blib/lib/Statistics/ANOVA/Page.pm | |||
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Criterion | Covered | Total | % |
statement | 69 | 81 | 85.1 |
branch | 4 | 8 | 50.0 |
condition | 1 | 2 | 50.0 |
subroutine | 17 | 20 | 85.0 |
pod | 7 | 7 | 100.0 |
total | 98 | 118 | 83.0 |
line | stmt | bran | cond | sub | pod | time | code |
---|---|---|---|---|---|---|---|
1 | package Statistics::ANOVA::Page; | ||||||
2 | |||||||
3 | 2 | 2 | 33190 | use 5.006; | |||
2 | 5 | ||||||
2 | 80 | ||||||
4 | 2 | 2 | 9 | use strict; | |||
2 | 2 | ||||||
2 | 65 | ||||||
5 | 2 | 2 | 6 | use warnings FATAL => 'all'; | |||
2 | 8 | ||||||
2 | 77 | ||||||
6 | 2 | 2 | 12 | use base qw(Statistics::Data); | |||
2 | 1 | ||||||
2 | 1188 | ||||||
7 | 2 | 2 | 50727 | use List::AllUtils qw(sum0); | |||
2 | 4 | ||||||
2 | 111 | ||||||
8 | 2 | 2 | 1199 | use Math::Cephes qw(:dists); | |||
2 | 10950 | ||||||
2 | 711 | ||||||
9 | 2 | 2 | 1066 | use Statistics::Data::Rank; | |||
2 | 6080 | ||||||
2 | 55 | ||||||
10 | 2 | 2 | 1063 | use Statistics::Zed; | |||
2 | 4309 | ||||||
2 | 1418 | ||||||
11 | |||||||
12 | =head1 NAME | ||||||
13 | |||||||
14 | Statistics::ANOVA::Page - Nonparametric analysis of variance by ranks for trend across dependent variables (Page and sign tests). | ||||||
15 | |||||||
16 | =head1 VERSION | ||||||
17 | |||||||
18 | Version 0.01 | ||||||
19 | |||||||
20 | =cut | ||||||
21 | |||||||
22 | our $VERSION = '0.01'; | ||||||
23 | |||||||
24 | =head1 SYNOPSIS | ||||||
25 | |||||||
26 | use Statistics::ANOVA::Page; | ||||||
27 | my $page = Statistics::ANOVA::Page->new(); | ||||||
28 | $page->load({1 => [2, 4, 6], 2 => [3, 3, 12], 3 => [5, 7, 11, 16]}); # note ordinal datanames | ||||||
29 | my $l_value = $page->observed(); # or expected(), variance() | ||||||
30 | my ($z_value, $p_value) = $page->zprob_test(ccorr => 2, tails => 1); | ||||||
31 | # or without pre-loading: | ||||||
32 | $l_value = $page->observed(data => {1 => [2, 4, 6], 2 => [5, 3, 12]}); | ||||||
33 | # or for subset of loaded data: | ||||||
34 | $l_value = $page->observed(lab => [1, 3]); | ||||||
35 | |||||||
36 | =head1 DESCRIPTION | ||||||
37 | |||||||
38 | Calculates Page statistics for nonparametric analysis of variance across given orders of dependent variables. Ranks are computed exactly as for the L -value read off the normal distribution. Similarly to the relationship between the Kruskal-Wallis and L |
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39 | |||||||
40 | With only two groups, the test statistic is equivalent to that provided by a B |
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41 | |||||||
42 | Build tests include comparison of return values with published data, viz. from Hollander and Wolfe (1999, p. 286ff); passing these tests means the results agree. | ||||||
43 | |||||||
44 | =head1 SUBROUTINES/METHODS | ||||||
45 | |||||||
46 | =head2 new | ||||||
47 | |||||||
48 | $page = Statistics::ANOVA::Page->new(); | ||||||
49 | |||||||
50 | New object for accessing methods and storing results. This "isa" Statistics::Data object. | ||||||
51 | |||||||
52 | =head2 load, add, unload | ||||||
53 | |||||||
54 | $page->load(1 => [1, 4], 2 => [3, 7]); | ||||||
55 | |||||||
56 | The given data can now be used by any of the following methods. This is inherited from L |
