ó áp7]c@sidZddlmZddlmZddlZddlmZm Z ddl m Z ddd„Z dd d „Zd dd „Zd d„Zdefd„ƒYZdefd„ƒYZdefd„ƒYZdefd„ƒYZdefd„ƒYZdefd„ƒYZdefd„ƒYZdefd„ƒYZeƒjZeƒjZeƒjZdS(sDStatistical power, solving for nobs, ... - trial version Created on Sat Jan 12 21:48:06 2013 Author: Josef Perktold Example roundtrip - root with respect to all variables calculated, desired nobs 33.367204205 33.367204205 effect 0.5 0.5 alpha 0.05 0.05 power 0.8 0.8 TODO: refactoring - rename beta -> power, beta (type 2 error is beta = 1-power) DONE - I think the current implementation can handle any kinds of extra keywords (except for maybe raising meaningful exceptions - streamline code, I think internally classes can be merged how to extend to k-sample tests? user interface for different tests that map to the same (internal) test class - sequence of arguments might be inconsistent, arg and/or kwds so python checks what's required and what can be None. - templating for docstrings ? i˙˙˙˙(tprint_function(t iteritemsN(tstatstoptimize(tbrentq_expandings two-sidedc CsE|}|d kr|d}n|d kr8|d}n%|d krM|}ntddƒ‚d }|d krĐtjj||ƒ}tjtj|ƒƒr¨tj}qĐtj j |||tj |ƒƒ}n|dkrAtjj ||ƒ} tjtj| ƒƒrtj}qA|tj j | ||tj |ƒƒ7}n|S(sCalculate power of a ttest is two-sidedt2sg@tsmallertlargers,alternative has to be 'two-sided', 'larger' s or 'smaller'iN(s two-sidedR(RR(s two-sidedRR(s two-sidedRR(tNonet ValueErrorRtttisftnptanytisnantnantnctt_sftsqrttppft_cdf( t effect_sizetnobstalphatdft alternativetdtalpha_tpow_tcrit_upptcrit_low((s6lib/python2.7/site-packages/statsmodels/stats/power.pyt ttest_power's*         (  ,gđ?c Csâ|}|d kr|d}n%|d kr4|}ntddƒ‚d}|d kr’tjj|ƒ}tjj||tj|ƒ|ƒ}n|d krŢtjj|ƒ}|tjj||tj|ƒ|ƒ7}n|S( s<Calculate power of a normal distributed test statistic s two-sidedRg@RRs,alternative has to be 'two-sided', 'larger' s or 'smaller'i(s two-sidedR(RR(s two-sidedRR(s two-sidedRR( R RtnormR tsfR RRtcdf( RRRRtsigmaRRRtcrit((s6lib/python2.7/site-packages/statsmodels/stats/power.pyt normal_powerIs      * .ic CsS||}|d}tjj|||ƒ}tjj||||d|ƒ}|S(sľpower for ftest for one way anova with k equal sized groups nobs total sample size, sum over all groups should be general nobs observations, k_groups restrictions ??? ii(RtfR tncfR!( RRRtk_groupsRtdf_numtdf_denomR$R((s6lib/python2.7/site-packages/statsmodels/stats/power.pytftest_anova_power`s   #icCsM|d|||}tjj|||ƒ}tjj||||ƒ}|S(sŃCalculate the power of a F-test. Parameters ---------- effect_size : float standardized effect size, mean divided by the standard deviation. effect size has to be positive. df_num : int or float numerator degrees of freedom. df_denom : int or float denominator degrees of freedom. alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. ncc : int degrees of freedom correction for non-centrality parameter. see Notes Returns ------- power : float Power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. Notes ----- sample size is given implicitly by df_num set ncc=0 to match t-test, or f-test in LikelihoodModelResults. ncc=1 matches the non-centrality parameter in R::pwr::pwr.f2.test ftest_power with ncc=0 should also be correct for f_test in regression models, with df_num and d_denom as defined there. (not verified yet) i(RR&R R'R!(RR)R*RtncctncR$R((s6lib/python2.7/site-packages/statsmodels/stats/power.pyt ftest_powerms%tPowercBsPeZdZd„Zd„Zd„Zd„Zdddddddd„ZRS( s[Statistical Power calculations, Base Class so far this could all be class methods cKs8|jj|ƒtddddddddd dd d d d ddƒ|_ddlm}|tƒ|_x6dd d dgD]"}tddddƒ|j|igę-™—q=tuppgŃÜ˙˙˙˙ď?