How does Delta2D compute the statistical measures (mean, rsd, etc.) shown in the statistics table?

Let's start with the mean. It is computed for every replicate group, using the relative volumes of the spots in a group. The formula for the mean is

$\overline{x} = \frac{1}{n}\sum_{i=1}^n x_i = \frac{x_1+x_2+\cdots+x_n}{n}$

where x_i are the normalized volumes of the spots in that group, and n is the number of spots in the group.

The relative standard deviation is shown in the column RSD, in percent. The absolute standard deviation is a measure of the spread of sample values, it is defined as

$\sigma = \sqrt{\frac{1}{n} \sum_{i=1}^n (x_i - \overline{x})^2}$

The relative standard deviation (RSD) is computed by normalizing the standard deviation (σ) with the mean, and then multiplying by 100 to get a percentage value:

$\textup{rsd} = \frac{\sigma}{\overline{x}} \cdot 100$

The median is defined such that at most half the spots in the group have values less than the median and at most half have values greater than the median. It is computed by sorting the intensities and then taking the middle one (if the number of spots is odd), or the average of the two middle ones (if there is an even number of spots). So, if

$(x_1, x_2, \dots, x_n)$

are the sorted spot quantities then the median is defined as

$\tilde x =\begin{cases} x_\frac{n+1}{2} & n \; \mathrm{ odd} \\ \frac{1}{2} \left( x_\frac{n}{2} + x_{\frac{n}{2}+1}\right) & n \;\mathrm{ even} \end{cases}$

Ratios are computed according to the setting at the top of the quantitation table. By default, it is the quotient of the group means of relative spot volumes. The denominator of the ratio is always taken from the first group displayed in the Light Table or Project Explorer. Hold the mouse pointer over the ratio column heading, the tooltip will show details about the ratio computation. You can have the ratio displayed in terms of fold change, where negative values mean decreases. For example, a fold change of -3 means a threefold decrease. To switch between normal and fold change display, go to Tools -> Options -> Delta2D tab -> tables tab and use the "Show Ratio of Spots as Fold Change" checkbox.

Delta2D computes t-Test values for certain pairs of replicate groups. The test is a unpaired two-sided Student's t-Test, with the assumptions of equal unknown variance and unpaired samples. The null hypothesis is that both groups have equal means. Delta2D computes the p-value, which is the probability that a test statistic at least as significant as the one observed would be obtained assuming that the null hypothesis were true (i.e. the differences in quantities are the result of mere chance). The value p is the t-Test value shown for the test applied to every group vs. the first one displayed in the Light Table or Project Explorer.

Up to Delta2D version 4.2 the value q shown in the statistics table is derived from the p-value as follows:

$q = \big(1-p) \cdot 100$

Last update on 2013-10-30 by Detlev Bielz.

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How does Delta2D compute the statistical measures (mean, rsd, etc.) shown in the statistics table?

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