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57 | |||||||
58 | =head2 observed | ||||||
59 | |||||||
60 | $val = $page->observed(); # data pre-loaded | ||||||
61 | $val = $page->observed(data => $hashref_of_arefs); | ||||||
62 | |||||||
63 | Returns the observed statistic I |
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64 | |||||||
65 | Optionally, if the data have not been pre-loaded, send as named argument B. | ||||||
66 | |||||||
67 | =cut | ||||||
68 | |||||||
69 | sub observed { | ||||||
70 | 1 | 1 | 1 | 802 | my ( $self, %args ) = @_; | ||
71 | 1 | 5 | return _calc_l_value( _get_data( $self, %args ) ); | ||||
72 | } | ||||||
73 | |||||||
74 | =head2 observed_r | ||||||
75 | |||||||
76 | $val = $page->observed_r(); # data pre-loaded | ||||||
77 | $val = $page->observed_r(data => $hashref_of_arefs); | ||||||
78 | |||||||
79 | This implements a "l2r" transformation: Hollander and Wolfe (1999) describe how Page's I |
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80 | |||||||
81 | =cut | ||||||
82 | |||||||
83 | sub observed_r { | ||||||
84 | 0 | 0 | 1 | 0 | my ( $self, %args ) = @_; | ||
85 | 0 | 0 | return _calc_l2r_value( _get_data( $self, %args ) ); | ||||
86 | } | ||||||
87 | |||||||
88 | =head2 expected | ||||||
89 | |||||||
90 | $val = $page->expected(); # data pre-loaded | ||||||
91 | $val = $page->expected(data => $hashref_of_arefs); | ||||||
92 | |||||||
93 | Returns the expected value of the I |
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94 | |||||||
95 | =cut | ||||||
96 | |||||||
97 | sub expected { | ||||||
98 | 1 | 1 | 1 | 7 | my ( $self, %args ) = @_; | ||
99 | 1 | 3 | return _calc_l_exp( _get_data( $self, %args ) ); | ||||
100 | } | ||||||
101 | |||||||
102 | =head2 variance | ||||||
103 | |||||||
104 | $val = $page->variance(); # data pre-loaded | ||||||
105 | $val = $page->variance(data => $hashref_of_arefs); | ||||||
106 | |||||||
107 | Return the variance expected to occur in the I |
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108 | |||||||
109 | =cut | ||||||
110 | |||||||
111 | sub variance { | ||||||
112 | 1 | 1 | 1 | 5 | my ( $self, %args ) = @_; | ||
113 | 1 | 2 | return _calc_l_var( _get_data( $self, %args ) ); | ||||
114 | } | ||||||
115 | |||||||
116 | =head2 zprob_test | ||||||
117 | |||||||
118 | $p_val = $page->zprob_test(); # data pre-loaded | ||||||
119 | $p_val = $page->zprob_test(data => $hashref_of_arefs); | ||||||
120 | ($z_val, $p_val) = $page->zprob_test(); # get z-score too | ||||||
121 | |||||||
122 | Calculates an expected I -value is read off the normal distribution. This is appropriate for "large" samples. Optional arguments are B |
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123 | |||||||
124 | =cut | ||||||
125 | |||||||
126 | sub zprob_test { | ||||||
127 | 1 | 1 | 1 | 5 | my ( $self, %args ) = @_; | ||
128 | 1 | 4 | my $href = _get_data( $self, %args ); | ||||
129 | 1 | 6 | my $zed = Statistics::Zed->new(); | ||||
130 | 1 | 24 | my ( $z_value, $p_value ) = $zed->z_value( | ||||
131 | observed => _calc_l_value($href), | ||||||
132 | expected => _calc_l_exp($href), | ||||||
133 | variance => _calc_l_var($href), | ||||||
134 | %args | ||||||
135 | ); | ||||||
136 | 1 | 50 | 173 | return wantarray ? ( $z_value, $p_value ) : $p_value; | |||
137 | } | ||||||
138 | |||||||
