Dear Alfonso,

I am currently finalizing the results for my PhD thesis, so I would be extremely grateful if you could help clarify this point.

I am running a seed-to-voxel paired analysis comparing V1 vs V3, with age and sex included as second-level covariates.

For three significant clusters, I opened the REX Results window, then the plot window and exported both:

• Export raw data


• Export effect sizes

From the exported rawdata.mat file, I obtained a 46 × 3 matrix (23 subjects × 2 conditions, 3 significant clusters). The first 23 rows correspond to V1 and the last 23 rows correspond to V3.

For the first cluster, the average raw connectivity values are:

• V1: 0.1904


• V3: 0.1802

Thus, the raw functional connectivity appears to decrease slightly from V1 to V3.

However, the exported effectsize.mat file contains:

effectsize.data =



          Cluster1   Cluster2   Cluster3

V1        -0.1256    -0.1184     0.1258

V3         0.6076     0.6259     0.7745

For the same cluster, the "Display effects" plot therefore shows a large increase from V1 to V3, which seems inconsistent with the raw connectivity values.

My question is:

What exactly do the two bars in the "Display effects" plot represent?

I initially thought that the bars represented the average functional connectivity for each condition, but the exported raw data suggest that this is not the case.

Thank you very much for your time !

Best regards,

Adele

Dear Adele,

I saw your message and was struggling with kind of the same thing a few days ago for my thesis.

I found this in the Conn handbook (see screenshot): Click on ‘plot effects’ to compute effect-sizes (e.g. connectivity values within each group) averaged across all voxels within each significant cluster.

So I think effect size is average connectivity within each group.

Maybe it helps!

Kind regards,

Fenna 

Dear Adele,

Effect-size refers to the effects estimated in your particular second-level model and used for statistical inference. In your case, for example, with a paired analysis comparing V1 vs V3 while controlling for age and gender, effect sizes represent the "adjusted means" in your model (i.e. the average difference between V1 and V3 estimated at the zero-level of your covariates; e.g. if your age/gender covariates are centered the zero-level of those covariates will correspond to the average age/gender in your sample)

More generally, if your second level model design matrix is X, your between-subjects contrast vector is C, and your between-conditions vector is M, then the second-level analysis will fit to your data matrix Y a model of the form:

Y ~ X*B 

where B is the estimated matrix of regressor coefficients. The "effect-sizes" displayed in CONN's plot always correspond to the elements of

effects = C*B*M'

In your particular case, X=[Subjects Age Gender], Y=[V1 V3], C=[1 0 0] and M=[-1 1], so the effect sizes are displaying the difference between B(1,1) and B(1,2), containing respectively the estimated adjusted means from your data Y.

Hope this helps

Alfonso 

Originally posted by adeleh:

Dear Alfonso,

I am currently finalizing the results for my PhD thesis, so I would be extremely grateful if you could help clarify this point.

I am running a seed-to-voxel paired analysis comparing V1 vs V3, with age and sex included as second-level covariates.

For three significant clusters, I opened the REX Results window, then the plot window and exported both:

• Export raw data


• Export effect sizes

From the exported rawdata.mat file, I obtained a 46 × 3 matrix (23 subjects × 2 conditions, 3 significant clusters). The first 23 rows correspond to V1 and the last 23 rows correspond to V3.

For the first cluster, the average raw connectivity values are:

• V1: 0.1904


• V3: 0.1802

Thus, the raw functional connectivity appears to decrease slightly from V1 to V3.

However, the exported effectsize.mat file contains:

effectsize.data =



          Cluster1   Cluster2   Cluster3

V1        -0.1256    -0.1184     0.1258

V3         0.6076     0.6259     0.7745

For the same cluster, the "Display effects" plot therefore shows a large increase from V1 to V3, which seems inconsistent with the raw connectivity values.

My question is:

What exactly do the two bars in the "Display effects" plot represent?

I initially thought that the bars represented the average functional connectivity for each condition, but the exported raw data suggest that this is not the case.

Thank you very much for your time !

Best regards,

Adele

Dear Alfonso,

Thank you very much for your explanation. It is now clear to me that the bars displayed in the "Display effects" window correspond to the adjusted means estimated by the second-level model!

However, I am still confused by the magnitude of the difference between the raw and adjusted values.

In my exported raw data, the average Fisher-transformed connectivity values are:

• V1 = 0.1904


• V3 = 0.1802

whereas the adjusted means displayed by CONN are:

• V1 = -0.1256


• V3 = 0.6076

Thus, the adjustment not only changes the absolute values, but also reverses the apparent direction of the V1–V3 difference.

My second-level model includes only two covariates (age and sex), and age and sex were entered without centering (and sex coded as 0/1).

Could this large discrepancy simply result from the lack of centering, or should I expect the adjusted means to remain relatively close to the raw means in this situation?

Also, if centering is recommended, should the age covariate be centered using the mean age of the subjects included in the second-level model (patients only), rather than all subjects in the project (patients + controls) ?

Thank you very much again for your help !

Adèle

Originally posted by Alfonso Nieto-Castanon:

Dear Adele,

Effect-size refers to the effects estimated in your particular second-level model and used for statistical inference. In your case, for example, with a paired analysis comparing V1 vs V3 while controlling for age and gender, effect sizes represent the "adjusted means" in your model (i.e. the average difference between V1 and V3 estimated at the zero-level of your covariates; e.g. if your age/gender covariates are centered the zero-level of those covariates will correspond to the average age/gender in your sample)

More generally, if your second level model design matrix is X, your between-subjects contrast vector is C, and your between-conditions vector is M, then the second-level analysis will fit to your data matrix Y a model of the form:

Y ~ X*B 

where B is the estimated matrix of regressor coefficients. The "effect-sizes" displayed in CONN's plot always correspond to the elements of

effects = C*B*M'

In your particular case, X=[Subjects Age Gender], Y=[V1 V3], C=[1 0 0] and M=[-1 1], so the effect sizes are displaying the difference between B(1,1) and B(1,2), containing respectively the estimated adjusted means from your data Y.

Hope this helps

Alfonso 

Originally posted by adeleh:

Dear Alfonso,

I am currently finalizing the results for my PhD thesis, so I would be extremely grateful if you could help clarify this point.

I am running a seed-to-voxel paired analysis comparing V1 vs V3, with age and sex included as second-level covariates.

For three significant clusters, I opened the REX Results window, then the plot window and exported both:

• Export raw data


• Export effect sizes

From the exported rawdata.mat file, I obtained a 46 × 3 matrix (23 subjects × 2 conditions, 3 significant clusters). The first 23 rows correspond to V1 and the last 23 rows correspond to V3.

For the first cluster, the average raw connectivity values are:

• V1: 0.1904


• V3: 0.1802

Thus, the raw functional connectivity appears to decrease slightly from V1 to V3.

However, the exported effectsize.mat file contains:

effectsize.data =



          Cluster1   Cluster2   Cluster3

V1        -0.1256    -0.1184     0.1258

V3         0.6076     0.6259     0.7745

For the same cluster, the "Display effects" plot therefore shows a large increase from V1 to V3, which seems inconsistent with the raw connectivity values.

My question is:

What exactly do the two bars in the "Display effects" plot represent?

I initially thought that the bars represented the average functional connectivity for each condition, but the exported raw data suggest that this is not the case.

Thank you very much for your time !

Best regards,

Adele