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This is my reconstruction of a chart that I used while teaching microprocessor programming. PDF Document This is the best choice if you want to print a copy. Word Document This is the best choice if you want to modify or add to the document. The left hand section contains the first 32 codes, those with hex values 00 through 1F, which are known as the 'non-printing' characters. The next section contains 32 more codes, those with hex values 20 through 3F. Remember, the bits are numbered 7 6 5 4 3 2 1 0.

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This F-test will be the main contrast of interest for our vertex analysis as it allows us to test for differences in either direction. When this is all set up correctly, save everything using the Save button in the smaller Glm window. Now exit the Glm GUI. We will do the analysis using --useReconMNI to reconstruct the surfaces in MNI space though note that an alternative would be to reconstruct the surfaces in the native space using --useReconNative. The other options specify that this command is to prepare an output for vertex analysis since it can also do other things in standard space --useReconMNI.

We will use randomise for this, as the FIRST segmentations are unlikely to have nice, indepedent Gaussian errors in them. Normally it is recommended to run at least permutations to end up with accurate p-values , but with a small set of subjects like this there is a limit to how many unique permutations are available, so in this analysis all unique permutations will be run. For multiple-comparison correction there are several options available in randomise and we will use the cluster-based one here -F , although other options may be better alternatives in many cases.

The most useful output of randomise is a corrected p-value image, where the values are stored as 1-p so that the interesting, small p-values appear "bright". The corrected p-value file is the one containing corrp in the name. This correction is the multiple-comparison correction, and it is only this output which is statistically valid for imaging data - uncorrected p-values should not be reported in general, although they can be useful to look at to get a feeling for what is in your data.

The statistically significant results are therefore the ones with values greater than 0. Note that this specifies the display range 0. Find the hippocampus in this image and look to see where the significant differences in shape have been found using this vertex analysis. Normally we would not expect to find much in a group of 8 subjects, but these were quite severe AD cases and so the differences are very marked.

In this section we look at a small study comparing patients and controls for local differences in grey matter volume, using FSL-VBM. Most of the steps have already been carried out, as there isn't enough time in this practical to run all of the registrations required to carry out a full analysis from scratch.

Do an ls in the directory. Note that we have renamed the image files with some prefixes so that all controls and patients would be organised in "blocks". This is to make the statistical design easily match the alphabetical order of the image files who will be later concatenated to be statistically analysed.

First, we need to define the statistical design, which here will be a simple two-tailed t-test to compare both groups. For this, use the Glm GUI to generate simple design. If the design looks correct, then save it by pressing Save in the GLM setup window and give it the output basename of design.

In this analysis, only the design. The contents of this file should therefore look like this:. This moved all the original files into the origdata folder; to see what they all look like, run this command to view the slicesdir report in a web browser:. Compare the different results from the two options by loading in the two web pages:. Next, all the brain images are segmented into the different tissue types, and then the study-specific GM template is created, by registering all GM segmentations to standard space, and averaging them together.

The command used was:. You can view all of the alignments to the MNI initial standard space by running the following, and turning on FSLeyes movie mode :. An initial GLM model-fit is run in order to allow you to view the raw tstat images at a range of potential smoothings.

This was achieved by running don't run this! So now you can have a look at the initial raw tstat images created at the different smoothing levels, pick the one you "like" best. You can change the colour maps for each tstat in FSLeyes to more clearly see the differences.

You are now ready to carry out the cross-subject statistics. We will use randomise for this, as the above steps are very unlikely to generate nice Gaussian distributions in the data. Normally we would run at least permutations to end up with accurate p-values , but this takes a few hours to run, so we will limit the number to to get a quick-and-dirty result.

We will also use TFCE thresholding Threshold-Free Cluster Enhancement - this is explained in the randomise lecture which is similar to cluster-based thresholding but generally more robust and sensitive. For example, if you decide that the appropriate amount of smoothing is with a sigma of 3mm, then the following will run randomise with TFCE and a reduced number of iterations:.

Once randomise has finished use FSLeyes to look at the results corrected for multiple comparisons showing the local differences in grey matter volume between the two groups:. Note that in this example we set the corrected p-threshold to 0. We are grateful to Dr. Giovanna Zamboni for providing the datasets used in this practical. Other modalities that can help the lesion segmentation e.

