channel as predicted. A significant main effect of acceleration was found, suggesting that MRI signals differ for different levels of acceleration (F 2,22 =13.6, p<.001), when collapsing across coils. Contrasts revealed that acceleration of a factor of 2 or 3 both differenced significantly from no acceleration (2factor: F 1,11 =6.1, p.1), suggesting that signal changes linearly with acceleration. Graphs reveal that the linear relationship is such that MRI signals decrease with increasing acceleration. This is consistent with our hypothesis. When reporting F, need degrees of freedom, first one is for the factor and is number of levels -1, second one is for error, which is (number of subjects -1) X (number of levels-1) 5

Should be able to answer: Are there main effects? Interactions? 6

Summary of results However!! There was a significant interaction of coil and acceleration (F 2,22 =9.9, p<.01). We therefore investigated the effect of acceleration separately for each coil. 12 channel: There is a significant main effect of acceleration using the GG (F 1.25, 13.8 =18.1, p<.001). Contrasts reveal that acceleration of a factor of 2 (F 1,11 =11.3, p<.01) and 3 (F 1,11 =131.1, p<.001) both differ from no acceleration. 32 channel: There is again a significant main effect of acceleration (F 2,22 =4.1, p<.05). However, contrasts revealed that only acceleration of factor 3 differed significantly from no acceleration (F 1,11 =7.9, p<.05). This suggests 32 channel coil is less affected by acceleration than 12 channel, as hypothesized. 7

Interpreting interactions via contrasts 8

Writing an abstract Background Objective Methods. May include: – (Sample size calculation / power) – Instruments – Procedure – Sample description (or may be in results) – Analysis (or may be in results) Results Discussion 9

Abstract format Background: Advances in MRI hardware have led to coils with greater numbers of channels, while software improvements have allowed MR data to be collected faster. Objective: Here, we set out to test whether more channels are better, and how MRI acceleration techniques might affect signal strength. Methods: Twelve subjects underwent fMRI with both a 12 (12ch) and a 32 channel (32ch) coil. For each coil, three levels of acceleration were tested (none, 2factor and 3factor). Average MR signal was extracted and used as the dependent measure in a repeated measures ANOVA. Results: There was a main effect of number of channels (F 1,11 )=37, p<.001), resulting from greater signal from the 32ch versus the 12ch. There was a main effect of acceleration (F 2,22 =13.6, p<.001), with signal decreasing as acceleration increased. In addition, there was an interaction between number of channels and acceleration (F 2,22 =9.9, p<.01). To investigate the interaction, repeated measure ANOVAs were performed for the simple effects. They revealed a significant main effect of acceleration for both the 12ch, where the Greenhouse-Geisser correction was used (F 1.25, 13.8 =18.1, p<.001), and for the 32ch (F 2,22 =4.1, p<.05). Simple contrasts revealed that for the 12ch, signals decreased significantly for both 2factor (F 1,11 =11.3, p<.01) and 3factor (F 1,11 =131.1, p<.001) acceleration. However, for the 3ch, signals decreased significantly for only the highest level of acceleration (F 1,11 =7.9, p<.05). Discussion: This suggests that signals are greater when collected with more channels, and as the amount of acceleration increases, signals decrease. This was particularly true for the 12ch data. 10

Next up: mixed design ANOA What if you have both within and between subjects factors? No worries, ANOVA can handle it What are between subject factors? 11

Mixed design: conditions of application 1.Normality within each factor level or group – Robust to violations as long as fully factorial -> no levels missing (like having only 2 of the three levels of acceleration for 32 channel data or group). – This can also be tested via histograms and tests for normality (see chapter 4??) 2.Homogeneity of variance: – Replaced by compound symmetry or sphericity in RM ANOVA – But now need to check for between subject factors with Levene’s test Tests the null hypothesis that the error variance of the dependent variable is equal across groups -> want nonsig need to be careful because can be positive from small deviations with large sample sizes If fail, can transform the data 12

Practical differences Must define between subject variables 13

Practical differences Can use posthoc tests to investigate differences: Scheffe 14