(t__dict__tupdatetdictt start_ttpt collectionsR3t start_bqexp(tselftkwdsR3tkey((s6lib/python2.7/site-packages/statsmodels/stats/power.pyt__init__Ąs   cOs t‚dS(N(tNotImplementedError(R=targsR>((s6lib/python2.7/site-packages/statsmodels/stats/power.pyR0ˇscOs#|jdƒ}|j||Ž|S(NR0(tpopR0(R=RBR>tpower_((s6lib/python2.7/site-packages/statsmodels/stats/power.pyt_power_identityşsc sAgtˆƒD]\}}|dkr |^q ‰tˆƒdkrRtdƒ‚nˆd‰ˆdkr|ˆd=ˆjˆSˆddkrďddl}ddlm}|jd |ƒˆdkr̈d Sˆd krŕˆdStd ƒ‚ndˆ_ ‡‡‡fd †}yˆj ˆ}WnLt k rld }ddl}ddlm }|jdj ˆƒ|ƒnXˆjˆ} g} y2t|dt| \} } t} | j| ƒWn$tk rŘt} | jdƒnXd}| rř| jrřd}nëtj|ƒsEtj||dtƒ\} }}}|d}| j|ƒnd}d}| jdgƒ|dkr‹tj|ƒdkr‹d}nXˆdkrÝtj|dddtƒ\} }|jrÇdnd}| j|ƒnd}|dks$ddl}ddlm}m}|j||ƒn| jd|ƒ| ˆ_| S(scsolve for any one of the parameters of a t-test for t-test the keywords are: effect_size, nobs, alpha, power exactly one needs to be ``None``, all others need numeric values *attaches* cache_fit_res : list Cache of the result of the root finding procedure for the latest call to ``solve_power``, mainly for debugging purposes. The first element is the success indicator, one if successful. The remaining elements contain the return information of the up to three solvers that have been tried. is%need exactly one keyword that is NoneiR0Ri˙˙˙˙N(tHypothesisTestWarnings"Warning: Effect size of 0 detectedRsACannot detect an effect-size of 0. Try changing your effect-size.csd|ˆˆ<ˆjˆ}ˆjd7_ˆjdkrFtdƒ‚ntj|ƒr\tjS|SdS(Niiôs possible endless loop (500 NaNs)(REt_countert RuntimeErrorR Rtinf(txtfval(R?R>R=(s6lib/python2.7/site-packages/statsmodels/stats/power.pytfuncěs gÍĚĚĚĚĚě?(t ValueWarnings*Warning: using default start_value for {0}t full_outputtfvecg-Cëâ6?g:Œ0âŽyE>(tConvergenceWarningtconvergence_doc(RR0RgGœĄú˙˙ď?(RRtlenR R0twarningststatsmodels.tools.sm_exceptionsRFtwarnRGR:tKeyErrorRMtformatR<RtTruetFalsetappendt convergedR RRtfsolvetabstbrentqRPRQtinsertt cache_fit_res(R=R>tktvRSRFRLt start_valueRMtfit_kwdstfit_restvaltrestfailedtsuccesstinfodicttiertmsgRKtrRPRQ((R?R>R=s6lib/python2.7/site-packages/statsmodels/stats/power.pyt solve_poweržsx1              !     Rgš™™™™™Š?c Ksˇddlm} ddlm} | j|ƒ\} }ddlj} | jj} d}d}|dkr| t |ƒƒ}gt j dd t |ƒƒD]}| |ƒ^q–}xĂt |ƒD]Z\}}|j ||||}|j||d |d |d ||d d|ƒd}qťWnX|dkrÜ| t |ƒƒ}gt j dd t |ƒƒD]}| |ƒ^qV}xt |ƒD]Z\}}|j ||||}|j||d |d |d ||d d|ƒd}q{Wn˜|dkrh| t |ƒƒ}xwt |ƒD]Z\}}|j ||||}|j||d |d |d ||d d|ƒd }qWn tdƒ‚|dkr‰d}n|j|ƒ|j|ƒ|jddƒ| S(sđplot power with number of observations or effect size on x-axis Parameters ---------- dep_var : string in ['nobs', 'effect_size', 'alpha'] This specifies which variable is used for the horizontal axis. If dep_var='nobs' (default), then one curve is created for each value of ``effect_size``. If dep_var='effect_size' or alpha, then one curve is created for each value of ``nobs``. nobs : scalar or array_like specifies the values of the number of observations in the plot effect_size : scalar or array_like specifies the values of the effect_size in the plot alpha : float or array_like The significance level (type I error) used in the power calculation. Can only be more than a scalar, if ``dep_var='alpha'`` ax : None or axis instance If ax is None, than a matplotlib figure is created. If ax is a matplotlib axis instance, then it is reused, and the plot elements are created with it. title : string title for the axis. Use an empty string, ``''``, to avoid a title. plt_kwds : None or dict not used yet kwds : optional keywords for power function These remaining keyword arguments are used as arguments to the power function. Many power function support ``alternative`` as a keyword argument, two-sample test support ``ratio``. Returns ------- fig : matplotlib figure instance Notes ----- This works only for classes where the ``power`` method has ``effect_size``, ``nobs`` and ``alpha`` as the first three arguments. If the second argument is ``nobs1``, then the number of observations in the plot are those for the first sample. TODO: fix this for FTestPower and GofChisquarePower TODO: maybe add line variable, if we want more than nobs and effectsize i˙˙˙˙(tutils(trainbowNiiRigÍĚĚĚĚĚě?tlwRtcolortlabelses=%4.2FsNumber of Observationss effect sizeRtessN=%4.2Fs Effect Sizesdepvar not implementeds Power of