blib/lib/Statistics/ANOVA/EffectSize.pm | |||
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Criterion | Covered | Total | % |
statement | 50 | 55 | 90.9 |
branch | 6 | 14 | 42.8 |
condition | n/a | ||
subroutine | 22 | 24 | 91.6 |
pod | 7 | 7 | 100.0 |
total | 85 | 100 | 85.0 |
line | stmt | bran | cond | sub | pod | time | code |
---|---|---|---|---|---|---|---|
1 | package Statistics::ANOVA::EffectSize; | ||||||
2 | |||||||
3 | 5 | 5 | 137748 | use 5.006; | |||
5 | 28 | ||||||
4 | 5 | 5 | 21 | use strict; | |||
5 | 8 | ||||||
5 | 99 | ||||||
5 | 5 | 5 | 22 | use warnings; | |||
5 | 6 | ||||||
5 | 128 | ||||||
6 | 5 | 5 | 22 | use base qw(Statistics::Data); | |||
5 | 8 | ||||||
5 | 1197 | ||||||
7 | 5 | 5 | 47904 | use Carp qw(croak); | |||
5 | 10 | ||||||
5 | 233 | ||||||
8 | 5 | 5 | 26 | use List::AllUtils qw(any); | |||
5 | 10 | ||||||
5 | 4573 | ||||||
9 | $Statistics::ANOVA::EffectSize::VERSION = '0.02'; | ||||||
10 | |||||||
11 | =head1 NAME | ||||||
12 | |||||||
13 | Statistics::ANOVA::EffectSize - Calculate effect-sizes from ANOVAs incl. eta-squared and omega-squared | ||||||
14 | |||||||
15 | =head1 VERSION | ||||||
16 | |||||||
17 | This is documentation for B |
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18 | |||||||
19 | =head1 SYNOPSIS | ||||||
20 | |||||||
21 | use Statistics::ANOVA::EffectSize; | ||||||
22 | my $es = Statistics::ANOVA::EffectSize->new(); | ||||||
23 | $es->load(HOA); # a hash of arefs, or other, as in Statistics::Data | ||||||
24 | my $etasq = $es->eta_squared(independent => BOOL, partial => 1); # or give data => HOA here | ||||||
25 | my $omgsq = $es->omega_squared(independent => BOOL); | ||||||
26 | # or calculate not from loaded data but directly: | ||||||
27 | |||||||
28 | =head2 DESCRIPTION | ||||||
29 | |||||||
30 | Calculates effect-sizes from ANOVAs. | ||||||
31 | |||||||
32 | For I |
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33 | |||||||
34 | For I |
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35 | |||||||
36 | =head1 SUBROUTINES/METHODS | ||||||
37 | |||||||
38 | Rather than working from raw data, these methods are given the statistics, like sums-of-squares, needed to calculate the effect-sizes. | ||||||
39 | |||||||
40 | =head2 eta_sq_partial_by_ss, r_squared | ||||||
41 | |||||||
42 | $es->eta_sq_partial_by_ss(ss_b => NUM, ss_w => NUM); | ||||||
43 | |||||||
44 | Returns partial I |
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45 | |||||||
46 | =for html η2P = SSb / ( SSb + SSw ) |
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47 | |||||||
48 | This is also what is commonly designated as I |
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49 | |||||||
50 | =cut | ||||||
51 | |||||||
52 | sub eta_sq_partial_by_ss { | ||||||
53 | 4 | 4 | 1 | 119 | my ( $self, %args ) = @_; | ||
54 | croak | ||||||
55 | 'Undefined values needed to calculate partial eta-squared by sums-of-squares' | ||||||
56 | 4 | 50 | 8 | 22 | if any { !defined $args{$_} } (qw/ss_b ss_w/); | ||
8 | 20 | ||||||
57 | 4 | 24 | return $args{'ss_b'} / ( $args{'ss_b'} + $args{'ss_w'} ); | ||||
58 | } | ||||||
59 | *r_squared = \&eta_sq_partial_by_ss; | ||||||
60 | |||||||
61 | =head2 r_squared_adj | ||||||
