Plot of
measures vs resampled time series indices
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A selection of measures computed on
resampled time series of a specific type, i.e. time series with names
containing indices after the string code of the specified resampling
type, can be plotted against the resampling indices in a figure window.
This type of figure visualizes the result of the resampling test for a
time series, comparing the measure(s) value for the original time series
at index 0 to the other values of the resampled time series at the other
indices. Further, the user is opted to select to get a graph of ordered
values and test results (p-values of a parametric test and nonparametric
test). First, the Resampling type must be chosen among the listed resampling types (RP, FT, AAFT, IAAFT, STAP, AMRB, see "Resampled Time Series" operation). Upon the selection of the resampling type the list of resampled time series is restricted to include only resampled time series of the specified type. If for example, the STAP resampling type is specified, the label on the top of the list reads Select STAP resampled time series and the list contains all the STAP surrogate time series for which measures have been computed in the last run of measures. The resampled time series in the list are identified for the specified resampling type by the time series name and the indices after the string code of the specified resampling type (if there is a string after the index this should be the same in the names of the segments). If no such resampled time series names exist the list of resampled time series is empty and this operation cannot run for this resampling type. Further, one or more measures can be selected from the measure list having the title Select one or more measures. For measures defined in terms of one or more measure specific parameters, the measure name regards a specified set of parameters (one parameter value for each name). A subset of resampled time series and measure names can be selected from the respective lists with standard use of the mouse: a click on a name and Shift^click on a another name further down in the list selects all names between the former and the latter; a click on a name and subsequent Ctrl^clicks on other names select these names including the first name; Ctrl^a selects the whole list. Tips: For the selection of a subset of resampled time series names from the list, click on the resampled time series of this subset appearing first in the list and then Shift^click at the last resampled time series in the list. In this way, all time series from the first selected to the last time series in the list will be marked and from those only the ones that have the same resampled time series name as the first one and differ only to the resampling index will be processed. |
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Resampling type |
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The user can choose one of the
following resampling types (for details of the resampling types see the
"Resampled Time Series" operation)
RP: Random Permutation, If there are time series of the selected resampling type in the list of time series names, they are displayed in the list of resampled time series. |
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Draw lines / points |
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The user can choose one of the following: Lines, Points, Both. This is the drawing type for the measure vs resampling index plot and a different drawing type is used for each measure, as explained in the legend or to "Running messages" text box (if more than 5 lines are displayed in one graph). | |
Normalize |
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If this checkbox is activated, the measures are first normalized to have mean zero and standard deviation one (z-score). In this way, the user can have all selected measures at the same range, and can assess visualize whether the measure value (test statistic) for the original time series is out of the limits of null distribution. | |
Display test |
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If this checkbox is activated, then one
graph for each of the selected measures will be generated (after the
user pushes the View selected plot button), and the test results will be
given in the form of p-values, provided that the original time series
name is in the list of the time series names. Each graph contains the
following: - At index value 0 the measure value for the original time series is displayed by an open circle. For index values 1 to M (the number of resampled time series), the measure values for the resampled time series are displayed (according to the Draw lines / points selection) in ascending or descending order (depending whether the measure value for the original time series is towards the left or right part of the distribution of the "resampled" values). - Two red broken horizontal lines display the critical values for the significant level á=0.05 and á=0.01 for a parametric (normal) test. Basically these two values define the tails (left or right depending on the original value) of the null distribution of the test statistic. So, the user can have a graphical representation of the test judging from the position of the original value (open circle at time index 0) with respect to these two horizontal lines. - Quantitative test results are given in the title of the graph in the form of two p-values, one for the parametric (normal) test and the other for the nonparametric test (based on rank ordering of the M+1 values, the original and the M resampled ones). Further the validity of the parametric test is examined with the Kolmogorov-Smirnov test for normality and the notification "normality accepted" is displayed along with the parametric p-value if the null hypothesis of the Kolmogorov-Smirnov test is not rejected, otherwise the notification is changed to "normality rejected". In this way, the user has evidence to whether rely or not on the parametric test result. |
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View selected plot |
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Pressing this button
will generate one or more figures in separate window(s), provided that a list of
at least two resampled time series names of the specified resampling
type and one or more measure names are selected. The generation of one
or possible more figures depends on the selection of the "Display test"
option as follows. If the "Display test" option is not selected, a single figure as the one shown below will be displayed containing lines or points (or both) of distinct type for each selected measure vs the resampling indices. When up to 5 measure names are selected, they are listed in a legend together with their corresponding drawing type, otherwise they are listed in the "Running messages" text box.
The resampling test here is for the null hypothesis of linear stochastic process using surrogate data generated by the STAP algorithm on a time series of EEG from an epileptic seizure (exhibiting rhythmic oscillations and thus expected nonlinear dynamics to be present and the null hypothesis to be rejected). We note that for two of the four measures displayed in the figure above, the cumulative bicorrelation for maximum lag 10 (blue line) and the cumulative mutual information using equiprobable binning of automatically selected number of bins and maximum lag 10 (red line), it is obvious that the original values for both measures are well above the respective values of the resampled data. The distinction is less clear for the measure of the fit with a local zero order model of 10 neighbors, lag one, embedding dimension 10 and predicting 5 time steps ahead using the direct prediction scheme (black dashed line). However, this does not mean that the rejection of the null hypothesis is less confident by this nonlinear measure. It is just that the range for this measure is much smaller, as is for the forth measure of the linear autoregressive (AR) fit for the same prediction and using AR order 10. To visualize better the graphs for the two last measures (the nonlinear and linear fit measures) we should use the option "Normalize". Moreover, to obtain quantitative results as well for these two measures, we select only these two, and activate the checkboxes "Normalize" and "Display test". By then pressing the button "View selected plot" two figures are generated in separate windows as shown below (for the test statistic of the linear fit on the first figure and the test statistic of the nonlinear fit on the second figure).
It is obvious that for the linear fit the value for the original EEG data is well within the distribution of the values from the STAP surrogate time series (the open circle is above both the two red horizontal lines and towards zero). Accordingly, the p-values of both the parametric and the nonparametric test are large (displayed at the title of the figure). We note that the set of measure values for the resampled data form a distribution that is accepted to be normal as given by the Kolmogorov-Smirnov test, and this result is displayed in the title as "normality accepted". So, we can trust the result of the parametric test. The test results for the nonlinear fit test statistic given in the second figure above, suggest that the null hypothesis for linear stochastic process should be rejected at very low significance level when using the parametric approach and at the smallest significant level of ≈0.025 when using the nonparametric approach. The Kolmogorov-Smirnov test suggests here that the test statistic values on the resampled data do not follow normal distribution (stated as "normality rejected" in the title), so we cannot trust the parametric result. |
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Running Messages |
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A text box displaying messages for the running operations. | |
Exit |
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By pressing this button the window of "Plot of Measures vs Resampled Time Series Indices" will disappear and the user will be moved to the "View Measures" window. Note that any created figures will remain until the user exits from the "View Measures" window. | |
Help |
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