├── .gitattributes
├── README.md
├── code
    ├── __init__.py
    └── bootstrap_routines.py
└── data
    ├── population_distribution-1.txt
    └── population_distribution-2.txt


/.gitattributes:
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1 | *.rb linguist-language=Python
2 | 


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/README.md:
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1 | bootstrap-tools
2 | ===============
3 | 
4 | Bootstrap analysis library (*Python*) used in the **Making do with what we have: use your bootstraps** paper (J Physiol. 2012 August 1; 590(Pt 15): 3403–3406)
5 | 
6 | Website: http://gcalmettes.github.io/bootstrap-tools/
7 | 
8 | Repos: https://github.com/gcalmettes/bootstrap-tools/tree/master
9 | 


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/code/__init__.py:
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1 | # Init for bootcode module
2 | 
3 | 


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/code/bootstrap_routines.py:
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  1 | # Copyright 2012 gcalmettes (gcalmettes@ucla.edu), BSD-style copyright and disclaimer apply
  2 | #!/usr/local/bin/python
  3 | 
  4 | # needed libraries
  5 | import numpy as np
  6 | import random as rd
  7 | 
  8 | ###################################################
  9 | def bootstrap(data, nboot=10000, replacement=True):
 10 |     """
 11 |         Generate n=nboot bootstrap samples of the data with/without replacement,
 12 |         and return a 2D numpy array of them.
 13 | 
 14 |         Input:    data (anything numpy can handle as a numpy array)
 15 |         Output:   2D numpy array of size (nboot x length of data)
 16 |     """
 17 | 
 18 |     # Ensure that our data is a 1D array.
 19 |     data = np.ravel(data)
 20 | 
 21 |     # Create a 2D array of bootstrap samples indexes
 22 |     if replacement==True: # with replacement (note: 50x-ish faster than without)
 23 |         idx = np.random.randint(data.size, size=(nboot, data.size))
 24 |     elif replacement==False: # without replacement
 25 |         idx = np.vstack([np.random.permutation(data.size) for x in np.arange(nboot)])
 26 | 
 27 |     return data[idx]
 28 | 
 29 | 
 30 | ###################################################
 31 | def bootci(data, stat=np.mean, nboot=10000, replacement=True, alpha=0.05, method='pi',
 32 |            keepboot=False):
 33 |     """
 34 |         Compute the (1-alpha) confidence interval of a statistic (i.e.: mean, median, etc)
 35 |         of the data using bootstrap resampling.
 36 |         
 37 |         Arguments:
 38 |             stat:        statistics we want the confidence interval for (must be a function)
 39 |             nboot:       number of bootstrap samples to generate
 40 |             replacement: resampling done with (True) or without (False) replacement
 41 |             alpha:       level of confidence interval
 42 |             method:      type of bootstrap we want to perform
 43 |             keepboot:    if True, return the nboot bootstrap statistics from which
 44 |                          the confidence intervals are extracted
 45 |         
 46 |         Methods available:
 47 |             - 'pi' = Percentile Interval
 48 |             - 'bca' = Bias-Corrected Accelerated Interval (available soon)
 49 |     """
 50 | 
 51 |     # apply bootstrap to data
 52 |     boot = bootstrap(data, nboot=nboot, replacement=replacement)
 53 | 
 54 |     # calculate the statistics for each bootstrap sample and sort them
 55 |     sorted_stat = np.sort(stat(boot, axis=1))
 56 | 
 57 |     # Percentile Interval method (for the moment the only one available) 
 58 |     if method == 'pi':
 59 |         ci = (sorted_stat[np.round(nboot*alpha/2).astype(int)], 
 60 |               sorted_stat[np.round(nboot*(1-alpha/2)).astype(int)])
 61 | 
 62 |     if keepboot == True:
 63 |         return ci, sorted_stat
 64 |     else:
 65 |         return ci
 66 |         
 67 | 
 68 | ###################################################
 69 | def bootci_diff(data1, data2, stat=np.mean, func=np.subtract, nboot=10000,
 70 |                 alpha=0.05, replacement=True, keepboot=False):
 71 |     """
 72 |         Calculate the effect size of a treatment and compute the confidence
 73 |         interval of that effect size using bootstrap resampling method.
 74 | 
 75 |         Arguments:
 76 |             stat:        statistics we want the confidence interval for (must be a function)
 77 |             nboot:       number of bootstrap samples to generate
 78 |             replacement: resampling done with (True) or without (False) replacement
 79 |             alpha:       level of confidence interval
 80 |             keepboot:    if True, return the nboot bootstrap statistics from which
 81 |                          the confidence intervals are extracted
 82 |     """
 83 | 
 84 |     # Ensure that our data is a 1D array.
 85 |     data1, data2 = np.ravel(data1), np.ravel(data2)
