:tocdepth: 3 .. _testing: Testing CICE ================ This section documents primarily how to use the CICE scripts to carry out CICE testing. Exactly what to test is a separate question and depends on the kinds of code changes being made. Prior to merging changes to the CICE Consortium master, changes will be reviewed and developers will need to provide a summary of the tests carried out. There is a base suite of tests provided by default with CICE and this may be a good starting point for testing. The testing scripts support several features - Ability to test individual (via ``--test``) or multiple tests (via ``--suite``) using an input file to define the suite - Ability to use test suites defined in the package or test suites defined by the user - Ability to store test results for regresssion testing (``--bgen``) - Ability to compare results to prior baselines to verify bit-for-bit (``--bcmp``) - Ability to define where baseline tests are stored (``--bdir``) - Ability to compare tests against each other (``--diff``) - Ability to set account number (``--acct``), which is otherwise not set and may result in tests not being submitted .. _indtests: Individual Tests ---------------- The CICE scripts support both setup of individual tests as well as test suites. Individual tests are run from the command line:: ./cice.setup --test smoke --mach conrad --env cray --set diag1,debug --testid myid Tests are just like cases but have some additional scripting around them. Individual tests can be created and manually modified just like cases. Many of the command line arguments for individual tests are similar to :ref:`case_options` for ``--case``. For individual tests, the following command line options can be set ``--test`` TESTNAME specifies the test type. This is probably either smoke or restart but see `cice.setup --help` for the latest. This is required instead of ``--case``. ``--testid`` ID specifies the testid. This is required for every use of ``--test`` and ``--suite``. This is a user defined string that will allow each test to have a unique case and run directory name. This is also required. ``--tdir`` PATH specifies the test directory. Testcases will be created in this directory. (default is .) ``--mach`` MACHINE (see :ref:`case_options`) ``--env`` ENVIRONMENT1 (see :ref:`case_options`) ``--set`` SET1,SET2,SET3 (see :ref:`case_options`) ``--acct`` ACCOUNT (see :ref:`case_options`) ``--grid`` GRID (see :ref:`case_options`) ``--pes`` MxNxBXxBYxMB (see :ref:`case_options`) There are several additional options that come with ``--test`` that are not available with ``--case`` for regression and comparision testing, ``--bdir`` DIR specifies the top level location of the baseline results. This is used in conjuction with ``--bgen`` and ``--bcmp``. The default is set by ICE_MACHINE_BASELINE in the env.[machine]_[environment] file. ``--bgen`` DIR specifies the name of the directory under [bdir] where test results will be stored. When this flag is set, it automatically creates that directory and stores results from the test under that directory. If DIR is set to ``default``, then the scripts will automatically generate a directory name based on the CICE hash and the date and time. This can be useful for tracking the baselines by hash. ``--bcmp`` DIR specifies the name of the directory under [bdir] that the current tests will be compared to. When this flag is set, it automatically invokes regression testing and compares results from the current test to those prior results. If DIR is set to ``default``, then the script will automatically generate the last directory name in the [bdir] directory. This can be useful for automated regression testing. ``--diff`` LONG_TESTNAME invokes a comparison against another local test. This allows different tests to be compared to each other for bit-for-bit-ness. This is different than ``--bcmp``. ``--bcmp`` is regression testing, comparing identical test results between different model versions. ``--diff`` allows comparison of two different test cases against each other. For instance, different block sizes, decompositions, and other model features are expected to produced identical results and ``--diff`` supports that testing. The restrictions for use of ``--diff`` are that the test has to already be completed and the testid has to match. The LONG_TESTNAME string should be of format [test]_[grid]_[pes]_[sets]. The [machine], [env], and [testid] will be added to that string to complete the testname being compared. (See also :ref:`examplediff` #5) The format of the case directory name for a test will always be ``[machine]_[env]_[test]_[grid]_[pes]_[sets].