Quartiles And Deciles

[Phuong Fulsom]

From there, I'd like to essentially split the dataframe into 10 groups based on whether the fpkm_val fits into one of these deciles. Then I'd like to plot the meth_val of each decile in ggplot as a box plot and perform a statistical test across deciles.

Put another way, 1st Quartile contains the part of data, 2nd Quartile contains of the data and 3rd Quartile contains the part of data. Repeating, it may be noted that the data should be arranged in
ascending or descending order of magnitude.

Quartiles and deciles are statistical concepts that are commonly used to analyze datasets. Quartiles divide a dataset into four equal parts, with the first quartile (Q1) representing the 25th percentile, the second quartile (Q2) representing the median or 50th percentile, and the third quartile (Q3) representing the 75th percentile. On the other hand, deciles divide a dataset into ten equal parts, with the first decile (D1) representing the 10th percentile, the second decile (D2) representing the 20th percentile, and so on, until the tenth decile (D10) which represents the maximum value of the data.

Quartiles Q1, Q2 (median), and Q3 are statistical measures that split a dataset into four equal parts. Specifically, Q1 represents the value below which 25% of the data falls, Q2 represents the midpoint value that splits the data into the lower and upper halves, and Q3 represents the value below which 75% of the data falls. Percentile is another statistical measure that divides a dataset into 100 equal parts, with each percentile representing the percentage of data below that point.

The decile formula is used to calculate the value of a specific decile for a dataset. The formula involves finding the position of the value in the ordered dataset and then calculating the decile value based on that position.

To sum up, quartiles, deciles, and percentiles serve as important tools to measure the spread of data and provide insights into its distribution. They are frequently utilized in data analysis and offer valuable information on the relative positions of individual values within a given dataset.

(looks like the 'GroupBy' node has a P^2 percentile approximation but no good old fashioned percentile method)

If there aren't any Nodes available that do this out of the box perhaps someone would be kind enough to point me to resources showing how to use the Python scripting node for accomplishing this type of mathematical task (assuming I would use something like this in Python: -docs/stable/generated/pandas.DataFrame.quantile.html)

many thanks!

Actually, I've always wondered why the Statistics node or any other not yet existing dedicated node which would carry the wonderful name "Quantiles" is not able to do this. Not to say that I would not be happy with the GroupBy solution but Statistics seemed a more intuitive place to look for such functionality.

For example, the Calculate median function in Statistics already does the preparation work to extract the median, why not extract a collection object with the desired n-tiles and let the user choose the quantile variety (quartiles, deciles, etc) in the configuration screen via a drop-down menu instead of the tick box?

Hi, you can calculate the percentiles (or percentile groups) in the way described above and then use the "Rule Engine" node to match test scores to percentiles (or percentile groups). I don't think that there is a simpler i.e. built-in function to do this.

I knew about the quantile function in groupby node but as I said in my last comment, I need to calculate the percentile rank for each record. In groupby node one value is given to the percent we choose but I want to determine the percentile rank for each record of a whole column.

I have a dataset which contains user IDs and their scores in some tests. I want to have the percentile rank for each user in each test. For example user 1 in test 1 is better than 32% of all users and so on.

In statistics and probability, quantiles are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities, or dividing the observations in a sample in the same way. There is one fewer quantile than the number of groups created. Common quantiles have special names, such as quartiles (four groups), deciles (ten groups), and percentiles (100 groups). The groups created are termed halves, thirds, quarters, etc., though sometimes the terms for the quantile are used for the groups created, rather than for the cut points.

As in the computation of, for example, standard deviation, the estimation of a quantile depends upon whether one is operating with a statistical population or with a sample drawn from it. For a population, of discrete values or for a continuous population density, the k-th q-quantile is the data value where the cumulative distribution function crosses k/q. That is, x is a k-th q-quantile for a variable X if

If, instead of using integers k and q, the "p-quantile" is based on a real number p with 0 < p < 1 then p replaces k/q in the above formulas. This broader terminology is used when quantiles are used to parameterize continuous probability distributions. Moreover, some software programs (including Microsoft Excel) regard the minimum and maximum as the 0th and 100th percentile, respectively. However, this broader terminology is an extension beyond traditional statistics definitions.

The first three are piecewise constant, changing abruptly at each data point, while the last six use linear interpolation between data points, and differ only in how the index h used to choose the point along the piecewise linear interpolation curve, is chosen.

Mathematica,[3] Matlab,[4] R[5] and GNU Octave[6] programming languages support all nine sample quantile methods. SAS includes five sample quantile methods, SciPy[7] and Maple[8] both include eight, EViews[9] and Julia[10] include the six piecewise linear functions, Stata[11] includes two, Python[12] includes two, and Microsoft Excel includes two. Mathematica, SciPy and Julia support arbitrary parameters for methods which allow for other, non-standard, methods.

The sample median is the most examined one amongst quantiles, being an alternative to estimate a location parameter, when the expected value of the distribution does not exist, and hence the sample mean is not a meaningful estimator of a population characteristic. Moreover, the sample median is a more robust estimator than the sample mean.

Computing approximate quantiles from data arriving from a stream can be done efficiently using compressed data structures. The most popular methods are t-digest[16] and KLL.[17] These methods read a stream of values in a continuous fashion and can, at any time, be queried about the approximate value of a specified quantile.

Both algorithms are based on a similar idea: compressing the stream of values by summarizing identical or similar values with a weight. If the stream is made of a repetition of 100 times v1 and 100 times v2, there is no reason to keep a sorted list of 200 elements, it is enough to keep two elements and two counts to be able to recover the quantiles. With more values, these algorithms maintain a trade-off between the number of unique values stored and the precision of the resulting quantiles. Some values may be discarded from the stream and contribute to the weight of a nearby value without changing the quantile results too much. The t-digest maintains a data structure of bounded size using an approach motivated by k-means clustering to group similar values. The KLL algorithm uses a more sophisticated "compactor" method that leads to better control of the error bounds at the cost of requiring an unbounded size if errors must be bounded relative to p.

Both methods belong to the family of data sketches that are subsets of Streaming Algorithms with useful properties: t-digest or KLL sketches can be combined. Computing the sketch for a very large vector of values can be split into trivially parallel processes where sketches are computed for partitions of the vector in parallel and merged later.

Standardized test results are commonly reported as a student scoring "in the 80th percentile", for example. This uses an alternative meaning of the word percentile as the interval between (in this case) the 80th and the 81st scalar percentile.[18] This separate meaning of percentile is also used in peer-reviewed scientific research articles.[19] The meaning used can be derived from its context.

If a distribution is symmetric, then the median is the mean (so long as the latter exists). But, in general, the median and the mean can differ. For instance, with a random variable that has an exponential distribution, any particular sample of this random variable will have roughly a 63% chance of being less than the mean. This is because the exponential distribution has a long tail for positive values but is zero for negative numbers.

Quantiles are useful measures because they are less susceptible than means to long-tailed distributions and outliers. Empirically, if the data being analyzed are not actually distributed according to an assumed distribution, or if there are other potential sources for outliers that are far removed from the mean, then quantiles may be more useful descriptive statistics than means and other moment-related statistics.

Closely related is the subject of least absolute deviations, a method of regression that is more robust to outliers than is least squares, in which the sum of the absolute value of the observed errors is used in place of the squared error. The connection is that the mean is the single estimate of a distribution that minimizes expected squared error while the median minimizes expected absolute error. Least absolute deviations shares the ability to be relatively insensitive to large deviations in outlying observations, although even better methods of robust regression are available.

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