 86 | 
 87 |     # bootstrap samples
 88 |     boot_d1 = bootstrap(data1, nboot=nboot, replacement=replacement)
 89 |     boot_d2 = bootstrap(data2, nboot=nboot, replacement=replacement)
 90 |     
 91 |     # stat of bootstrap samples
 92 |     boot_d1stat = stat(boot_d1, axis=1)
 93 |     boot_d2stat = stat(boot_d2, axis=1)
 94 |     #boot_d1stat = np.array([stat(x) for x in boot_d1])
 95 |     #boot_d2stat = np.array([stat(x) for x in boot_d2])
 96 |     
 97 |     # ci
 98 |     bootdiff = func(boot_d1stat, boot_d2stat)
 99 |     sorted_bootdiff = np.sort(bootdiff)
100 |     
101 |     ci_diff = (sorted_bootdiff[np.round(nboot*alpha/2).astype(int)], 
102 |              sorted_bootdiff[np.round(nboot*(1-alpha/2)).astype(int)])
103 | 
104 |     if keepboot == True:
105 |         return ci_diff, sorted_bootdiff
106 |     else:
107 |         return ci_diff
108 | 
109 | 
110 | ###################################################
111 | def bootpv(data1, data2, stat=np.mean, func=np.subtract, nboot=10000, 
112 |            replacement=True, printout=True, keepboot=False):
113 |     """
114 |         Assuming that there is no significant difference in the means of 
115 |         the two samples, return the one-tailed pvalue to see the probability of
116 |         getting a difference greater than or equal to the observed difference
117 |         in the means by chance alone.
118 |         Permutation (replacement = False) or bootstrapping (default, replacement = True)
119 |         is used to get a distribution to compare to the observed statistic.
120 | 
121 |         Input:  data1 and data2 (anything numpy can handle as a numpy array)
122 |         Output: one-tailed pvalue
123 | 
124 |         Arguments:
125 |             stat:        statistics we want the pvalue for (mean, median, etc..)
126 |             func:        the function we want to use to compare data (default algebric diff)
127 |             nboot:       number of bootstrap samples to generate
128 |             replacement: resampling done with (True) or without (False) replacement
129 |             printout:    if True (default), print the result of the analysis
130 |             keepboot:    if True, return the nboot bootstrap statistics from which
131 |                          the confidence intervals are extracted        
132 |     """
133 | 
134 |     # Ensure that our data are 1D arrays
135 |     data1, data2 = np.ravel(data1), np.ravel(data2)
136 | 
137 |     # Mesure the difference of the statistic between the two groups
138 |     diff_groups = func(stat(data1), stat(data2))
139 | 
140 |     # Size of the two samples
141 |     samplesize1, samplesize2 = data1.size, data2.size
142 | 
143 |     # Put all the values from the two groups in one array
144 |     pool = np.hstack((data1, data2))
145 | 
146 |     if replacement == False: # resampling without replacement (permutation)
147 |         # Create a matrix of n_samples shuffled indexes of the pool
148 |         pool_idxtable = np.array([np.random.permutation(pool.size) for n in range(nboot)])
149 | 
150 |         # Create n_samples sets of data from size of the two groups 
151 |         sample1 = pool[pool_idxtable[:, :samplesize1]]
152 |         sample2 = pool[pool_idxtable[:, samplesize1:]]
153 | 
154 |     elif replacement == True: # bootstrap
155 |         bootpool = bootstrap(pool, nboot=nboot, replacement=True)
156 |         sample1 = bootpool[:, :samplesize1]
157 |         sample2 = bootpool[:, samplesize1:]
158 | 
159 |     param_sample1 = np.array([stat(x) for x in sample1])
160 |     param_sample2 = np.array([stat(x) for x in sample2])
161 |     
162 |     param_func = func(param_sample1, param_sample2)
163 |     
164 |     # Warning: the criteria set is > or < zero (ok for difference)
165 |     # if the func argument is not np.subtract (algebric difference),
166 |     # this has to be changed (ex: if np.divide is used, criteria will be
167 |     # > or < 1, since a ratio cannot be negative)
168 |     if diff_groups < 0:
169 |         pvalue = np.sum(param_func <= diff_groups)/float(nboot)
170 |     elif diff_groups > 0:
171 |         pvalue = np.sum(param_func >= diff_groups)/float(nboot)
172 |     
173 |     if printout == True:
174 |         sign = "greater than or equal to"
175 |         ndiff = np.sum(param_func >= diff_groups)
176 |         if diff_groups < 0:
177 |             sign = "less than or equal to"
178 |             ndiff = np.sum(param_func <= diff_groups)
179 |         print("Observed difference of two means: {0:.2f}".format(diff_groups))
180 |         print("{0:d} out of {1:d} experiments had a difference of two means {2:s} {3:.2f}"\
181 |             .format(ndiff, nboot, sign, diff_groups))
182 |         print("The chance of getting a difference of two means {0:s} {1:.2f} is {2:.4f}"\
183 |               .format(sign, diff_groups, pvalue))
184 |        
185 |     if keepboot == True:
186 |         return pvalue, param_func
187 |     else:
188 |         return pvalue
189 | 