[testid]`` The [sets] will always be sorted alphabetically by the script so ``--set debug,diag1`` and ``--set diag1,debug`` produces the same testname and test with _debug_diag1 in that order. To build and run a test after invoking the ./cice.setup command, the process is the same as for a case. cd to the test directory, run the build script, and run the submit script:: cd [test_case] ./cice.build ./cice.submit The test results will be generated in a local file called **test_output**. To check those results:: cat test_output Tests are defined under **configuration/scripts/tests/**. Some tests currently supported are: - smoke - Runs the model for default length. The length and options can be set with the ``--set`` command line option. The test passes if the model completes successfully. - restart - Runs the model for 10 days, writing a restart file at the end of day 5 and again at the end of the run. Runs the model a second time starting from the day 5 restart and writes a restart at then end of day 10 of the model run. The test passes if both runs complete and if the restart files at the end of day 10 from both runs are bit-for-bit identical. - decomp - Runs a set of different decompositions on a given configuration Please run ``./cice.setup --help`` for the latest information. Adding a new test ~~~~~~~~~~~~~~~~~~~~~~~~ See :ref:`dev_testing` .. _examplediff: Individual Test Examples ~~~~~~~~~~~~~~~~~~~~~~~~ 1) **Basic default single test** Define the test, mach, env, and testid. :: ./cice.setup --test smoke --mach wolf --env gnu --testid t00 cd wolf_gnu_smoke_col_1x1.t00 ./cice.build ./cice.submit ./cat test_output 2) **Simple test with some options** Add ``--set`` :: ./cice.setup --test smoke --mach wolf --env gnu --set diag1,debug --testid t00 cd wolf_gnu_smoke_col_1x1_debug_diag1.t00 ./cice.build ./cice.submit ./cat test_output 3) **Single test, generate a baseline dataset** Add ``--bgen`` :: ./cice.setup --test smoke --mach wolf -env gnu --bgen cice.v01 --testid t00 --set diag1 cd wolf_gnu_smoke_col_1x1_diag1.t00 ./cice.build ./cice.submit ./cat test_output 4) **Single test, compare results to a prior baseline** Add ``--bcmp``. For this to work, the prior baseline must exist and have the exact same base testname [machine]_[env]_[test]_[grid]_[pes]_[sets] :: ./cice.setup --test smoke --mach wolf -env gnu --bcmp cice.v01 --testid t01 --set diag1 cd wolf_gnu_smoke_col_1x1_diag1.t01 ./cice.build ./cice.submit ./cat test_output 5) **Simple test, generate a baseline dataset and compare to a prior baseline** Use ``--bgen`` and ``--bcmp``. The prior baseline must exist already. :: ./cice.setup --test smoke --mach wolf -env gnu --bgen cice.v02 --bcmp cice.v01 --testid t02 --set diag1 cd wolf_gnu_smoke_col_1x1_diag1.t02 ./cice.build ./cice.submit ./cat test_output 6) **Simple test, comparison against another test** ``--diff`` provides a way to compare tests with each other. For this to work, the tests have to be run in a specific order and the testids need to match. The test is always compared relative to the current case directory. To run the first test, :: ./cice.setup --test smoke --mach wolf -env gnu --testid tx01 --set debug cd wolf_gnu_smoke_col_1x1_debug.tx01 ./cice.build ./cice.submit ./cat test_output Then to run the second test and compare to the results from the first test :: ./cice.setup --test smoke --mach wolf -env gnu --testid tx01 --diff smoke_col_1x1_debug cd wolf_gnu_smoke_col_1x1.tx01 ./cice.build ./cice.submit ./cat test_output The scripts will add a [machine]_[environment] to the beginning of the diff argument and the same testid to the end of the diff argument. Then the runs will be compared for bit-for-bit and a result will be produced in test_output. Specific Test Cases ~~~~~~~~~~~~~~~~~~~ In addition to the test implemented in the general testing framework, specific tests have been developed to validate specific portions of the model. These specific tests are detailed in this section. .. _box2001: ``box2001`` ^^^^^^^^^^^^ The ``box2001`` test case is configured to perform the rectangular-grid box test detailed in :cite:`Hunke01`. It is configured to run a 72-hour simulation with thermodynamics disabled in a rectangular domain (80 x 80 grid cells) with a land boundary around the entire domain. It includes the following namelist modifications: - ``dxrect``: ``16.e5`` cm - ``dyrect``: ``16.e5`` cm - ``ktherm``: ``-1`` (disables thermodynamics) - ``coriolis``: ``zero`` (zero coriolis force) - ``ice_data_type`` : ``box2001`` (special ice concentration initialization) - ``atm_data_type`` : ``box2001`` (special atmospheric and ocean forcing) Ocean stresses are computed as in :cite:`Hunke01` where they are circular and centered in the square domain. The ice distribution is fixed, with a constant 2 meter ice thickness and a concentration field that varies linearly in the x-direction from ``0`` to ``1`` and is constant in the y-direction. No islands are included in this configuration. The test is configured to run on a single processor. To run the test:: ./cice.setup -m --test smoke -s box2001 --testid --grid gbox80 --acct -p 1x1 .. _boxslotcyl: ``boxslotcyl`` ^^^^^^^^^^^^^^ The ``boxslotcyl`` test case is an advection test configured to perform the slotted cylinder test detailed in :cite:`Zalesak79`. It is configured to run a 12-day simulation with thermodynamics, ridging and dynamics disabled, in a square domain (80 x 80 grid cells) with a land boundary around the entire domain. It includes the following namelist modifications: - ``dxrect``: ``10.e5`` cm (10 km) - ``dyrect``: ``10.e5`` cm (10 km) - ``ktherm``: ``-1`` (disables thermodynamics) - ``kridge``: ``-1`` (disables ridging) - ``kdyn``: ``-1`` (disables dynamics) - ``ice_data_type`` : ``boxslotcyl`` (special ice concentration and velocity initialization) Dynamics is disabled because we directly impose a constant ice velocity. The ice velocity field is circular and centered in the square domain, and such that the slotted cylinder makes a complete revolution with a period :math:`T=` 12 days : .. math:: (u,v) = {u_0}\left( \frac{2y - L}{L}, \frac{-2x + L}{L}\right) :label: ice-vel-boxslotcyl where :math:`L` is the physical domain length and :math:`u_0 = \pi L / T`. The initial ice distribution is a slotted cylinder of radius :math:`r = 3L/10` centered at :math:`(x,y) = (L/2, 3L/4)`. The slot has a width of :math:`L/6` and a depth of :math:`5L/6` and is placed radially. The time step is one hour, which with the above speed and mesh size yields a Courant number of 0.86. The test can run on multiple processors. To run the test:: ./cice.setup -m --test smoke -s boxslotcyl --testid --grid gbox80 --acct -p nxm .. _testsuites: Test suites ------------ Test suites support running multiple tests specified via an input file. When invoking the test suite option (``--suite``) with **cice.setup**, all tests will be created, built, and submitted automatically under a local directory called testsuite.[testid] as part of involing the suite.:: ./cice.setup --suite base_suite --mach wolf --env gnu --testid myid Like an individual test, the ``--testid`` option must be specified and can be any string. Once the tests are complete, results can be checked by running the results.csh script in the [suite_name].[testid]:: cd testsuite.[testid] ./results.csh To report the test results, as is required for Pull Requests to be accepted into the master the CICE Consortium code see :ref:`testreporting`. If using the ``--tdir`` option, that directory must not exist before the script is run. The tdir directory will be created by the script and it will be populated by all tests as well as scripts that support the test suite:: ./cice.setup --suite base_suite --mach wolf --env gnu --testid myid --tdir /scratch/$user/testsuite.myid Multiple suites are supported on the command line as comma separated arguments:: ./cice.setup --suite base_suite,decomp_suite --mach wolf --env gnu --testid myid If a user adds ``--set`` to the suite, all tests in that suite will add that option:: ./cice.setup --suite base_suite,decomp_suite --mach wolf --env gnu --testid myid -s debug The option settings defined in the suite have precendent over the command line values if there are conflicts. The predefined test suites are defined under **configuration/scripts/tests** and the files defining the suites have a suffix of .ts in that directory. The format for the test suite file is relatively simple. It is a text file with white space delimited columns that define a handful of values in a specific order. The first column is the test name, the second the grid, the third the pe count, the fourth column is the ``--set`` options and the fifth column is the ``--diff`` argument. The fourth and fifth columns are optional. Lines that begin with # or are blank are ignored. For example, :: #Test Grid PEs Sets Diff smoke col 1x1 diag1 smoke col 1x1 diag1,run1year