Testtlocs lower right(s effect sizeRRt(R(tstatsmodels.graphicsRotstatsmodels.graphics.plottoolsRpt create_mpl_axtmatplotlib.pyplottpyplottcmtDark2RRR tlinspacet enumerateR0tplotR Rt set_xlabelt set_titletlegend(R=tdep_varRRRtaxttitletplt_kwdsR>RoRptfigtplttcolormapt plt_alphaRqtcolorstitiiRtR0txlabeltn((s6lib/python2.7/site-packages/statsmodels/stats/power.pyt plot_power4sJ/  4  4        N( t__name__t __module__t__doc__R@R0RERnRR(((s6lib/python2.7/site-packages/statsmodels/stats/power.pyR/›s    v t TTestPowercBs5eZdZddd„Zdddddd„ZRS(sKStatistical Power calculations for one sample or paired sample t-test s two-sidedcCst|||d|d|ƒS(sđCalculate the power of a t-test for one sample or paired samples. Parameters ---------- effect_size : float standardized effect size, mean divided by the standard deviation. effect size has to be positive. nobs : int or float sample size, number of observations. alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. df : int or float degrees of freedom. By default this is None, and the df from the one sample or paired ttest is used, ``df = nobs1 - 1`` alternative : string, 'two-sided' (default), 'larger', 'smaller' extra argument to choose whether the power is calculated for a two-sided (default) or one sided test. The one-sided test can be either 'larger', 'smaller'. . Returns ------- power : float Power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. RR(R(R=RRRRR((s6lib/python2.7/site-packages/statsmodels/stats/power.pyR0“s c Cs1tt|ƒjd|d|d|d|d|ƒS(sˆ solve for any one parameter of the power of a one sample t-test for the one sample t-test the keywords are: effect_size, nobs, alpha, power Exactly one needs to be ``None``, all others need numeric values. This test can also be used for a paired t-test, where effect size is defined in terms of the mean difference, and nobs is the number of pairs. Parameters ---------- effect_size : float standardized effect size, mean divided by the standard deviation. effect size has to be positive. nobs : int or float sample size, number of observations. alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. power : float in interval (0,1) power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. alternative : string, 'two-sided' (default) or 'one-sided' extra argument to choose whether the power is calculated for a two-sided (default) or one sided test. 'one-sided' assumes we are in the relevant tail. Returns ------- value : float The value of the parameter that was set to None in the call. The value solves the power equation given the remaining parameters. *attaches* cache_fit_res : list Cache of the result of the root finding procedure for the latest call to ``solve_power``, mainly for debugging purposes. The first element is the success indicator, one if successful. The remaining elements contain the return information of the up to three solvers that have been tried. Notes ----- The function uses scipy.optimize for finding the value that satisfies the power equation. It first uses ``brentq`` with a prior search for bounds. If this fails to find a root, ``fsolve`` is used. If ``fsolve`` also fails, then, for ``alpha``, ``power`` and ``effect_size``, ``brentq`` with fixed bounds is used. However, there can still be cases where this fails. RRRR0R(tsuperR”Rn(R=RRRR0R((s6lib/python2.7/site-packages/statsmodels/stats/power.pyRnˇs ;N(R‘R’R“RR0Rn(((s6lib/python2.7/site-packages/statsmodels/stats/power.pyR”Žs$ t TTestIndPowercBs;eZdZdddd„Zddddddd„ZRS(ssStatistical Power calculations for t-test for two independent sample currently only uses pooled variance is two-sidedc Cs]||}|dkr+|d|d}ndd|d|}t|||d|d|ƒS(sĄCalculate the power of a t-test for two independent sample Parameters ---------- effect_size : float standardized effect size, difference between the two means divided by the standard