139 | =head2 chiprob_test | ||||||
140 | |||||||
141 | $p_val = $page->chiprob_test(); # data pre-loaded | ||||||
142 | $p_val = $page->chiprob_test(data => $hashref_of_arefs); | ||||||
143 | ($chi_val, $p_val) = $page->chiprob_test(); # get z-score too | ||||||
144 | |||||||
145 | Calculates a chi-square statistic based on the observed value of |
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146 | |||||||
147 | =cut | ||||||
148 | |||||||
149 | sub chiprob_test { | ||||||
150 | 1 | 1 | 1 | 1703 | my ( $self, %args ) = @_; | ||
151 | 1 | 4 | my $data_href = _get_data( $self, %args ); | ||||
152 | 1 | 3 | my $l = _calc_l_value($data_href); | ||||
153 | 1 | 2 | my $n_bt = scalar keys %{$data_href}; | ||||
1 | 2 | ||||||
154 | 1 | 4 | my $n_wt = __PACKAGE__->equal_n( data => $data_href ); | ||||
155 | 1 | 22 | my $num = ( ( 12 * $l ) - ( 3 * $n_wt * $n_bt ) * ( $n_bt + 1 )**2 )**2; | ||||
156 | 1 | 3 | my $chi = | ||||
157 | $num / ( ( $n_wt * $n_bt**2 ) * ( $n_bt**2 - 1 ) * ( $n_bt + 1 ) ); | ||||||
158 | 1 | 18 | my $p_value = chdtrc( 1, $chi ); # Math::Cephes fn | ||||
159 | 1 | 50 | 6 | $args{'tails'} ||= 2; | |||
160 | 1 | 50 | 4 | $p_value /= 2 if $args{'tails'} == 1; | |||
161 | 1 | 50 | 5 | return wantarray ? ( $chi, 1, ( $n_bt * $n_wt ), $p_value ) : $p_value; | |||
162 | } | ||||||
163 | |||||||
164 | =head2 chiprob_str | ||||||
165 | |||||||
166 | $str = $page->chiprob_str(data => HOA, correct_ties => 1); | ||||||
167 | |||||||
168 | Performs the same test as for L |
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169 | |||||||
170 | =cut | ||||||
171 | |||||||
172 | sub chiprob_str { | ||||||
173 | 0 | 0 | 1 | 0 | my ( $self, %args ) = ( shift, @_ ); | ||
174 | 0 | 0 | my ( $chi_value, $df, $count, $p_value ) = $self->chiprob_test(%args); | ||||
175 | 0 | 0 | return "chi^2($df, N = $count) = $chi_value, p = $p_value"; | ||||
176 | } | ||||||
177 | |||||||
178 | sub _calc_l_value { | ||||||
179 | 3 | 3 | 2 | my $data = shift; | |||
180 | 3 | 14 | my $ranks = Statistics::Data::Rank->sum_of_ranks_within( data => $data ); | ||||
181 | 3 | 696 | my $c = 0; | ||||
182 | 15 | 24 | return sum0( | ||||
183 | 22 | 21 | map { ++$c * $ranks->{$_} } | ||||
184 | 3 | 4 | sort { $a <=> $b } keys %{$ranks} | ||||
3 | 9 | ||||||
185 | ); | ||||||
186 | } | ||||||
187 | |||||||
188 | sub _calc_l2r_value { | ||||||
189 | 0 | 0 | 0 | my $data = shift; | |||
190 | 0 | 0 | my $l = _calc_l_value($data); | ||||
191 | 0 | 0 | my $n_bt = scalar keys %{$data}; | ||||
0 | 0 | ||||||
192 | 0 | 0 | my $n_wt = __PACKAGE__->equal_n( data => $data ); | ||||
193 | 0 | 0 | return ( ( ( 12 * $l ) / ( $n_wt * $n_bt * ( $n_bt**2 - 1 ) ) ) - | ||||
194 | ( ( 3 * ( $n_bt + 1 ) ) / ( $n_bt - 1 ) ) ); | ||||||
195 | } | ||||||
196 | |||||||
197 | sub _calc_l_exp { | ||||||
198 | 2 | 2 | 3 | my $data = shift; | |||
199 | 2 | 2 | my $n_bt = scalar keys %{$data}; | ||||
2 | 3 | ||||||
200 | 2 | 12 | my $n_wt = __PACKAGE__->equal_n( data => $data ); | ||||
201 | 2 | 73 | return ( $n_wt * $n_bt * ( $n_bt + 1 )**2 ) / 4; | ||||
202 | } | ||||||
203 | |||||||
204 | sub _calc_l_var { | ||||||
205 | 2 | 2 | 3 | my $data = shift; | |||
206 | 2 | 2 | my $n_bt = scalar keys %{$data}; | ||||
2 | 3 | ||||||
207 | 2 | 5 | my $n_wt = __PACKAGE__->equal_n( data => $data ); | ||||
