Chapter 12: Statistical Analysis

 

 

 

Study Questions  

 

1.   What is the difference between descriptive and inferential statistics? Which do we use to assess statistical significance in fMRI?

Descriptive statistics are limited to describing features of the particular data set in question (e.g. the mean, median, etc.). Inferential statistics are used to determine what the data collected from a sample of a population can indicate about that population as a whole (i.e. what we can infer from the data about the limited group to the larger group in general). 

 

2.   What are Type I and Type II errors? Which is typically minimized in fMRI data analysis?

 

Type I error is rejecting your hypothesis when it is really true.  In the case of fMRI it would be a voxel labeled as active when it really is not.  Type II error is the opposite, retaining your hypothesis when it is false.  Type I errors are minimized in fMRI. 

 

3.   What is an alpha value? Does it relate to Type I or Type II errors?

 

The alpha value is the arbitrary threshold set to determine if data is statistically significant.  If the obtained probability for the sample is less than the alpha value the sample is said to be statistically significant and the hypothesis is rejected.  Yes the alpha value relates to type I and II errors.  As the alpha value decreases you decrease the probability of making a Type I error, but increase the probability of making a Type II error. 

 

4.   Describe the basic principles of a t-test. In what sorts of analyses are t-tests most commonly used?

 

The t-test compares two distributions and identifies differences in the means of the samples.  It is most commonly used in blocked designs to compare two conditions, although it may be used for certain event-related designs.  

 

5.   What are the advantages and disadvantages of the Kolmogorov–Smirnov test compared to the t-test? Why is it infrequently used?

 

 The K-S test has the advantage of being sensitive to changes in variability and shape in sample means.  The disadvantage is that the K-S test is less sensitivity to changes in the sample means.   The K-S test is not frequently used because fMRI studies are usually not looking for variability caused to the dependent variable, but a change in the sample means.  i.e. brain has more activity when doing this- not more variability.  

 

6.   What are the basic principles of a correlation analysis? Over what range do correlation coefficients vary?

 

 Correlation analysis is a statistical test, which evaluates the strength of the relationship between two variables on a scale from -1 to 1.  A correlation of -1 means the objects are negatively correlated, as one increases the other decreases.  The closer to 1 or -1 the stronger the relationship between the variables is.  Correlation analysis allows comparision between the observed and predicted hemodynamic response. 

 

 

7.   What are the effects of signal averaging upon a correlation analysis?

 

Signal averaging can reduce the correlation found in correlation analysis.  Low-frequency changes in the data caused by scanner drift can cause the correlation between the data and predicted to decrease in strength. 

 

 

8.   What does a Fourier transform do to a time series of data?

 It converts a time series into a frequency series, which means that it only works on experiments (e.g. alternating blocked design), that have some sort of regularity or frequency in its pattern of conditions. Data transformed into a power spectrum displays the frequencies of the data.

 

9.   What is the Nyquist Sampling Theorem? Why is it important for fMRI?

 

 

The Nyquist sampling theory states that to accurately measure a given frequency, you must sample at a minimum of twice that frequency. 

 

10. What are some different ways in which fMRI data can be displayed? What are their advantages and disadvantages?

 

 

 

The most common way fMRI data is displayed is in a single anatomical slice, which shows activity through the use of color (generally, bright = high significance, dull=low).  The advantages for a single slice display are activity is easily seen and they require little processing after the experiment.  The disadvantages with single slice are it is difficult to identify activity in gyri and sucli because of the variability in the individual brain.  Additionally, determining which single slices to use for experimental data is difficult.  Another type of fMRI display is a rendered image, which converts the 2D images from the experimental data into a 3D image.  In rendered images activity is easily identified, even in the sulci and gyri.  A disadvantage to rendered images is they do not show internal nuclei, so activation of internal structures is not seen.  Researchers get around this by using glass brain views, which present fMRI data in 2D, as if the brain is transparent and only activation is shown.  Glass brain views are present in three images to zone in on the area of activation

 

 

11. What is the difference between radiological and neurological conventions for displaying MRI data?

 

 

In radiological convention, the left side of the image corresponds to the right hemisphere of the subject.  In neurological convention, the left side of the image corresponds to the left hemisphere of the brain.