T1 , all registered to the main image. Click here to see how it was obtained. Now we need to put the information on where to find these files for each subject in a text file master file , which we will later give as input to BIANCA. The master file is a text file containing one row per subject and, on each row, a list of all files for that subject columns.

Now we can give the master file as input to BIANCA, together with details on where to find the information inside it, and some additional information:. However, for most of the applications we want a binary lesion mask, so we need to apply a threshold and binarise the image.

In this case we chose a threshold of 0. Keep FSLeyes open. To further reduce false positive voxels, we can mask our output. For example, we can exclude areas we are either not interested in e. Have a look at it on FSLeyes.

How do you apply the mask to the lesion map using fslmaths? Check the command line here. After creating the mask, do you need to run any other FSL tool in order to use the masks? Which one s? Check your answer here. The other structures are identified in MNI space, non-linearly registered to the single-subject image, and removed from the brain mask.

Volume calculation. How would you calculate the volume in mm 3 of the final lesion map using fslstats? First, we need to create a new masterfile with the information about the files for the new subject e. If you want to run BIANCA on more than one new subject, you can either create a single master file for each subject and change the input each time with --querysubjectnum always 1, or you can add all the information about the new subjects in a common masterfile and point --querysubjectnum at a different row each time.

SIENA is a package for both single-time-point "cross-sectional" and two-time-point "longitudinal" analysis of brain change, in particular, the estimation of atrophy volumetric loss of brain tissue. The example data is two time points, 24 months apart, from a subject with probable Alzheimer's disease.

The command that was used to create the example analysis is don't run this - it takes too long! The -d flag tells the siena script not to clean up the many intermediate images it creates - you would not normally use this. The other options are explained later. To view the output report, open report. The next few sections take you through the different parts of the webpage report, which correspond to the different stages of the SIENA analysis.

First BET was run on the two input images, with options telling it to create the skull surface image and the binary mask image, as well as the default brain image. Other BET options can be included in the call to siena by adding -B "betopts" - for example.

You also might need to use the -c option to BET if you need to tell BET where to center the initial brain surface, such as when you have a huge amount of neck in the image. For example, if it looks like the centre of the brain is at ,,78 in voxels , e. You can see the two brain and skull extractions in the webpage report. If you want to see these in more detail, open the relevant images in FSLeyes, for example:.

Be aware that the skull estimate is usually very noisy but that it is only used to determine the overall scaling and this process is not very sensitive to the noise as long as the majority of points lie on the skull. This runs the 3-step registration brains, then skulls, then brains again. The transformation is "halved" so that each image can be transformed into the space halfway between the two.

The webpage report shows the alignment of the two brains in this halfway space. You need to check that the two timepoints are fundamentally well-aligned, with only small e. Look out for mistakes such as: the two images coming from different subjects, one image being left-right flipped relative to the other one, or one image having bad artefacts.

The transforms and their inverses are saved. The two brains are registered separately and their transforms compared to test for consistency. The webpage report shows the two images transformed into standard space, with the overlaying red lines derived from the edges of the standard space template, for comparison. If the -m option was set, a standard space brain mask is now transformed into the native image space and applied to the original brain masks produced by BET. This is in most areas a fairly liberal dilated brain mask, except around the eyes.

If the -t or -b options are set then an upper or lower limit in the Z direction in standard space is defined, to supplement the masking. This is useful, for example, to restrict the field-of-view of the analysis if you have variable field-of-view at the top or bottom of the head in different subjects. Here you can see the bottom of the temporal lobes have not been included in the regions fed into the boundary edge movement analysis. It is this intersection that is what gets finally used.

The GM and WM voxels are combined into a single mask, and the mask edges including internal ventricle edges are used to find edge motion discussed below. The webpage report shows the two segmentations. The final step is to carry out change analysis on the registered masked brain images. At all points which are reported as boundaries between brain and non-brain, the distance that the brain surface has moved between the two time points is estimated. The mean perpendicular surface motion is computed and converted to PBVC percentage brain volume change.

The webpage report shows the edge motion colour coded at the brain edge points, and then shows the final global PBVC value. To see the edge motion image in more detail:. Can you tell what's wrong? If you're unsure, click here. The subject IDs have gotten mixed up - the two timepoint images are from different subjects!

