0todd0000
commented
3 years ago Can we use additional SPM in non-normally distributed SPM data ( nonparametric procedures in spm1d.stats.nonparam)?
Yes, nonparametric procedures are suitable for any distribution.
How can we interpret the t value in further analysis (not just for hypothesis purpose)?
In spm1d, nonparametric t tests use the exact same t value as parametric tests, so the interpretation of the t value is identical to parametric procedures. The t value effectively indicates effect size, but unlike effect size, its probabilistic properties are precisely known. Just as effect sizes can be interpreted in contexts other than hypothesis testing, so too can t values.
We believe that the beginning of the statistical difference between normal and potentiated muscle contraction can be interesting information.
SPM procedures can indeed be used to detect the beginning of signals, but this is not their primary purpose. Their primary purpose is to conduct domain-wide tests, where "domain" usually means 0% - 100% time. If the main purpose of your analysis is to detect signal onset, then an event detection procedure like this one might be more appropriate. SPM results will likely be similar to event-detection results, but not necessarily.
The maximal value of t over the threshold and the significance of t area over the threshold can be useful information about the intensity and duration of potentiation and fatigue. Integral of t over the threshold can be defined as potentiation impulse.
These may indeed be interesting metrics to consider.
- The probability associated with the maximum t value can be calculated using
spm1d.rft1d.t.sf - The probability associated with the entire excursion set (i.e., all t value clusters over the threshold) is given by
p_set, which is returned automatically in both parametric and nonparametric procedures. See the "set-level inference" section on this documentation page. - Non-parametric procedures in spm1d use t cluster integrals by default for cluster-level probabilities. See the example code below for accessing cluster integrals.
# This code is copied from ./spm1d/examples/nonparam/1d/ex_ttest2.py
import numpy as np
from matplotlib import pyplot
import spm1d
#(0) Load dataset:
dataset = spm1d.data.uv1d.t2.PlantarArchAngle()
yB,yA = dataset.get_data() #normal and fast walking
#(1) Conduct non-parametric test:
np.random.seed(0)
alpha = 0.05
two_tailed = True
snpm = spm1d.stats.nonparam.ttest2(yA, yB)
snpmi = snpm.inference(alpha, two_tailed=two_tailed, iterations=500)
cluster = snpmi.clusters[0]
print( cluster )[Cluster (NonParam)
threshold : -3.023
centroid : (96.607, -4.414)
isinterpolated : True
iswrapped : False
endpoints : (92.218, 100.000)
extent : 7.782
metric : ClusterIntegral
metric_value : 11.11875
nPermUnique : 184756 unique permutations possible
nPermActual : 500 actual permutations
P : 0.00000
]You'll see that the metric is ClusterIntegral and that its value is 11.11875. You can access the value directly using the metric_value property:
x = cluster.metric_value
print( x )11.118746826689936
(The question below is copied from an email conversation)