62 | |||||||
63 | $es->r_squared_adj(ss_b => NUM, ss_w => NUM, df_b => NUM, df_w => NUM); | ||||||
64 | |||||||
65 | Returns adjusted I |
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66 | |||||||
67 | =cut | ||||||
68 | |||||||
69 | sub r_squared_adj { | ||||||
70 | 0 | 0 | 1 | 0 | my ( $self, %args ) = @_; | ||
71 | 0 | 0 | my $r_squared = $self->r_squared(%args); # will check for ss_b and ss_w | ||||
72 | croak 'Could not obtain values to calculate adjusted r-squared' | ||||||
73 | 0 | 0 | 0 | 0 | if any { !defined $args{$_} } (qw/df_b df_w/); | ||
0 | 0 | ||||||
74 | return 1 - | ||||||
75 | 0 | 0 | ( ( $args{'df_b'} + $args{'df_w'} ) / $args{'df_w'} ) * | ||||
76 | ( 1 - $r_squared ); | ||||||
77 | } | ||||||
78 | |||||||
79 | =head2 eta_sq_partial_by_f | ||||||
80 | |||||||
81 | $es->eta_sq_partial_by_f(f_value => NUM , df_b => NUM, df_w => NUM); | ||||||
82 | |||||||
83 | Returns partial I |
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84 | |||||||
85 | =for html η2P = ( dfb . F ) / ( dfb . F + dfw ) |
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86 | |||||||
87 | =cut | ||||||
88 | |||||||
89 | sub eta_sq_partial_by_f { | ||||||
90 | 2 | 2 | 1 | 660 | my ( $self, %args ) = @_; | ||
91 | croak 'Could not obtain values to calculate partial eta-squared by F-value' | ||||||
92 | 2 | 50 | 6 | 11 | if any { !defined $args{$_} } (qw/df_b df_w f_value/); | ||
6 | 12 | ||||||
93 | return ( $args{'df_b'} * $args{'f_value'} ) / | ||||||
94 | 2 | 15 | ( $args{'df_b'} * $args{'f_value'} + $args{'df_w'} ); | ||||
95 | } | ||||||
96 | |||||||
97 | =head2 omega_sq_partial_by_ss | ||||||
98 | |||||||
99 | $es->omega_sq_partial_by_ss(df_b => NUM, df_w => NUM, ss_b => NUM, ss_w => NUM, count => NUM); | ||||||
100 | |||||||
101 | Returns partial I |
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102 | |||||||
103 | =for html ω2P = ( ssb — (dfb . SSw / dfw) ) / ( SSb + (N – dfb ) SSw / dfw ) |
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104 | |||||||
105 | (as in, e.g., Olejnik & Algina, 2003, p. 435). | ||||||
106 | |||||||
107 | =cut | ||||||
108 | |||||||
109 | sub omega_sq_partial_by_ss { | ||||||
110 | 2 | 2 | 1 | 304 | my ( $self, %args ) = @_; | ||
111 | croak | ||||||
112 | 'Undefined values for calculating partial omega-squared by sums-of-squares' | ||||||
113 | 2 | 50 | 10 | 11 | if any { !defined $args{$_} } (qw/ss_b ss_w df_b df_w count/); | ||
10 | 17 | ||||||
114 | 2 | 7 | return _omega_numerator_ss( \%args ) / _omega_denominator_ss( \%args ); | ||||
115 | } | ||||||
116 | |||||||
117 | =head2 omega_sq_partial_by_ms | ||||||
118 | |||||||
119 | $es->omega_sq_partial_by_ms(df_b => NUM, ms_b => NUM, ms_w => NUM, count => NUM); | ||||||
120 | |||||||
121 | Returns partial I |
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122 | |||||||
123 | =for html ω2P = dfb ( MSb – MSw ) / ( dfb . MSb + ( N – dfb ) MSw ) |
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124 | |||||||
125 | (as in, e.g., Lakens, 2013, Eq. 15). | ||||||
126 | |||||||
127 | =cut | ||||||
128 | |||||||
129 | sub omega_sq_partial_by_ms { | ||||||
130 | 1 | 1 | 1 | 228 | my ( $self, %args ) = @_; | ||
131 | croak | ||||||
