﻿ STD Calculator

Signal Detection Theory

Background:

Most of the time perception involves both bottom-up (data driven) and top-down (conceptually driven) processing. The thresholds in classical psychophysics are described as being determined only by the intensity of the stimulus (bottom-up) and ignore the influence of top-down processing. However, it is well established that our expectations and knowledge (top-down processes) influence our perceptions -- you are more likely to think that your phone is vibrating when you are expecting an important call than when you are not expecting a call.

Signal Detection Theory (SDT) attempts to address this shortcoming of classical psychophysics. Rather than having a single value, the threshold, SDT provides two parameters -- d' (dee prime) and β d' is similar to idea of a threshold. A person who has a low threshold (and therefore is sensitive to the stimulus) will have a largish d' while a person who has a high threshold (and therefore is insensitive to the stimulus) will have a d' that is close to 0. That is, d' is a measure of how sensitive the person is and is usually driven by bottom-up concerns.

β is a measure of how willing a person is to say that the stimulus was present. If you are expecting an important phone call, you are more willing to say that your phone is vibrating. That is, β measures top-down processing. A conservative person requires much evidence that the signal is present before they are willing to say that the stimulus is present. Such a person will have a β that is larger than 1. A liberal person requires little evidence that the signal is present before they are willing to say that the stimulus is present. Such a person will have a β greater than or equal to 0 but less than 1. When β equals 1, the person is unbiased -- neither conservative nor liberal.

In a signal detection study, the observer (what SDT calls a participant) is sometimes presented with a signal (say a beep) that is embedded in noise (say static that you might hear if you tuned a radio to a frequency on which no station is currently broadcasting.) The loudness of the signal and the noise are adjusted so that it difficult to hear the signal over the noise. On some trials, only the noise is presented. For each trial, the observer must indicate whether or not they think the signal is present. If the observer correctly states that the signal was present, a "hit" is scored. If the observer incorrectly states that the signal was present, a "false alarm" is scored. If the observer correctly states that the signal was not present, a "correct rejection" is scored. If the observer incorrectly states that the signal was not present, a "miss" is scored.

 Signal Present No Yes Observer's Response Signal Not Present Correct Rejection Miss Signal Present False Alarm Hit

After performing hundreds of trials, the researcher calculates the probability that the observer scored a hit and the probability that the observer scored a false alarm. From those two probabilities, the researcher can calculate d' and β.

The Activity:

In this activity, you will learn how to calculate d' and β from the probability of a hit and false alarm. Enter the probabilities (between 0 and 1) below and click on the "Next Step" button. A person who is a very sensitive observer should have a large p(hit) (close to, but not equal to 1 -- probabilities of 1 and 0 lead to problems and in practice should not occur) and a small p(false alarm) (close to, but not equal to 0). You can try p(hit) = 0.9 and p(false alarm) = 0.2 as a starting point.