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/data/population_distribution-1.txt:
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   1 | 5.868278775909139711e+00
   2 | 5.995968828382741478e+00
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2501 | 


--------------------------------------------------------------------------------
/data/population_distribution-2.txt:
--------------------------------------------------------------------------------
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2461 | 4.696100628475991634e+00
2462 | 7.692597674149650899e+00
2463 | 4.521055545340542103e+00
2464 | 5.555421688297422556e+00
2465 | 5.363359232476171634e+00
2466 | 5.269150730040616182e+00
2467 | 4.497426834769081339e+00
2468 | 6.051736484727131327e+00
2469 | 6.192627773122789669e+00
2470 | 5.539143969238971010e+00
2471 | 6.649420366581745512e+00
2472 | 8.632254506666104277e+00
2473 | 5.173610923252525140e+00
2474 | 8.250228454728869565e+00
2475 | 6.008204975829366745e+00
2476 | 6.076069802383883278e+00
2477 | 6.807045733210005167e+00
2478 | 5.512990890433147939e+00
2479 | 4.536810978968812691e+00
2480 | 4.933522224132184775e+00
2481 | 5.931258525411394089e+00
2482 | 4.221070833777638143e+00
2483 | 5.327463326630169860e+00
2484 | 6.257954646484181538e+00
2485 | 4.244804674384386800e+00
2486 | 4.296063004242526517e+00
2487 | 5.345889882588564568e+00
2488 | 5.295931627012045340e+00
2489 | 4.308453748740308065e+00
2490 | 7.549388538838588403e+00
2491 | 6.423976323589341675e+00
2492 | 4.525036193147527364e+00
2493 | 5.046639744183768705e+00
2494 | 8.031278811977831111e+00
2495 | 5.183470586985147399e+00
2496 | 4.034721235787840143e+00
2497 | 5.753637849442869268e+00
2498 | 5.934576553805804622e+00
2499 | 4.187118678078816103e+00
2500 | 4.852172756347741256e+00
2501 | 


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