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Lab3: writing up results and ANOVAs with within and between factors. Should be able to answer:. What are the independent and dependent variables? Are the conditions of application met? Compound symmetry? Sphericity ?. Conditions of application. Normality:
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Lab3: writing up results and ANOVAs with within and between factors
Should be able to answer: • What are the independent and dependent variables? • Are the conditions of application met? • Compound symmetry? • Sphericity?
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
Should be able to answer: • Are there main effects? • Contrasts: to learn about others, p. 371
Summary of results • A significant main effect of coil was observed, suggesting that the fMRI signal varies for coils with different numbers of channels (F1,11)=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 (F2,22=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: F1,11=6.1, p<.05; 3factor: F1,11=57.1, p<.001). In addition, a significant linear contrast was observed (F1,11=57.1, p<.001) with a non-significant quadratic contrast (F1,11=0.0, 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)
Should be able to answer: • Are there main effects? • Interactions?
Summary of results • However!! There was a significant interaction of coil and acceleration (F2,22=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 (F1.25, 13.8=18.1, p<.001). Contrasts reveal that acceleration of a factor of 2 (F1,11=11.3, p<.01) and 3 (F1,11=131.1, p<.001) both differ from no acceleration. • 32 channel: There is again a significant main effect of acceleration (F2,22=4.1, p<.05). However, contrasts revealed that only acceleration of factor 3 differed significantly from no acceleration (F1,11=7.9, p<.05). This suggests 32 channel coil is less affected by acceleration than 12 channel, as hypothesized.
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
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 (F1,11)=37, p<.001), resulting from greater signal from the 32ch versus the 12ch. There was a main effect of acceleration (F2,22=13.6, p<.001), with signal decreasing as acceleration increased. In addition, there was an interaction between number of channels and acceleration (F2,22=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 (F1.25, 13.8=18.1, p<.001), and for the 32ch (F2,22=4.1, p<.05). Simple contrasts revealed that for the 12ch, signals decreased significantly for both 2factor (F1,11=11.3, p<.01) and 3factor (F1,11=131.1, p<.001) acceleration. However, for the 3ch, signals decreased significantly for only the highest level of acceleration (F1,11=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.
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?
Mixed design: conditions of application • 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??) • 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
Practical differences • Must define between subject variables
Practical differences • Can use posthoc tests to investigate differences: Scheffe
Practical differences • Making plots
Practical differences • Levene’s test
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.
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