smoke_col_1x1_diag1 smoke col 1x1 debug,run1year restart col 1x1 debug restart col 1x1 diag1 restart col 1x1 pondcesm restart col 1x1 pondlvl restart col 1x1 pondtopo The argument to ``--suite`` defines the test suite (.ts) filename and that argument can contain a path. **cice.setup** will look for the filename in the local directory, in **configuration/scripts/tests/**, or in the path defined by the ``--suite`` option. Because many of the command line options are specified in the input file, ONLY the following options are valid for suites, ``--suite`` filename required, input filename with list of suites ``--mach`` MACHINE required ``--env`` ENVIRONMENT1,ENVIRONMENT2 strongly recommended ``--set`` SET1,SET2 optional ``--acct`` ACCOUNT optional ``--tdir`` PATH optional ``--testid`` ID required ``--bdir`` DIR optional, top level baselines directory and defined by default by ICE_MACHINE_BASELINE in **env.[machine]_[environment]**. ``--bgen`` DIR recommended, test output is copied to this directory under [bdir] ``--bcmp`` DIR recommended, test output are compared to prior results in this directory under [bdir] ``--report`` This is only used by ``--suite`` and when set, invokes a script that sends the test results to the results page when all tests are complete. Please see :ref:`testreporting` for more information. Please see :ref:`case_options` and :ref:`indtests` for more details about how these options are used. Test Suite Examples ~~~~~~~~~~~~~~~~~~~~~~~~ 1) **Basic test suite** Specify suite, mach, env, testid. :: ./cice.setup --suite base_suite --mach conrad --env cray --testid v01a cd testsuite.v01a # wait for runs to complete ./results.csh 2) **Basic test suite with user defined test directory** Specify suite, mach, env, testid, tdir. :: ./cice.setup --suite base_suite --mach conrad --env cray --testid v01a --tdir /scratch/$user/ts.v01a cd /scratch/$user/ts.v01a # wait for runs to complete ./results.csh 3) **Basic test suite on multiple environments** Specify multiple envs. :: ./cice.setup --suite base_suite --mach conrad --env cray,pgi,intel,gnu --testid v01a cd testsuite.v01a # wait for runs to complete ./results.csh Each env can be run as a separate invokation of `cice.setup` but if that approach is taken, it is recommended that different testids be used. 4) **Basic test suite with generate option defined** Add ``--set`` :: ./cice.setup --suite base_suite --mach conrad --env gnu --testid v01b --set diag1 cd testsuite.v01b # wait for runs to complete ./results.csh If there are conflicts between the ``--set`` options in the suite and on the command line, the suite will take precedent. 5) **Multiple test suites from a single command line** Add comma delimited list of suites :: ./cice.setup --suite base_suite,decomp_suite --mach conrad --env gnu --testid v01c cd testsuite.v01c # wait for runs to complete ./results.csh If there are redundant tests in multiple suites, the scripts will understand that and only create one test. 6) **Basic test suite, store baselines in user defined name** Add ``--bgen`` :: ./cice.setup --suite base_suite --mach conrad --env cray --testid v01a --bgen cice.v01a cd testsuite.v01a # wait for runs to complete ./results.csh This will store the results in the default [bdir] directory under the subdirectory cice.v01a. 7) **Basic test suite, store baselines in user defined top level directory** Add ``--bgen`` and ``--bdir`` :: ./cice.setup --suite base_suite --mach conrad --env cray --testid v01a --bgen cice.v01a --bdir /tmp/user/CICE_BASELINES cd testsuite.v01a # wait for runs to complete ./results.csh This will store the results in /tmp/user/CICE_BASELINES/cice.v01a. 8) **Basic test suite, store baselines in auto-generated directory** Add ``--bgen default`` :: ./cice.setup --suite base_suite --mach conrad --env cray --testid v01a --bgen default cd testsuite.v01a # wait for runs to complete ./results.csh This will store the results in the default [bdir] directory under a directory name generated by the script that includes the hash and date. 9) **Basic test suite, compare to prior baselines** Add ``--bcmp`` :: ./cice.setup --suite base_suite --mach conrad --env cray --testid v02a --bcmp cice.v01a cd testsuite.v02a # wait for runs to complete ./results.csh This will compare to results saved in the baseline [bdir] directory under the subdirectory cice.v01a. With the ``--bcmp`` option, the results will be tested against prior baselines to verify bit-for-bit, which is an important step prior to approval of many (not all, see :ref:`compliance`) Pull Requests to incorporate code into the CICE Consortium master code. You can use other regression options as well. (``--bdir`` and ``--bgen``) 10) **Basic test suite, use of default string in regression testing** default is a special argument to ``--bgen`` and ``--bcmp``. When used, the scripts will automate generation of the directories. In the case of ``--bgen``, a unique directory name consisting of the hash and a date will be created. In the case of ``--bcmp``, the latest directory in [bdir] will automatically be used. This provides a number of useful features - the ``--bgen`` directory will be named after the hash automatically - the ``--bcmp`` will always find the most recent set of baselines - the ``--bcmp`` reporting will include information about the comparison directory name which will include hash information - automation can be invoked easily, especially if ``--bdir`` is used to create separate baseline directories as needed. Imagine the case where the default settings are used and ``--bdir`` is used to create a unique location. You could easily carry out regular builds automatically via, :: set mydate = `date -u "+%Y%m%d"` git clone https://github.com/myfork/cice cice.$mydate --recursive cd cice.$mydate ./cice.setup --suite base_suite --mach conrad --env cray,gnu,intel,pgi --testid $mydate --bcmp default --bgen default --bdir /tmp/work/user/CICE_BASELINES_MASTER When this is invoked, a new set of baselines will be generated and compared to the prior results each time without having to change the arguments. 11) **Reusing a test suite** Add the buildincremental option (``-s buildincremental``). This permits the suite to be rerun without recompiling the whole code. :: ./cice.setup --suite base_suite --mach conrad --env intel --testid v01b --set buildincremental cd testsuite.v01b # wait for runs to complete ./results.csh # modify code ./suite.submit # or ./suite.run to run the suite interactively # wait for runs to complete ./results.csh Only modified files will be recompiled, and the suite will be rerun. 12) **Create and test a custom suite** Create your own input text file consisting of 5 columns of data, - Test - Grid - pes - sets (optional) - diff test (optional) such as :: > cat mysuite smoke col 1x1 diag1,debug restart col 1x1 restart col 1x1 diag1,debug restart_col_1x1 restart col 1x1 mynewoption,diag1,debug then use that input file, mysuite :: ./cice.setup --suite mysuite --mach conrad --env cray --testid v01a --bgen default cd testsuite.v01a # wait for runs to complete ./results.csh You can use all the standard regression testing options (``--bgen``, ``--bcmp``, ``--bdir``). Make sure any "diff" testing that goes on is on tests that are created earlier in the test list, as early as possible. Unfortunately, there is still no absolute guarantee the tests will be completed in the correct sequence. .. _testreporting: Test Reporting --------------- The CICE testing scripts have the capability to post test results to the official CICE Consortium Test-Results `wiki page `_. You may need write permission on the wiki. If you are interested in using the wiki, please contact the Consortium. Note that in order for code to be accepted to the CICE master through a Pull Request it is necessary for the developer to provide proof that their code passes relevant tests. This can be accomplished by posting the full results to the wiki, or by copying the testing summary to the Pull Request comments. To post results, once a test suite is complete, run ``results.csh`` and ``report_results.csh`` from the suite directory, :: ./cice.setup --suite base_suite --mach conrad --env cray --testid v01a cd testsuite.v01a #wait for runs to complete ./results.csh ./report_results.csh The reporting can also be automated by adding ``--report`` to ``cice.setup`` :: ./cice.setup --suite base_suite --mach conrad --env cray --testid v01a --report With ``--report``, the suite will create all the tests, build and submit them, wait for all runs to be complete, and run the results and report_results scripts. .. _compliance: Code Compliance Test (non bit-for-bit validation) ---------------------------------------------------- A core tenet of CICE dycore and CICE innovations is that they must not change the physics and biogeochemistry of existing model configurations, notwithstanding obsolete model components. Therefore, alterations to existing CICE Consortium code must only fix demonstrable numerical or scientific inaccuracies or bugs, or be necessary to introduce