1 // Copyright John Maddock 2006
2 // Copyright Paul A. Bristow 2007, 2008, 2010
3
4 // Use, modification and distribution are subject to the
5 // Boost Software License, Version 1.0.
6 // (See accompanying file LICENSE_1_0.txt
7 // or copy at http://www.boost.org/LICENSE_1_0.txt)
8
9 #ifdef _MSC_VER
10 # pragma warning(disable: 4512) // assignment operator could not be generated.
11 # pragma warning(disable: 4510) // default constructor could not be generated.
12 # pragma warning(disable: 4610) // can never be instantiated - user defined constructor required.
13 # pragma warning(disable: 4180) // qualifier has no effect (in Fusion).
14 #endif
15
16 #include <iostream>
17 using std::cout; using std::endl;
18 using std::left; using std::fixed; using std::right; using std::scientific;
19 #include <iomanip>
20 using std::setw;
21 using std::setprecision;
22
23 #include <boost/math/distributions/fisher_f.hpp>
24
f_test(double sd1,double sd2,double N1,double N2,double alpha)25 void f_test(
26 double sd1, // Sample 1 std deviation
27 double sd2, // Sample 2 std deviation
28 double N1, // Sample 1 size
29 double N2, // Sample 2 size
30 double alpha) // Significance level
31 {
32 //
33 // An F test applied to two sets of data.
34 // We are testing the null hypothesis that the
35 // standard deviation of the samples is equal, and
36 // that any variation is down to chance. We can
37 // also test the alternative hypothesis that any
38 // difference is not down to chance.
39 // See http://www.itl.nist.gov/div898/handbook/eda/section3/eda359.htm
40 //
41 // Avoid "using namespace boost::math;" because of potential name ambiguity.
42 using boost::math::fisher_f;
43
44 // Print header:
45 cout <<
46 "____________________________________\n"
47 "F test for equal standard deviations\n"
48 "____________________________________\n\n";
49 cout << setprecision(5);
50 cout << "Sample 1:\n";
51 cout << setw(55) << left << "Number of Observations" << "= " << N1 << "\n";
52 cout << setw(55) << left << "Sample Standard Deviation" << "= " << sd1 << "\n\n";
53 cout << "Sample 2:\n";
54 cout << setw(55) << left << "Number of Observations" << "= " << N2 << "\n";
55 cout << setw(55) << left << "Sample Standard Deviation" << "= " << sd2 << "\n\n";
56 //
57 // Now we can calculate and output some stats:
58 //
59 // F-statistic:
60 double F = (sd1 / sd2);
61 F *= F;
62 cout << setw(55) << left << "Test Statistic" << "= " << F << "\n\n";
63 //
64 // Finally define our distribution, and get the probability:
65 //
66 fisher_f dist(N1 - 1, N2 - 1);
67 double p = cdf(dist, F);
68 cout << setw(55) << left << "CDF of test statistic: " << "= "
69 << setprecision(3) << scientific << p << "\n";
70 double ucv = quantile(complement(dist, alpha));
71 double ucv2 = quantile(complement(dist, alpha / 2));
72 double lcv = quantile(dist, alpha);
73 double lcv2 = quantile(dist, alpha / 2);
74 cout << setw(55) << left << "Upper Critical Value at alpha: " << "= "
75 << setprecision(3) << scientific << ucv << "\n";
76 cout << setw(55) << left << "Upper Critical Value at alpha/2: " << "= "
77 << setprecision(3) << scientific << ucv2 << "\n";
78 cout << setw(55) << left << "Lower Critical Value at alpha: " << "= "
79 << setprecision(3) << scientific << lcv << "\n";
80 cout << setw(55) << left << "Lower Critical Value at alpha/2: " << "= "
81 << setprecision(3) << scientific << lcv2 << "\n\n";
82 //
83 // Finally print out results of null and alternative hypothesis:
84 //
85 cout << setw(55) << left <<
86 "Results for Alternative Hypothesis and alpha" << "= "
87 << setprecision(4) << fixed << alpha << "\n\n";
88 cout << "Alternative Hypothesis Conclusion\n";
89 cout << "Standard deviations are unequal (two sided test) ";
90 if((ucv2 < F) || (lcv2 > F))
91 cout << "NOT REJECTED\n";
92 else
93 cout << "REJECTED\n";
94 cout << "Standard deviation 1 is less than standard deviation 2 ";
95 if(lcv > F)
96 cout << "NOT REJECTED\n";
97 else
98 cout << "REJECTED\n";
99 cout << "Standard deviation 1 is greater than standard deviation 2 ";
100 if(ucv < F)
101 cout << "NOT REJECTED\n";
102 else
103 cout << "REJECTED\n";
104 cout << endl << endl;
105 }
106
main()107 int main()
108 {
109 //
110 // Run tests for ceramic strength data:
111 // see http://www.itl.nist.gov/div898/handbook/eda/section4/eda42a1.htm
112 // The data for this case study were collected by Said Jahanmir of the
113 // NIST Ceramics Division in 1996 in connection with a NIST/industry
114 // ceramics consortium for strength optimization of ceramic strength.
