fMRI: Biological Basis and Experiment Design
Lecture 25: Significance
• Review of GLM results
• Baseline trends
• Block designs; Fourier
analysis (correlation)
• Significance and
confidence intervals
Simulating experiments: a design tool
• What if I run with a TR of 2s instead of 1.5s?
– Alias cardiac rhythm; decrease SNR
• What if I use an average ISI of 8s instead of 10s?
– CNR drops; more trials ... break even?
• What if I don't jitter the ISIs?
– Deconvolution analysis breaks
• Should I use a block design or event-related design?
– Simulate both for 2 different exp'ts
• How many scans will I need to detect activation?
Confidence intervals and t-tests ... general idea
• Mean (or slope) will be (approximately) normally
distributed, with an associated standard error (SE, or M)
– Simplest case: data (N samples) drawn from normal distribution
with variance 2 will have variance 2/N (M =  /N)
Data sample:  = 1
Distribution of means of samples:  = 0.1
Confidence intervals and t-tests ... general idea
• Confidence of mean is based on SEM M
–  M: 67% confidence
– 1.645M: 90% confidence
– 1.96M: 95% confidence
• In regression, confidence of slope (b) is
based on SEb
– Estimate of variance in data comes from fit
residuals
– SEb is further normalized by distribution of data
Significance thresholds
• For a given set of assumptions about the
noise in the data ....
– Calculate t-value ( when N is not very large )
– Decide probability (p) that it was generated
by null hypothesis/distribution
– Significant if p < ???
B = 33
SEb = 18 (includes d.o.f.)
t = 1.8333
with d.o.f. > 9, a winner! (p < 0.05)
with d.o.f. <= 9, a lower (p >= 0.05)
Assumptions
• Relationship between data and model is linear
• Errors (noise samples) are
– normally distributed
– uncorrelated
• Can you check these assumptions?
"Good" model
"Good" model
Differences between data and
model don't look structured
Residuals are not correlated
with stimulus/model
When your baseline "basis" is insufficient
When your baseline "basis" is insufficient
Correlation is apparent in noise
Residuals are no longer uncorrelated
with stimulus/model
Assuming wrong shape of HIRF
Residuals are no longer uncorrelated with stimulus/model
Correlation between data and fit is much worse