Also, BET is including too much neck, but that's not the main problem One of the datasets has been left-right flipped look at the axial slices in the registration animation , despite one of them having been marked with a right-side marker at some point Both original images have some movement artefact ringing and are quite noisy. It's probably not worth keeping data of this quality. Look in the coronal slices in the registration animation. Also, something else is odd The slight boundary differences must be due to slightly different BET results caused by only one of the images having the right-side marker seen in the top BET result image.

The second dataset has bad motion artefact, and one of the datasets has been left-right flipped Open report. The example data is one time point from a subject with probable Alzheimer's disease. The command that was used to create the example analysis is don't run this!

Next a standard space brain mask is always used to supplement the BET segmentation. Next, FAST is used, with partial volume estimation turned on, to provide an accurate estimate of grey and white matter volumes. Having considered the boundary corrected segmentation previously, we now turn to look at the uncorrected segmentation. Here we focus on how the normal distribution helps us summarize data. Rather than using data, the normal distribution is defined with a mathematical formula.

Here is what the normal distribution looks like when the average is 0 and the SD is The fact that the distribution is defined by just two parameters implies that if a dataset is approximated by a normal distribution, all the information needed to describe the distribution can be encoded in just two numbers: the average and the standard deviation. We now define these values for an arbitrary list of numbers.

The pre-built functions mean and sd note that for reasons explained in Section The normal distribution does appear to be quite a good approximation here. We now will see how well this approximation works at predicting the proportion of values within intervals. For data that is approximately normally distributed, it is convenient to think in terms of standard units. The standard unit of a value tells us how many standard deviations away from the average it is.

Why is this convenient? Remember that it does not matter what the original units are, these rules apply to any data that is approximately normal. To further confirm that, in fact, the approximation is a good one, we can use quantile-quantile plots. A systematic way to assess how well the normal distribution fits the data is to check if the observed and predicted proportions match.

In general, this is the approach of the quantile-quantile plot QQ-plot. We can do this using the mean and sd arguments in the pnorm and qnorm function. For example, we can use qnorm to determine quantiles of a distribution with a specific average and standard deviation. For the normal distribution, all the calculations related to quantiles are done without data, thus the name theoretical quantiles. But quantiles can be defined for any distribution, including an empirical one.

The idea of a QQ-plot is that if your data is well approximated by normal distribution then the quantiles of your data should be similar to the quantiles of a normal distribution. To construct a QQ-plot, we do the following:. To obtain the theoretical normal distribution quantiles with the corresponding average and SD, we use the qnorm function:. The above code is included to help describe QQ-plots. However, in practice it is easier to use the ggplot2 code described in Section 8. Percentiles are special cases of quantiles that are commonly used.

The most famous percentile is the 50th, also known as the median. For the normal distribution the median and average are the same, but this is generally not the case. To introduce boxplots we will go back to the US murder data.

Suppose we want to summarize the murder rate distribution. Using the data visualization technique we have learned, we can quickly see that the normal approximation does not apply here:. In this case, the histogram above or a smooth density plot would serve as a relatively succinct summary. Now suppose those used to receiving just two numbers as summaries ask us for a more compact numerical summary.

Here Tukey offered some advice. Provide a five-number summary composed of the range along with the quartiles the 25th, 50th, and 75th percentiles. Tukey further suggested that we ignore outliers when computing the range and instead plot these as independent points. We provide a detailed explanation of outliers later.

The distance between these two is called the interquartile range. The median is shown with a horizontal line. Today, we call these boxplots. From just this simple plot, we know that the median is about 2. We discuss how to make boxplots in Section 8. In data analysis we often divide observations into groups based on the values of one or more variables associated with those observations. For example in the next section we divide the height values into groups based on a sex variable: females and males.

We call this procedure stratification and refer to the resulting groups as strata. Stratification is common in data visualization because we are often interested in how the distribution of variables differs across different subgroups. We will see several examples throughout this part of the book. We will revisit the concept of stratification when we learn regression in Chapter 17 and in the Machine Learning part of the book. Using the histogram, density plots, and QQ-plots, we have become convinced that the male height data is well approximated with a normal distribution.

