Mini Tutorial: Signal to noise ratio

This tutorial complements Tutorial 2, 3 and 4: the aim of the current mini-tutorial is to help you better understand the relationship between signal and noise in fMRI data. Other tutorials (like Tutorial 5 and 6) will show you how we can increase the signal to noise ratio.

In tutorial 2 and 3, we explained that the activation we record is composed of two parts: signal and noise. The signal is the variation in the BOLD activation we CAN explain. For example, if the activation in a given voxel increases at the start of an experimental condition (e.g., presenting faces) and decreases at the end of the experimental condition (e.g., fixation), then we can say that the variation in the activation (the increase and decrease of BOLD activation) is explained (at least in part) by the experimental protocol. The noise is the variation in th BOLD activation that we CANNOT explain (or put simply, it is left over variance once we have subtracted out the variance we can explain).

Importantly, the degree to which we can make inferences depends on the ratio of signal to noise in our data. In the first part of the tutorial, you will develop intuitive understanding about how different levels of signal and noise are related to the reliability of activation for a single voxel. In the second part, we will introduce various measures of signal-to-noise ratio used in fMRI analyses.

Move the "signal" slider up and down in the BOLD controls section.

Question 1: a) What effect does moving the "signal" slider on the BOLD activation(grey)?

b) What effect does moving the "signal" slider on the scatter plot?

Now, move the "noise" slider up and down.

Question 2: a) What effect does moving the "noise" slider on the BOLD activation(grey)?

b) What effect does moving the "noise" slider on the scatter plot?

Reset the widget by refreshing the webpage. Now fit the predictor (pink) to the BOLD activation using the B1 and Constant sliders(Predictor controls). You can use the Optimize GLM button if you wish to obtain the optimal solution.

Question 3: a) What is the correlation coefficient for this model? How much of the variance is explained in this model? (Hint: you can find the percent of explained variance by squaring the correlation coefficient.)

We will now examine four cases:

• high signal + low noise (signal = 0.80, noise = 0.20)
• high signal + high noise (signal = 0.80, noise = 0.80)
• low signal + low noise (signal = 0.20, noise = 0.20)
• low signal + high noise (signal = 0.20, noise = 0.80)

For each case, set the signal and noise values to the ones specified in the parentheses, fit the model using the Optimize GLM button, and record the correlation coefficient. (Tip: you can use the arrows on your keyboard to get exact slider values.)

Question 4:

a) Which case has the highest signal to noise ratio? Which case has the lowest signal to noise ratio? What correlation coefficient do each of these cases have?

Now set the signal value to 0.50 and the noise value to 0.50.

b) Fill in the blanks with either "increase" or "decrease": When you increase the signal value while keeping the noise term constant, the correlation coefficient ___. When you decrease the signal value, the correlation coeffcient ___. When you increase the noise value while keeping the noise term constant, the correlation coefficient ___. When you decrease the noise value, the correlation coeffcient ___.

c) Does changing the predictor sliders change the correlation coefficient? Why or why not?

d) When it comes to determining whether a voxel is reliabily activated to a given condition, does a higher signal necessarily mean better reliability?

Download the Signal-to-noise spreadsheet. The spreadsheet includes information about 2 voxels (Voxel A and Voxel C) including the raw BOLD signal, the predictor(obtained by estimating the optimal slope and intercept, and then calculating the predicted scores for the timecourse) and the residuals (BOLD - signal).

Question 5: Using the information given in the spreadsheet, estimate the tSNR for both voxels.

Question 6: Using the same Excel sheet, calculate the tCNR for Voxel A and Voxel C. Which one has the highest CNR?

Go back to the widget at the start of the tutorial and reexamine the four cases (high signal+low noise, high signal+high noise...), but now take note of the tCNR.

Question 7: You may have noticed that two of these cases have the same correlation coefficient. Brifely (1-2 sentences) explain how it is possible for two sets of signal and noise values to have the same tCNR.