 

 

 

12. What are the principles of the General Linear Model (GLM)? How do we evaluate the significance of activity using the GLM? 

The GLM models observed data as a function of a linear combination of multiple independent factors plus a constant (noise). Linear refers to the notion that they can simply be summed, that they do not influence each other (e.g. the effect of a particular variable would be the same with or without the others). The GLM assumes that the hemodynamic response is linear. 

 

13. What is a design matrix?

  

 A design matrix is used in GLM and specifies how the linear model changes over time. It is a hypothesis about which factors are causing the variance in the measured data.

 

 

14. What are nuisance factors, and why might they be included in an analysis model?

  

Nuisance factors are additional factors within the design matrix that are associated with known outside sources of variability.  Nuisance factors are included because they can reduce the amount of residual variability.  Additionally, by using nuisance factors, experimenters increase the validity of their GLM because sources of variability are being identified and accounted for. 

  

 

15. What assumptions does the GLM make? How valid are these assumptions for fMRI?

  

One assumption of GLM is the use of the same design matrix throughout the brain, which can decrease region variability, but increase residual error.  This assumption as said can cause problems with data analysis, but can be overcome by combining GLM with a region-of-interest analysis.  A second assumption is all voxels are analyzed independently.  Thirdly, is all time points are independently distributed, so the residuals will be similarly distributed.  This assumption can become a problem when the subject moves or when there is scanner drift.  Finally, design matrixes contain factors that accurately reflect changes in BOLD due to neural activity.  This assumption is some what valid, but a problem arises when the neural response takes time after the stimulus to occur because in most data the stimulus and any neural changes directly after the stimulus is applied are grouped (when really the neural change from the stimulus happens seconds later).

 

 16. What are data-driven analyses? What advantages and disadvantages do they present for fMRI?

   

In data-driven analyses, experimenters search the structure of the data in hopes of finding task-related activations.  An advantage of data-driven is it is not as dependent on hemodynamic response as traditional analysis, but grouping the data into clusters creates a new problem: How many clusters do you have in a data set?   Another advantage of data-driven is it has been shown to yield similar results as hypothesis driven analysis.  Finally, a disadvantage of data-driven is it can increase the intersubject variability.  

  

17. Why is random field theory used to estimate the number of independent tests in fMRI analyses? What are its principles?

 

RFT is used to estimate the number of independent tests because it is based on the smoothness of the experimental data, which is the degree to which neighboring voxels are temporally correlated.

 

18. What are the advantages and disadvantages of cluster size thresholding?

 

An advantage of cluster size thresholding is it reduces the amount of false positives through increasing the cluster size.  Also, by reducing the alpha value, cluster-size threshold decreases the number of Type II errors or missing a true activation.  One disadvantage of it is cluster-size looks over a large area and thereby looking over the areas of smaller activation, which could be just as meaningful.  Another disadvantage it will over look nonspeherical areas.  A final disadvantage is cluster-size does not correlate activity among adjacent voxels.  It assumes all voxels have the same likelihood of being active, which is false.

 

19. What are region-of-interest (ROI) analyses? Why might a study use ROI analyses instead of voxelwise analyses, or vice versa?

 

ROI analysis is a process for evaluating statistical data in regions that are predetermined, usually before the experiment, and usually based on anatomical differences.  ROI could be used over voxelwise because it reduces the number of comparisons, but it is difficult using ROI because it is difficult to find a way to create the separate regions.  Additionally, ROI present the advantages of reducing the problems in comparing subjects because ROI are individually created and do not becoming skewed by normalizing.

 

20. What is the difference between fixed-effects and random-effects analyses? Which is considered more appropriate for generalizing fMRI results to the population from which the subjects were drawn?

 

Fixed-effects allow inferences to be made about the particular subject in the experiment, while random-effects allows for inferences to be made about the population.  Random effects analysis is considered more appropriate for fMRI research because it deals with making inferences on the population.

 

21. What challenges must be overcome in order to use fMRI as a diagnostic tool for presurgical patients

In order for fMRI to be used as a presurgical tool, the creation of data and the analysis of it must be done quickly and accurately.  Also, the interpretation of the significant activations needs to be refined and become more accurate.