deviation. `effect_size` has to be positive. nobs1 : int or float number of observations of sample 1. The number of observations of sample two is ratio times the size of sample 1, i.e. ``nobs2 = nobs1 * ratio`` alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. ratio : float ratio of the number of observations in sample 2 relative to sample 1. see description of nobs1 The default for ratio is 1; to solve for ratio given the other arguments, it has to be explicitly set to None. df : int or float degrees of freedom. By default this is None, and the df from the ttest with pooled variance is used, ``df = (nobs1 - 1 + nobs2 - 1)`` alternative : string, 'two-sided' (default), 'larger', 'smaller' extra argument to choose whether the power is calculated for a two-sided (default) or one sided test. The one-sided test can be either 'larger', 'smaller'. Returns ------- power : float Power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. igđ?RRN(RR( R=RR1RR2RRtnobs2R((s6lib/python2.7/site-packages/statsmodels/stats/power.pyR0s &  gđ?c Cs7tt|ƒjd|d|d|d|d|d|ƒS(s solve for any one parameter of the power of a two sample t-test for t-test the keywords are: effect_size, nobs1, alpha, power, ratio exactly one needs to be ``None``, all others need numeric values Parameters ---------- effect_size : float standardized effect size, difference between the two means divided by the standard deviation. `effect_size` has to be positive. nobs1 : int or float number of observations of sample 1. The number of observations of sample two is ratio times the size of sample 1, i.e. ``nobs2 = nobs1 * ratio`` alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. power : float in interval (0,1) power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. ratio : float ratio of the number of observations in sample 2 relative to sample 1. see description of nobs1 The default for ratio is 1; to solve for ratio given the other arguments it has to be explicitly set to None. alternative : string, 'two-sided' (default), 'larger', 'smaller' extra argument to choose whether the power is calculated for a two-sided (default) or one sided test. The one-sided test can be either 'larger', 'smaller'. Returns ------- value : float The value of the parameter that was set to None in the call. The value solves the power equation given the remaining parameters. Notes ----- The function uses scipy.optimize for finding the value that satisfies the power equation. It first uses ``brentq`` with a prior search for bounds. If this fails to find a root, ``fsolve`` is used. If ``fsolve`` also fails, then, for ``alpha``, ``power`` and ``effect_size``, ``brentq`` with fixed bounds is used. However, there can still be cases where this fails. RR1RR0R2R(R•R–Rn(R=RR1RR0R2R((s6lib/python2.7/site-packages/statsmodels/stats/power.pyRn0s 4N(R‘R’R“RR0Rn(((s6lib/python2.7/site-packages/statsmodels/stats/power.pyR–řs  / tNormalIndPowercBsDeZdZdd„Zddd„Zddddddd„ZRS( suStatistical Power calculations for z-test for two independent samples. currently only uses pooled variance icKs#||_tt|ƒj|dS(N(tddofR•R˜R@(R=R™R>((s6lib/python2.7/site-packages/statsmodels/stats/power.pyR@rs is two-sidedc Cs`|j}|dkr@||}dd||d||}n ||}t|||d|ƒS(sĆCalculate the power of a z-test for two independent sample Parameters ---------- effect_size : float standardized effect size, difference between the two means divided by the standard deviation. effect size has to be positive. nobs1 : int or float number of observations of sample 1. The number of observations of sample two is ratio times the size of sample 1, i.e. ``nobs2 = nobs1 * ratio`` ``ratio`` can be set to zero in order to get the power for a one sample test. alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. ratio : float ratio of the number of observations in sample 2 relative to sample 1. see description