new science into the code. New physics and biogeochemistry introduced into the model must not change model answers when switched off, and in that case CICEcore and CICE must reproduce answers bit-for-bit as compared to previous simulations with the same namelist configurations. This bit-for-bit requirement is common in Earth System Modeling projects, but often cannot be achieved in practice because model additions may require changes to existing code. In this circumstance, bit-for-bit reproducibility using one compiler may not be unachievable on a different computing platform with a different compiler. Therefore, tools for scientific testing of CICE code changes have been developed to accompany bit-for-bit testing. These tools exploit the statistical properties of simulated sea ice thickness to confirm or deny the null hypothesis, which is that new additions to the CICE dycore and CICE have not significantly altered simulated ice volume using previous model configurations. Here we describe the CICE testing tools, which are applies to output from five-year gx-1 simulations that use the standard CICE atmospheric forcing. A scientific justification of the testing is provided in :cite:`Hunke18`. The following sections follow :cite:`Roberts18`. .. _paired: Two-Stage Paired Thickness Test ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The first quality check aims to confirm the null hypotheses :math:`H_0\!:\!\mu_d{=}0` at every model grid point, given the mean thickness difference :math:`\mu_d` between paired CICE simulations ‘:math:`a`’ and ‘:math:`b`’ that should be identical. :math:`\mu_d` is approximated as :math:`\bar{h}_{d}=\tfrac{1}{n}\sum_{i=1}^n (h_{ai}{-}h_{bi})` for :math:`n` paired samples of ice thickness :math:`h_{ai}` and :math:`h_{bi}` in each grid cell of the gx-1 mesh. Following :cite:`Wilks06`, the associated :math:`t`-statistic expects a zero mean, and is therefore .. math:: t=\frac{\bar{h}_{d}}{\sigma_d/\sqrt{n_{eff}}} :label: t-distribution given variance :math:`\sigma_d^{\;2}=\frac{1}{n-1}\sum_{i=1}^{n}(h_{di}-\bar{h}_d)^2` of :math:`h_{di}{=}(h_{ai}{-}h_{bi})` and effective sample size .. math:: n_{eff}{=}n\frac{({1-r_1})}{({1+r_1})} :label: neff for lag-1 autocorrelation: .. math:: r_1=\frac{\sum\limits_{i=1}^{n-1}\big[(h_{di}-\bar{h}_{d1:n-1})(h_{di+1}-\bar{h}_{d2:n})\big]}{\sqrt{\sum\limits_{i=1}^{n-1} (h_{di}-\bar{h}_{d1:n-1})^2 \sum\limits_{i=2}^{n} (h_{di}-\bar{h}_{d2:n})^2 }}. :label: r1 Here, :math:`\bar{h}_{d1:n-1}` is the mean of all samples except the last, and :math:`\bar{h}_{d2:n}` is the mean of samples except the first, and both differ from the overall mean :math:`\bar{h}_d` in equations (:eq:`t-distribution`). That is: .. math:: \bar{h}_{d1:n-1}=\frac{1}{n{-}1} \sum \limits_{i=1}^{n-1} h_{di},\quad \bar{h}_{d2:n}=\frac{1}{n{-}1} \sum \limits_{i=2}^{n} h_{di},\quad \bar{h}_d=\frac{1}{n} \sum \limits_{i=1}^{n} {h}_{di} :label: short-means Following :cite:`Zwiers95`, the effective sample size is limited to :math:`n_{eff}\in[2,n]`. This definition of :math:`n_{eff}` assumes ice thickness evolves as an AR(1) process :cite:`vonstorch99`, which can be justified by analyzing the spectral density of daily samples of ice thickness from 5-year records in CICE Consortium member models :cite:`Hunke18`. The AR(1) approximation is inadmissible for paired velocity samples, because ice drift possesses periodicity from inertia and tides :cite:`Hibler06,Lepparanta12,Roberts15`. Conversely, tests of paired ice concentration samples may be less sensitive to ice drift than ice thickness. In short, ice thickness is the best variable for CICE Consortium quality control (QC), and for the test of the mean in particular. Care is required in analyzing mean sea ice thickness changes using (:eq:`t-distribution`) with :math:`N{=}n_{eff}{-}1` degrees of freedom. :cite:`Zwiers95` demonstrate that the :math:`t`-test in (:eq:`t-distribution`) becomes conservative when :math:`n_{eff} < 30`, meaning that :math:`H_0` may be erroneously confirmed for highly auto-correlated series. Strong autocorrelation frequently occurs in modeled sea ice thickness, and :math:`r_1>0.99` is possible in parts of the gx-1 domain for the five-year QC simulations. In the event that :math:`H_0` is confirmed but :math:`2\leq n_{eff}<30`, the :math:`t`-test progresses to the ‘Table Lookup Test’ of :cite:`Zwiers95`, to check that the first-stage test using (:eq:`t-distribution`) was not conservative. The Table Lookup Test chooses critical :math:`t` values :math:`|t|