208 | 2 | 44 | return ( $n_wt * $n_bt**2 * ( $n_bt + 1 ) * ( $n_bt**2 - 1 ) ) / 144; | ||||
209 | } | ||||||
210 | |||||||
211 | sub _get_data { | ||||||
212 | 5 | 5 | 5 | my ( $self, %args ) = @_; | |||
213 | 5 | 6 | my $hoa; | ||||
214 | 5 | 50 | 8 | if ( ref $args{'data'} ) { | |||
215 | 0 | 0 | $hoa = delete $args{'data'}; | ||||
216 | } | ||||||
217 | else { | ||||||
218 | 5 | 16 | $hoa = $self->get_hoa_by_lab(%args); | ||||
219 | } | ||||||
220 | 5 | 225 | return $hoa; | ||||
221 | } | ||||||
222 | |||||||
223 | =head1 REFERENCES | ||||||
224 | |||||||
225 | Hollander, M., & Wolfe, D. A. (1999). I |
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226 | |||||||
227 | Page, E. B. (1963). Ordered hypotheses for multiple treatments: A significance test for linear ranks. I |
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228 | |||||||
229 | =head1 DEPENDENCIES | ||||||
230 | |||||||
231 | L |
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232 | |||||||
233 | L |
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234 | |||||||
235 | L |
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236 | |||||||
237 | L |
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238 | |||||||
239 | L |
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240 | |||||||
241 | =head1 AUTHOR | ||||||
242 | |||||||
243 | Roderick Garton, C<< |
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244 | |||||||
245 | =head1 BUGS | ||||||
246 | |||||||
247 | Please report any bugs or feature requests to C |
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248 | the web interface at L |
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249 | automatically be notified of progress on your bug as I make changes. | ||||||
250 | |||||||
251 | =head1 SUPPORT | ||||||
252 | |||||||
253 | You can find documentation for this module with the perldoc command. | ||||||
254 | |||||||
255 | perldoc Statistics::ANOVA::Page | ||||||
256 | |||||||
257 | |||||||
258 | You can also look for information at: | ||||||
259 | |||||||
260 | =over 4 | ||||||
261 | |||||||
262 | =item * RT: CPAN's request tracker (report bugs here) | ||||||
263 | |||||||
264 | L |
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265 | |||||||
266 | =item * AnnoCPAN: Annotated CPAN documentation | ||||||
267 | |||||||
268 | L |
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269 | |||||||
270 | =item * CPAN Ratings | ||||||
271 | |||||||
272 | L |
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273 | |||||||
274 | =item * Search CPAN | ||||||
275 | |||||||
276 | L |
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277 | |||||||
278 | =back | ||||||
279 | |||||||
280 | |||||||
281 | =head1 ACKNOWLEDGEMENTS | ||||||
282 | |||||||
283 | |||||||
284 | =head1 LICENSE AND COPYRIGHT | ||||||
285 | |||||||
286 | Copyright 2015 Roderick Garton. | ||||||
287 | |||||||
288 | This program is free software; you can redistribute it and/or modify it | ||||||
289 | under the terms of either: the GNU General Public License as published | ||||||
290 | by the Free Software Foundation; or the Artistic License. | ||||||
291 | |||||||
292 | See L |
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293 | |||||||
294 | |||||||
295 | =cut | ||||||
296 | |||||||
297 | 1; # End of Statistics::ANOVA::Page |