of nobs1 alternative : string, 'two-sided' (default), 'larger', 'smaller' extra argument to choose whether the power is calculated for a two-sided (default) or one sided test. The one-sided test can be either 'larger', 'smaller'. Returns ------- power : float Power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. igđ?R(R™R%( R=RR1RR2RR™R—R((s6lib/python2.7/site-packages/statsmodels/stats/power.pyR0vs #   ! gđ?c Cs7tt|ƒjd|d|d|d|d|d|ƒS(są solve for any one parameter of the power of a two sample z-test for z-test the keywords are: effect_size, nobs1, alpha, power, ratio exactly one needs to be ``None``, all others need numeric values Parameters ---------- effect_size : float standardized effect size, difference between the two means divided by the standard deviation. If ratio=0, then this is the standardized mean in the one sample test. nobs1 : int or float number of observations of sample 1. The number of observations of sample two is ratio times the size of sample 1, i.e. ``nobs2 = nobs1 * ratio`` ``ratio`` can be set to zero in order to get the power for a one sample test. alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. power : float in interval (0,1) power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. ratio : float ratio of the number of observations in sample 2 relative to sample 1. see description of nobs1 The default for ratio is 1; to solve for ration given the other arguments it has to be explicitly set to None. alternative : string, 'two-sided' (default), 'larger', 'smaller' extra argument to choose whether the power is calculated for a two-sided (default) or one sided test. The one-sided test can be either 'larger', 'smaller'. Returns ------- value : float The value of the parameter that was set to None in the call. The value solves the power equation given the remaining parameters. Notes ----- The function uses scipy.optimize for finding the value that satisfies the power equation. It first uses ``brentq`` with a prior search for bounds. If this fails to find a root, ``fsolve`` is used. If ``fsolve`` also fails, then, for ``alpha``, ``power`` and ``effect_size``, ``brentq`` with fixed bounds is used. However, there can still be cases where this fails. RR1RR0R2R(R•R˜Rn(R=RR1RR0R2R((s6lib/python2.7/site-packages/statsmodels/stats/power.pyRnĽs 8N(R‘R’R“R@R0RRn(((s6lib/python2.7/site-packages/statsmodels/stats/power.pyR˜ks   . t FTestPowercBs8eZdZdd„Zdddddddd„ZRS(s7Statistical Power calculations for generic F-test icCst||||d|ƒ}|S(sECalculate the power of a F-test. Parameters ---------- effect_size : float standardized effect size, mean divided by the standard deviation. effect size has to be positive. df_num : int or float numerator degrees of freedom. df_denom : int or float denominator degrees of freedom. alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. ncc : int degrees of freedom correction for non-centrality parameter. see Notes Returns ------- power : float Power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. Notes ----- sample size is given implicitly by df_num set ncc=0 to match t-test, or f-test in LikelihoodModelResults. ncc=1 matches the non-centrality parameter in R::pwr::pwr.f2.test ftest_power with ncc=0 should also be correct for f_test in regression models, with df_num and d_denom as defined there. (not verified yet) R,(R.(R=RR)R*RR,R((s6lib/python2.7/site-packages/statsmodels/stats/power.pyR0ęs&c Cs7tt|ƒjd|d|d|d|d|d|ƒS(sWsolve for any one parameter of the power of a F-test for the one sample F-test the keywords are: effect_size, df_num, df_denom, alpha, power Exactly one needs to be ``None``, all others need numeric values. Parameters ---------- effect_size : float standardized effect size, mean divided by the standard deviation. effect size has to be positive. nobs : int or float sample size, number of observations. alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. power : float in interval (0,1) power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. alternative : string, 'two-sided' (default) or 'one-sided' extra argument to choose whether the power is calculated for a two-sided (default) or one sided test. 