In this case, we report back to ET a very succinct summary: male heights follow a normal distribution with an average of With this information, ET will have a good idea of what to expect when he meets our male students. However, to provide a complete picture we need to also provide a summary of the female heights. We learned that boxplots are useful when we want to quickly compare two or more distributions. Here are the heights for men and women:.

The plot immediately reveals that males are, on average, taller than females. The standard deviations appear to be similar. But does the normal approximation also work for the female height data collected by the survey?

We expect that they will follow a normal distribution, just like males. However, exploratory plots reveal that the approximation is not as useful:. Also, the QQ-plot shows that the highest points tend to be taller than expected by the normal distribution.

Finally, we also see five points in the QQ-plot that suggest shorter than expected heights for a normal distribution. When reporting back to ET, we might need to provide a histogram rather than just the average and standard deviation for the female heights. If we look at other female height distributions, we do find that they are well approximated with a normal distribution.

So why are our female students different? Is our class a requirement for the female basketball team? Are small proportions of females claiming to be taller than they are? Another, perhaps more likely, explanation is that in the form students used to enter their heights, FEMALE was the default sex and some males entered their heights, but forgot to change the sex variable.

In any case, data visualization has helped discover a potential flaw in our data. Because these are reported heights, a possibility is that the student meant to enter 5'1" , 5'2" , 5'3" or 5'5". Instead, we will look at the percentiles. Then create a data frame with these two as columns.

If we use a log transformation, which continent shown above has the largest interquartile range? What proportion of the data is between 69 and 72 inches taller than 69, but shorter or equal to 72? Hint: use a logical operator and mean. Suppose all you know about the data is the average and the standard deviation. Use the normal approximation to estimate the proportion you just calculated.

Hint: start by computing the average and standard deviation. Then use the pnorm function to predict the proportions. Notice that the approximation calculated in question nine is very close to the exact calculation in the first question. Now perform the same task for more extreme values. Compare the exact calculation and the normal approximation for the interval 79,81].

How many times bigger is the actual proportion than the approximation? Approximate the distribution of adult men in the world as normally distributed with an average of 69 inches and a standard deviation of 3 inches. Using this approximation, estimate the proportion of adult men that are 7 feet tall or taller, referred to as seven footers. Hint: use the pnorm function. There are about 1 billion men between the ages of 18 and 40 in the world.

Use your answer to the previous question to estimate how many of these men year olds are seven feet tall or taller in the world? There are about players that are at least that tall. In answering the previous questions, we found that it is not at all rare for a seven footer to become an NBA player. What would be a fair critique of our calculations:. In Chapter 7 , we introduced the ggplot2 package for data visualization.

Here we demonstrate how to generate plots related to distributions, specifically the plots shown earlier in this chapter. The default is to count the number of each category and draw a bar. Here is the plot for the regions of the US. We often already have a table with a distribution that we want to present as a barplot. Here is an example of such a table:. By looking at the help file for this function, we learn that the only required argument is x , the variable for which we will construct a histogram.

We dropped the x because we know it is the first argument. The code looks like this:. Pick better value with binwidth. Finally, if for aesthetic reasons we want to add color, we use the arguments described in the help file. We also add labels and a title:. To make a smooth density plot with the data previously shown as a histogram we can use this code:. To change the smoothness of the density, we use the adjust argument to multiply the default value by that adjust.

For example, if we want the bandwidth to be twice as big we use:. As discussed, boxplots are useful for comparing distributions. For example, below are the previously shown heights for women, but compared to men. For this geometry, we need arguments x as the categories, and y as the values.

From the help file, we learn that we need to specify the sample we will learn about samples in a later chapter. Here is the qqplot for men heights. By default, the sample variable is compared to a normal distribution with average 0 and standard deviation 1.

To change this, we use the dparams arguments based on the help file. Adding an identity line is as simple as assigning another layer. Another option here is to scale the data first and then make a qqplot against the standard normal. Images were not needed for the concepts described in this chapter, but we will use images in Section They behave similarly; to see how they differ, please consult the help file.

To create an image in ggplot2 we need a data frame with the x and y coordinates as well as the values associated with each of these. Here is a data frame. Note that this is the tidy version of a matrix, matrix , 12, To plot the image we use the following code:.

With these images you will often want to change the color scale. In Section 7. We can also use qplot to make histograms, density plots, boxplot, qqplots and more. Although it does not provide the level of control of ggplot , qplot is definitely useful as it permits us to make a plot with a short snippet of code. The function guesses that we want to make a histogram because we only supplied one variable.