132 | 'Could not obtain values to calculate partial omega-squared by mean sums-of-squares' | ||||||
133 | 1 | 50 | 4 | 6 | if any { !defined $_ } values %args; | ||
4 | 7 | ||||||
134 | 1 | 3 | return _omega_numerator_ms( \%args ) / _omega_denominator_ms( \%args ); | ||||
135 | } | ||||||
136 | |||||||
137 | =head2 omega_sq_partial_by_f | ||||||
138 | |||||||
139 | $es->omega_sq_partial_by_ms(f_value => NUM, df_b => NUM, df_w => NUM); | ||||||
140 | |||||||
141 | Returns partial I |
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142 | |||||||
143 | =for html ω2P(est.) = ( F - 1 ) / ( F + ( dfw + 1 ) / dfb ) |
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144 | |||||||
145 | This is an estimate provided by L |
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146 | |||||||
147 | =cut | ||||||
148 | |||||||
149 | sub omega_sq_partial_by_f { | ||||||
150 | 2 | 2 | 1 | 257 | my ( $self, %args ) = @_; | ||
151 | croak | ||||||
152 | 'Could not obtain values to calculate partial omega-squared by mean sums-of-squares' | ||||||
153 | 2 | 50 | 6 | 12 | if any { !defined $_ } values %args; | ||
6 | 11 | ||||||
154 | return ( $args{'f_value'} - 1 ) / | ||||||
155 | 2 | 13 | ( $args{'f_value'} + ( $args{'df_w'} + 1 ) / $args{'df_b'} ); | ||||
156 | } | ||||||
157 | |||||||
158 | =head2 eta_to_omega | ||||||
159 | |||||||
160 | $es->eta_to_omega(df_b => NUM, df_w => NUM, eta_sq => NUM); | ||||||
161 | |||||||
162 | Returns I |
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163 | |||||||
164 | =for html ω2P = ( η2P(dfb + dfw) – dfb ) / ( η2P(dfb + dfw) – dfb ) + ( (dfw + 1)(1 – η2P) ) ) |
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165 | |||||||
166 | =cut | ||||||
167 | |||||||
168 | sub eta_to_omega { | ||||||
169 | 2 | 2 | 1 | 490 | my ( $self, %args ) = @_; | ||
170 | croak | ||||||
171 | 'Could not obtain values to calculate partial omega-squared by mean sums-of-squares' | ||||||
172 | 2 | 50 | 6 | 13 | if any { !defined $_ } values %args; | ||
6 | 11 | ||||||
173 | my $num = | ||||||
174 | 2 | 11 | $args{'eta_sq'} * ( $args{'df_b'} + $args{'df_w'} ) - $args{'df_b'}; | ||||
175 | return $num / | ||||||
176 | 2 | 11 | ( $num + ( ( $args{'df_w'} + 1 ) * ( 1 - $args{'eta_sq'} ) ) ); | ||||
177 | } | ||||||
178 | |||||||
179 | sub _omega_numerator_ss { | ||||||
180 | 3 | 3 | 263 | my $args = shift; | |||
181 | return $args->{'ss_b'} - | ||||||
182 | 3 | 11 | $args->{'df_b'} * $args->{'ss_w'} / $args->{'df_w'}; | ||||
183 | } | ||||||
184 | |||||||
185 | sub _omega_numerator_ms { | ||||||
186 | 2 | 2 | 10 | my $args = shift; | |||
187 | 2 | 6 | return $args->{'df_b'} * ( $args->{'ms_b'} - $args->{'ms_w'} ); | ||||
188 | } | ||||||
189 | |||||||
190 | sub _omega_denominator_ss { | ||||||
191 | 3 | 3 | 237 | my $args = shift; | |||
192 | |||||||
193 | #return ( $args->{'ss_b'} + $args->{'ss_w'} ) + $args->{'ss_w'} / $args->{'df_w'}; | ||||||
194 | return $args->{'ss_b'} + | ||||||
195 | ( $args->{'count'} - $args->{'df_b'} ) * | ||||||
196 | $args->{'ss_w'} / | ||||||
197 | 3 | 12 | $args->{'df_w'}; | ||||
198 | } | ||||||
199 | |||||||
200 | sub _omega_denominator_ms { | ||||||
201 | 2 | 2 | 8 | my $args = shift; | |||
202 | return $args->{'df_b'} * $args->{'ms_b'} + | ||||||