'one-sided' assumes we are in the relevant tail. Returns ------- value : float The value of the parameter that was set to None in the call. The value solves the power equation given the remainding parameters. Notes ----- The function uses scipy.optimize for finding the value that satisfies the power equation. It first uses ``brentq`` with a prior search for bounds. If this fails to find a root, ``fsolve`` is used. If ``fsolve`` also fails, then, for ``alpha``, ``power`` and ``effect_size``, ``brentq`` with fixed bounds is used. However, there can still be cases where this fails. RR)R*RR0R,(R•RšRn(R=RR)R*RRR0R,((s6lib/python2.7/site-packages/statsmodels/stats/power.pyRns .N(R‘R’R“R0RRn(((s6lib/python2.7/site-packages/statsmodels/stats/power.pyRšĺs + tFTestAnovaPowercBsJeZdZdd„Zdddddd„Zdddddd„ZRS(sIStatistical Power calculations F-test for one factor balanced ANOVA icCst|||d|ƒS(s“Calculate the power of a F-test for one factor ANOVA. Parameters ---------- effect_size : float standardized effect size, mean divided by the standard deviation. effect size has to be positive. nobs : int or float sample size, number of observations. alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. k_groups : int or float number of groups in the ANOVA or k-sample comparison. Default is 2. Returns ------- power : float Power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. R((R+(R=RRRR(((s6lib/python2.7/site-packages/statsmodels/stats/power.pyR0Osc CsŠ|d k rD|d|jdiRNgGœĄú˙˙ď?(RR^RXR[tprint( R=RRRR0R(RLRfRm((RR(RR0R=s6lib/python2.7/site-packages/statsmodels/stats/power.pyRœ§s !  N(R‘R’R“R0RRnRœ(((s6lib/python2.7/site-packages/statsmodels/stats/power.pyR›Js    < tGofChisquarePowercBs2eZdZdd„Zdddddd„ZRS(sBStatistical Power calculations for one sample chisquare test icCs)ddlm}|||||ddƒS(sľCalculate the power of a chisquare test for one sample Only two-sided alternative is implemented Parameters ---------- effect_size : float standardized effect size, according to Cohen's definition. see :func:`statsmodels.stats.gof.chisquare_effectsize` nobs : int or float sample size, number of observations. alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. n_bins : int number of bins or cells in the distribution. Returns ------- power : float Power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. i˙˙˙˙(tchisquare_powerR™i(tstatsmodels.stats.gofRŸ(R=RRRtn_binsR™RŸ((s6lib/python2.7/site-packages/statsmodels/stats/power.pyR0žsic Cs1tt|ƒjd|d|d|d|d|ƒS(sţsolve for any one parameter of the power of a one sample chisquare-test for the one sample chisquare-test the keywords are: effect_size, nobs, alpha, power Exactly one needs to be ``None``, all others need numeric values. n_bins needs to be defined, a default=2 is used. Parameters ---------- effect_size : float standardized effect size, according to Cohen's definition. see :func:`statsmodels.stats.gof.chisquare_effectsize` nobs : int or float sample size, number of observations. alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. power : float in interval (0,1) power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. n_bins : int number of bins or cells in the distribution Returns ------- value : float The value of the parameter that was set to None in the call. The value solves the power equation given the remaining parameters. Notes ----- The function uses scipy.optimize for finding the value that satisfies the power equation. It first uses ``brentq`` with a prior search for bounds. If this fails