Practical differences Making plots 15

Practical differences Levene’s test 16

New output 17

Now you try! Expansion of MRI methods study from last week. Again tested two different MRI coils (12 channel and 32 channel coils), and 3 levels of acceleration (a0,a2,a3). Same hypotheses as before: – Signal should be larger for 32 than 12 channel coil – Signal should decrease with increasing levels of acceleration In addition, half of the subjects (12) were scanned with a resolution of 2mm (voxels 2x2x2mm) and half (12) with 3mm. – Hypothesize that large voxels result in more signal. 18

Should be able to answer: What are the independent and dependent variables? Are they within or between? Are the conditions of application met? – Sphericity? – Homogeneity of variance? Are there main effects? Interactions: investigate with simple effects and the contrasts What can you conclude: try writing up an abstract 19

Anything weird about this dataset? Degrees of freedom? When reporting F, need degrees of freedom, first one is for the factor and is number of levels -1, second one is for error, which is (number of subjects -1) X (number of levels-1) -> for mixed design, looks like its number of subjects -1 –(number of levels for between group variable -1)X (number of levels-1) 20

Conditions of application Sphericity: 21

Conditions of application Homogeneity of variance: 22

Can check variances so know how badly this fails 23

Can transform data Very dependent upon your data, and your field – No clear cut answers, heavily debated topic 24

Results similar…. But! 25

Coil x Resolution 26

Main effects Main effect of coil (F 1,20 =72.98, p<.001) irrespective of acceleration or resolution Main effect of acceleration (F 2,40 =34.98, p<.001), collapsing across coil and resolution. Simple contrasts reveal acceleration of a factor of 2 (F 1,20 =68.5, p<.001) and 3 (F 1,20 =22.4, p<.001) differ from no acceleration. Main effect of resolution (F 1,20 = , p<.001), irrespective of coil or acceleration 27

Interactions Significant interaction between acceleration and resolution (F 2,40 =72.3, p<.001) Significant interaction between coil and acceleration (F 2,40 =220.32, p<.001). Close to failing sphericity so good to keep in mind when look at results. Nonsignficant (p>.05) interactions between coil and resolution, and between all three factors 28

Follow up with contrasts Acceleration versus resolution – Level 2 versus 1: (F 1,20 =117.12, p<.001) – Level 3 versus 1: (F 1,20 =99.56, p<.001) Suggests that affect of acceleration differs depending on resolution This is when collapsing across coil. If there was a three way interaction than we wouldn’t be able to interpret this easily, because it would suggest that the affect of acceleration on resolution varies for each coil Can also follow up with simple effects. To do this need to average two coils together Find via pairwise comparisons – 2mm: 0factor differs from 3 factor – 3mm: every condition differs. 29

Follow up with contrasts Acceleration versus coil – Level 2 versus 1: (F 1,20 =28.58, p<.001) – Level 3 versus 1: (F 1,20 =27.2, p<.001) Suggests that affect of acceleration differs depending on coil This is when collapsing across resolution. 30

Abstract summary Background: Advances in MRI hardware have led to coils with greater numbers of channels, while software improvements have allowed MR data to be collected faster. Objective: Here, we set out to test for two different scan resolutions whether more channels are better, and how MRI acceleration techniques might affect signal strength. Methods: Twenty-four subjects underwent fMRI with both a 12 (12ch) and a 32 channel (32ch) coil. For each coil, three levels of acceleration were tested none (0factor), or 2-factor and 3- factor (2factor and 3factor). For half of the subjects, data was collected at 2x2x2mm (res2) while the other half was collected at 3x3x3mm (res3). Average MR signal was extracted and used as the dependent measure in a repeated measures ANOVA. Results: There was a significant interaction between acceleration and resolution (F 2,40 )=37, p<.001). Simple contrasts revealed signals changed differently for each resolution when going from 0factor to 2factor (F 1,20 =117.12, p<.001) and from 0factor to 3factor (F 1,20 =99.56 p<.001). This reflects the fact that signal increased for 3res, but decreases for 2res when going from no acceleration to any amount of acceleration. There was also a significant interaction between coil and acceleration (F 2,40 =220.32, p<.001). Simple contrasts revealed that signals increased differently for each coil when going from 0factor to 2factor (F 1,20 =28.58, p<.001) or 3factor (F 1,20 =27.2, p<.001), such that signals increased more for 32ch for 2factor and 3factor acceleration. Discussion: This suggests that signals behaved very differently depending on the resolution they were collected at. For res3, acceleration increased signals, while for res2 acceleration decreased signals. 31