115 //
116 f_test(65.54909, 61.85425, 240, 240, 0.05);
117 //
118 // And again for the process change comparison:
119 // see http://www.itl.nist.gov/div898/handbook/prc/section3/prc32.htm
120 // A new procedure to assemble a device is introduced and tested for
121 // possible improvement in time of assembly. The question being addressed
122 // is whether the standard deviation of the new assembly process (sample 2) is
123 // better (i.e., smaller) than the standard deviation for the old assembly
124 // process (sample 1).
125 //
126 f_test(4.9082, 2.5874, 11, 9, 0.05);
127 return 0;
128 }
129
130 /*
131
132 Output:
133
134 f_test.cpp
135 F-test_example1.vcxproj -> J:\Cpp\MathToolkit\test\Math_test\Debug\F_test_example1.exe
136 ____________________________________
137 F test for equal standard deviations
138 ____________________________________
139
140 Sample 1:
141 Number of Observations = 240
142 Sample Standard Deviation = 65.549
143
144 Sample 2:
145 Number of Observations = 240
146 Sample Standard Deviation = 61.854
147
148 Test Statistic = 1.123
149
150 CDF of test statistic: = 8.148e-001
151 Upper Critical Value at alpha: = 1.238e+000
152 Upper Critical Value at alpha/2: = 1.289e+000
153 Lower Critical Value at alpha: = 8.080e-001
154 Lower Critical Value at alpha/2: = 7.756e-001
155
156 Results for Alternative Hypothesis and alpha = 0.0500
157
158 Alternative Hypothesis Conclusion
159 Standard deviations are unequal (two sided test) REJECTED
160 Standard deviation 1 is less than standard deviation 2 REJECTED
161 Standard deviation 1 is greater than standard deviation 2 REJECTED
162
163
164 ____________________________________
165 F test for equal standard deviations
166 ____________________________________
167
168 Sample 1:
169 Number of Observations = 11.00000
170 Sample Standard Deviation = 4.90820
171
172 Sample 2:
173 Number of Observations = 9.00000
174 Sample Standard Deviation = 2.58740
175
176 Test Statistic = 3.59847
177
178 CDF of test statistic: = 9.589e-001
179 Upper Critical Value at alpha: = 3.347e+000
180 Upper Critical Value at alpha/2: = 4.295e+000
181 Lower Critical Value at alpha: = 3.256e-001
182 Lower Critical Value at alpha/2: = 2.594e-001
183
184 Results for Alternative Hypothesis and alpha = 0.0500
185
186 Alternative Hypothesis Conclusion
187 Standard deviations are unequal (two sided test) REJECTED
188 Standard deviation 1 is less than standard deviation 2 REJECTED
189 Standard deviation 1 is greater than standard deviation 2 NOT REJECTED
190
191
192 ____________________________________
193 F test for equal standard deviations
194 ____________________________________
195
196 Sample 1:
197 Number of Observations = 240
198 Sample Standard Deviation = 65.549
199
200 Sample 2:
201 Number of Observations = 240
202 Sample Standard Deviation = 61.854
203
204 Test Statistic = 1.123
205
206 CDF of test statistic: = 8.148e-001
207 Upper Critical Value at alpha: = 1.238e+000
208 Upper Critical Value at alpha/2: = 1.289e+000
209 Lower Critical Value at alpha: = 8.080e-001
210 Lower Critical Value at alpha/2: = 7.756e-001
211
212 Results for Alternative Hypothesis and alpha = 0.0500
213
214 Alternative Hypothesis Conclusion
215 Standard deviations are unequal (two sided test) REJECTED
216 Standard deviation 1 is less than standard deviation 2 REJECTED
217 Standard deviation 1 is greater than standard deviation 2 REJECTED
218
219
220 ____________________________________
221 F test for equal standard deviations
222 ____________________________________
223
224 Sample 1:
225 Number of Observations = 11.00000
226 Sample Standard Deviation = 4.90820
227
228 Sample 2:
229 Number of Observations = 9.00000
230 Sample Standard Deviation = 2.58740
231
232 Test Statistic = 3.59847
233
234 CDF of test statistic: = 9.589e-001
235 Upper Critical Value at alpha: = 3.347e+000
236 Upper Critical Value at alpha/2: = 4.295e+000
237 Lower Critical Value at alpha: = 3.256e-001
238 Lower Critical Value at alpha/2: = 2.594e-001
239
240 Results for Alternative Hypothesis and alpha = 0.0500
241
242 Alternative Hypothesis Conclusion
243 Standard deviations are unequal (two sided test) REJECTED
244 Standard deviation 1 is less than standard deviation 2 REJECTED
245 Standard deviation 1 is greater than standard deviation 2 NOT REJECTED
246
247
248
249 */
250
251