203 | 2 | 7 | ( $args->{'count'} - $args->{'df_b'} ) * $args->{'ms_w'}; | ||||
204 | } | ||||||
205 | |||||||
206 | =head1 DEPENDENCIES | ||||||
207 | |||||||
208 | L |
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209 | |||||||
210 | L |
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211 | |||||||
212 | =head1 DIAGNOSTICS | ||||||
213 | |||||||
214 | =over 4 | ||||||
215 | |||||||
216 | =item Could not obtain values to calculate ... | ||||||
217 | |||||||
218 | C |
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219 | |||||||
220 | =back | ||||||
221 | |||||||
222 | =head1 REFERENCES | ||||||
223 | |||||||
224 | Cohen, J. (1969). I |
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225 | |||||||
226 | Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4, 863. doi:L<10.3389/fpsyg.2013.00863|http://dx.doi.org/10.3389/fpsyg.2013.00863> | ||||||
227 | |||||||
228 | Lakens, D. (2015). Why you should use omega-squared instead of eta-squared, I |
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229 | |||||||
230 | Maxwell, S. E., & Delaney, H. D. (1990). I |
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231 | |||||||
232 | Olejnik, S., & Algina, J. (2003). Generalized eta and omega squared statistics: Measures of effect size for some common research designs. I |
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233 | |||||||
234 | =head1 AUTHOR | ||||||
235 | |||||||
236 | Roderick Garton, C<< |
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237 | |||||||
238 | =head1 BUGS | ||||||
239 | |||||||
240 | Please report any bugs or feature requests to C |
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241 | automatically be notified of progress on your bug as I make changes. | ||||||
242 | |||||||
243 | =head1 SUPPORT | ||||||
244 | |||||||
245 | You can find documentation for this module with the perldoc command. | ||||||
246 | |||||||
247 | perldoc Statistics::ANOVA::EffectSize | ||||||
248 | |||||||
249 | |||||||
250 | You can also look for information at: | ||||||
251 | |||||||
252 | =over 4 | ||||||
253 | |||||||
254 | =item * RT: CPAN's request tracker (report bugs here) | ||||||
255 | |||||||
256 | L |
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257 | |||||||
258 | =item * AnnoCPAN: Annotated CPAN documentation | ||||||
259 | |||||||
260 | L |
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261 | |||||||
262 | =item * CPAN Ratings | ||||||
263 | |||||||
264 | L |
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265 | |||||||
266 | =item * Search CPAN | ||||||
267 | |||||||
268 | L |
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269 | |||||||
270 | =back | ||||||
271 | |||||||
272 | =head1 LICENSE AND COPYRIGHT | ||||||
273 | |||||||
274 | Copyright 2015-2018 Roderick Garton. | ||||||
275 | |||||||
276 | This program is free software; you can redistribute it and/or modify it | ||||||
277 | under the terms of either: the GNU General Public License as published | ||||||
278 | by the Free Software Foundation; or the Artistic License. | ||||||
279 | |||||||
280 | See L |
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281 | |||||||
282 | =cut | ||||||
283 | |||||||
284 | 1; # End of Statistics::ANOVA::EffectSize |