CPU and GPU implementations of Permutation Testing using the libraries Armadillo and Arrayfire. The permutation testing schemes implemented herein are based on two-sample and one-sample t-test.
Download homebrew
Download the C++ linear algebra library, Armadillo. Do NOT use apt-get to install Armadillo, this will install a very old version (4.2). This software has been tested against Armadillo 5.*, 6.1 and 6.2. So go to http://arma.sourceforge.net/download.html download the latest stable version and follow the README.txt instruction on how to install Armadillo. It is VERY important that you install all the requirements (section 3 of the README.txt) before you proceed to build and install Armadillo (section 4 of the README.txt).
GLM models observed data (dependent variable) as a linear combination
of predictor variables (independent variables, covariates etc). Y (observed data matrix), X (design matrix, predictor variables), b (parameter estimate vector), and e (error vector).
Y = X * b + e
Many statistical techniques are special cases of the general linear model. For example:
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ANOVA asks whether different experimental conditions (X1, X2, etc) are associated with different scores.
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Multiple regression asks whether scores are related to predictor variables (X1, X2, etc)
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T-test is a special case of ANOVA where there are only two groups X1 and X2
The three of them are asking the same question. Is there a relationship between a dependent variable (Yi) and one or more independent variables (Xi).
1. Paired Sample t-test: Used to compare two population means in the case of two samples that are correlated. Commonly used in 'before and after' studies, case-control studies.The typical workflow for two-sample t-test hypothesis testing is:
2. One-Sample t-test: The one sample t test is an appropriate analysis when the research looks to compare the mean of a sample with a hypothesized mean to assess if differences occur. The assumptions of the one sample t test include: the data must be normally distributed within the population and the data should be independent; scores of one participant are not dependent upon scores of another.
3. Two-Sample t-test: Used to determine if two population means are equal.
Hypothesis testing is a group of techniques in Statistics that are often used in medical images to identify regions that display statistical significant activity. So how do we classify a voxel as statistically significant?
1. Select univariate test-statistic: The job of this test statistic is to act as the mapping from data to a detection threshold.
2. Hypothesis setup: Setup two hypothesis. The null hypothesis (H0) says that there is no mean difference between both samples. The alternate hypothesis says that they are different.
3. Select Significance Level: Choose the significance level. Usually 5% in most studies and 1% in medical studies. This is usually denoted as alpha, and it tells us the probability of making a Type I error; that is the probability of deciding erroneously on the alternative when, in fact, the null hypothesis is true.
4. Calculate the Parameter: To calculate the parameter using the fo
5. Testing of hypothesis: Compare result to table value.