to find a root, ``fsolve`` is used. If ``fsolve`` also fails, then, for ``alpha``, ``power`` and ``effect_size``, ``brentq`` with fixed bounds is used. However, there can still be cases where this fails. RRRĄRR0(R•RžRn(R=RRRR0RĄ((s6lib/python2.7/site-packages/statsmodels/stats/power.pyRnÜs .N(R‘R’R“R0RRn(((s6lib/python2.7/site-packages/statsmodels/stats/power.pyRžšs  t_GofChisquareIndPowercBs8eZdZddd„Zddddddd„ZRS(sStatistical Power calculations for chisquare goodness-of-fit test TODO: this is not working yet for 2sample case need two nobs in function no one-sided chisquare test, is there one? use normal distribution? -> drop one-sided options? is two-sidedc Cs@ddlm}||}dd|d|}||||ƒS(sßCalculate the power of a chisquare for two independent sample Parameters ---------- effect_size : float standardize effect size, difference between the two means divided by the standard deviation. effect size has to be positive. nobs1 : int or float number of observations of sample 1. The number of observations of sample two is ratio times the size of sample 1, i.e. ``nobs2 = nobs1 * ratio`` alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. ratio : float ratio of the number of observations in sample 2 relative to sample 1. see description of nobs1 The default for ratio is 1; to solve for ration given the other arguments it has to be explicitely set to None. alternative : string, 'two-sided' (default) or 'one-sided' extra argument to choose whether the power is calculated for a two-sided (default) or one sided test. 'one-sided' assumes we are in the relevant tail. Returns ------- power : float Power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. i˙˙˙˙(RŸgđ?(R RŸ( R=RR1RR2RRŸR—R((s6lib/python2.7/site-packages/statsmodels/stats/power.pyR0s# gđ?c Cs7tt|ƒjd|d|d|d|d|d|ƒS(sâsolve for any one parameter of the power of a two sample z-test for z-test the keywords are: effect_size, nobs1, alpha, power, ratio exactly one needs to be ``None``, all others need numeric values Parameters ---------- effect_size : float standardize effect size, difference between the two means divided by the standard deviation. nobs1 : int or float number of observations of sample 1. The number of observations of sample two is ratio times the size of sample 1, i.e. ``nobs2 = nobs1 * ratio`` alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. power : float in interval (0,1) power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. ratio : float ratio of the number of observations in sample 2 relative to sample 1. see description of nobs1 The default for ratio is 1; to solve for ration given the other arguments it has to be explicitely set to None. alternative : string, 'two-sided' (default) or 'one-sided' extra argument to choose whether the power is calculated for a two-sided (default) or one sided test. 'one-sided' assumes we are in the relevant tail. Returns ------- value : float The value of the parameter that was set to None in the call. The value solves the power equation given the remainding parameters. Notes ----- The function uses scipy.optimize for finding the value that satisfies the power equation. It first uses ``brentq`` with a prior search for bounds. If this fails to find a root, ``fsolve`` is used. If ``fsolve`` also fails, then, for ``alpha``, ``power`` and ``effect_size``, ``brentq`` with fixed bounds is used. However, there can still be cases where this fails. RR1RR0R2R(R•R˘Rn(R=RR1RR0R2R((s6lib/python2.7/site-packages/statsmodels/stats/power.pyRnDs 4N(R‘R’R“R0RRn(((s6lib/python2.7/site-packages/statsmodels/stats/power.pyR˘s  ) (R“t __future__Rtstatsmodels.compat.pythonRtnumpyR tscipyRRtstatsmodels.tools.rootfindingRRRR%R+R.tobjectR/R”R–R˜RšR›RžR˘Rnttt_solve_powerttt_ind_solve_powertzt_ind_solve_power(((s6lib/python2.7/site-packages/statsmodels/stats/power.pyt s( " .ójszeoWp