To make a quick qqplot you have to use the sample argument. Note that we can add layers just as we do with ggplot. If we supply a factor and a numeric vector, we obtain a plot like the one below. Note that in the code below we are using the data argument. Because the data frame is not the first argument in qplot , we have to use the dot operator.

We can also select a specific geometry by using the geom argument. So to convert the plot above to a boxplot, we use the following code:. We can also use the geom argument to generate a density plot instead of a histogram:. Although not as much as with ggplot , we do have some flexibility to improve the results of qplot.

Looking at the help file we see several ways in which we can improve the look of the histogram above. Here is an example:. Technical note : The reason we use I "black" is because we want qplot to treat "black" as a character rather than convert it to a factor, which is the default behavior within aes , which is internally called here.

When reading the documentation for this function we see that it requires just one mapping, the values to be used for the histogram. Make a histogram of all the plots. Now create a ggplot object using the pipe to assign the heights data to a ggplot object.

Assign height to the x values through the aes function. Now we are ready to add a layer to actually make the histogram. Use the binwidth argument to change the histogram made in the previous exercise to use bins of size 1 inch. Instead of a histogram, we are going to make a smooth density plot. In this case we will not make an object, but instead render the plot with one line of code.

Change the geometry in the code previously used to make a smooth density instead of a histogram. Now we are going to make a density plot for males and females separately. We can do this using the group argument.

We assign groups via the aesthetic mapping as each point needs to a group before making the calculations needed to estimate a density. We can also assign groups through the color argument. This has the added benefit that it uses color to distinguish the groups. Change the code above to use color. We can also assign groups through the fill argument.

This has the added benefit that it uses colors to distinguish the groups, like this:. However, here the second density is drawn over the other. We can make the curves more visible by using alpha blending to add transparency. Set the alpha parameter to 0. What does this book cover? What is not covered by this book? Introduction to Data Science. Chapter 8 Visualizing data distributions You may have noticed that numerical data is often summarized with the average value.

We collect the data and save it in the heights data frame: library tidyverse library dslabs data heights.

We advise people to pick and choose based on their own particular interests; everyone should do FAST, but after that the parts are quite separate and can be done in any order e.

Rbi cautions against use of bitcoins Occasionally, a second number is reported: the standard deviation. Changing plot colours In order to see the plots for the different voxels in different colours you need to set the colours explicitly for each plot. We begin by segmenting the left hippocampus and amygdala from a single T1-weighted image. We now define these values for an arbitrary list of numbers. Here is an example of such a table:. The command that was used to create the example analysis is don't run this!
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Vector data overlay definition betting The most useful output of randomise kyb lowfer sports review betting a corrected p-value image, where the values are stored as 1-p so that the interesting, small p-values appear "bright". The next few sections take you through the different parts of the webpage report, which correspond vector data overlay definition betting the different stages of the SIENA analysis. Look at the alignment of the subcortical structures. In order to visualise the segmentation outputs of FIRST on a large number of subjects it is useful to generate summary reports that can be assessed efficiently. We must first run an additional pre-processing script which will erode your FA images slightly to remove brain-edge artifacts and zero the end slices again to remove likely outliers from the diffusion tensor fitting. The histogram plots these counts as bars with the base of the bar defined by the intervals.
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Rbi cautions against use of bitcoins The final column hertha vs dortmund betting tips the "total readout time", which is the time in seconds between the collection of the centre of the first echo and the centre of the last echo. In this first section of the practical we will familiarise ourselves with diffusion data. Some numerical data can be treated as ordered categorical. It is this file that you will feed into voxelwise statistics in the next section. Most of the steps have already been carried out, as there isn't enough time in this practical to run all of the registrations required to carry out a full analysis from scratch.
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Boylesports football betting rules for holdem Finally, save the design as filename designand in the terminal use less to look at the design. As computers gained more speed and power and fell in cost, they became easier to use and more common within companies and agencies. This list of values has a distribution, like any list of values, and this larger distribution is really what we want to report to ET since it is much more general. In Chapter 7we introduced the ggplot2 package for data visualization. Now, let's have a look at all the data associated with a voxel.
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