1.    Enter p(hit) and p(fa)

z Above z Ordinate
z Above z Ordinate
-3.000.99870.0044
-2.990.99860.0046
-2.980.99860.0047
-2.970.99850.0048
-2.960.99850.0050
-2.950.99840.0051
-2.940.99840.0053
-2.930.99830.0055
-2.920.99820.0056
-2.910.99820.0058
-2.900.99810.0060
-2.890.99810.0061
-2.880.99800.0063
-2.870.99790.0065
-2.860.99790.0067
-2.850.99780.0069
-2.840.99770.0071
-2.830.99770.0073
-2.820.99760.0075
-2.810.99750.0077
-2.800.99740.0079
-2.790.99740.0081
-2.780.99730.0084
-2.770.99720.0086
-2.760.99710.0088
-2.750.99700.0091
-2.740.99690.0093
-2.730.99680.0096
-2.720.99670.0099
-2.710.99660.0101
-2.700.99650.0104
-2.690.99640.0107
-2.680.99630.0110
-2.670.99620.0113
-2.660.99610.0116
-2.650.99600.0119
-2.640.99590.0122
-2.630.99570.0126
-2.620.99560.0129
-2.610.99550.0132
-2.600.99530.0136
-2.590.99520.0139
-2.580.99510.0143
-2.570.99490.0147
-2.560.99480.0151
-2.550.99460.0154
-2.540.99450.0158
-2.530.99430.0163
-2.520.99410.0167
-2.510.99400.0171
-2.500.99380.0175
-2.490.99360.0180
-2.480.99340.0184
-2.470.99320.0189
-2.460.99310.0194
-2.450.99290.0198
-2.440.99270.0203
-2.430.99240.0208
-2.420.99220.0213
-2.410.99200.0219
-2.400.99180.0224
-2.390.99160.0229
-2.380.99130.0235
-2.370.99110.0241
-2.360.99090.0246
-2.350.99060.0252
-2.340.99040.0258
-2.330.99010.0264
-2.320.98980.0270
-2.310.98960.0277
-2.300.98930.0283
-2.290.98900.0290
-2.280.98870.0297
-2.270.98840.0303
-2.260.98810.0310
-2.250.98780.0317
-2.240.98750.0325
-2.230.98710.0332
-2.220.98680.0339
-2.210.98640.0347
-2.200.98610.0355
-2.190.98570.0363
-2.180.98540.0371
-2.170.98500.0379
-2.160.98460.0387
-2.150.98420.0396
-2.140.98380.0404
-2.130.98340.0413
-2.120.98300.0422
-2.110.98260.0431
-2.100.98210.0440
-2.090.98170.0449
-2.080.98120.0459
-2.070.98080.0468
-2.060.98030.0478
-2.050.97980.0488
-2.040.97930.0498
-2.030.97880.0508
-2.020.97830.0519
-2.010.97780.0529
-2.000.97720.0540
-1.990.97670.0551
-1.980.97610.0562
-1.970.97560.0573
-1.960.97500.0584
-1.950.97440.0596
-1.940.97380.0608
-1.930.97320.0620
-1.920.97260.0632
-1.910.97190.0644
-1.900.97130.0656
-1.890.97060.0669
-1.880.96990.0681
-1.870.96930.0694
-1.860.96860.0707
-1.850.96780.0721
-1.840.96710.0734
-1.830.96640.0748
-1.820.96560.0761
-1.810.96480.0775
-1.800.96410.0790
-1.790.96330.0804
-1.780.96250.0818
-1.770.96160.0833
-1.760.96080.0848
-1.750.95990.0863
-1.740.95910.0878
-1.730.95820.0893
-1.720.95730.0909
-1.710.95640.0925
-1.700.95540.0940
-1.690.95450.0957
-1.680.95350.0973
-1.670.95250.0989
-1.660.95150.1006
-1.650.95050.1023
-1.640.94950.1040
-1.630.94840.1057
-1.620.94740.1074
-1.610.94630.1092
-1.600.94520.1109
-1.590.94410.1127
-1.580.94290.1145
-1.570.94180.1163
-1.560.94060.1182
-1.550.93940.1200
-1.540.93820.1219
-1.530.93700.1238
-1.520.93570.1257
-1.510.93450.1276
-1.500.93320.1295
-1.490.93190.1315
-1.480.93060.1334
-1.470.92920.1354
-1.460.92780.1374
-1.450.92650.1394
-1.440.92510.1415
-1.430.92360.1435
-1.420.92220.1456
-1.410.92070.1476
-1.400.91920.1497
-1.390.91770.1518
-1.380.91620.1539
-1.370.91460.1561
-1.360.91310.1582
-1.350.91150.1604
-1.340.90990.1626
-1.330.90820.1647
-1.320.90660.1669
-1.310.90490.1691
-1.300.90320.1714
-1.290.90150.1736
-1.280.89970.1758
-1.270.89790.1781
-1.260.89610.1804
-1.250.89430.1826
-1.240.89250.1849
-1.230.89060.1872
-1.220.88870.1895
-1.210.88680.1919
-1.200.88490.1942
-1.190.88300.1965
-1.180.88100.1989
-1.170.87900.2012
-1.160.87700.2036
-1.150.87490.2059
-1.140.87280.2083
-1.130.87070.2107
-1.120.86860.2131
-1.110.86650.2155
-1.100.86430.2179
-1.090.86210.2203
-1.080.85990.2227
-1.070.85770.2251
-1.060.85540.2275
-1.050.85310.2299
-1.040.85080.2323
-1.030.84850.2347
-1.020.84610.2371
-1.010.84370.2396
-1.000.84130.2420
-0.990.83890.2444
-0.980.83640.2468
-0.970.83400.2492
-0.960.83140.2516
-0.950.82890.2541
-0.940.82640.2565
-0.930.82380.2589
-0.920.82120.2613
-0.910.81860.2637
-0.900.81590.2661
-0.890.81320.2685
-0.880.81050.2709
-0.870.80780.2732
-0.860.80510.2756
-0.850.80230.2780
-0.840.79950.2803
-0.830.79670.2827
-0.820.79390.2850
-0.810.79100.2874
-0.800.78810.2897
-0.790.78520.2920
-0.780.78230.2943
-0.770.77930.2966
-0.760.77630.2989
-0.750.77330.3011
-0.740.77030.3034
-0.730.76730.3056
-0.720.76420.3079
-0.710.76110.3101
-0.700.75800.3123
-0.690.75490.3144
-0.680.75170.3166
-0.670.74850.3187
-0.660.74530.3209
-0.650.74210.3230
-0.640.73890.3251
-0.630.73560.3271
-0.620.73230.3292
-0.610.72900.3312
-0.600.72570.3332
-0.590.72240.3352
-0.580.71900.3372
-0.570.71560.3391
-0.560.71220.3410
-0.550.70880.3429
-0.540.70540.3448
-0.530.70190.3467
-0.520.69840.3485
-0.510.69490.3503
-0.500.69140.3521
-0.490.68790.3538
-0.480.68440.3555
-0.470.68080.3572
-0.460.67720.3589
-0.450.67360.3605
-0.440.67000.3621
-0.430.66640.3637
-0.420.66270.3653
-0.410.65910.3668
-0.400.65540.3683
-0.390.65170.3697
-0.380.64800.3712
-0.370.64430.3725
-0.360.64050.3739
-0.350.63680.3752
-0.340.63300.3765
-0.330.62930.3778
-0.320.62550.3790
-0.310.62170.3802
-0.300.61790.3814
-0.290.61410.3825
-0.280.61020.3836
-0.270.60640.3847
-0.260.60250.3857
-0.250.59870.3867
-0.240.59480.3876
-0.230.59090.3885
-0.220.58700.3894
-0.210.58310.3902
-0.200.57920.3910
-0.190.57530.3918
-0.180.57140.3925
-0.170.56750.3932
-0.160.56350.3939
-0.150.55960.3945
-0.140.55560.3951
-0.130.55170.3956
-0.120.54770.3961
-0.110.54380.3965
-0.100.53980.3970
-0.090.53580.3973
-0.080.53180.3977
-0.070.52790.3980
-0.060.52390.3982
-0.050.51990.3984
-0.040.51590.3986
-0.030.51190.3988
-0.020.50790.3989
-0.010.50390.3989
0.000.50000.3989
0.010.49600.3989
0.020.49200.3989
0.030.48800.3988
0.040.48400.3986
0.050.48000.3984
0.060.47600.3982
0.070.47210.3980
0.080.46810.3977
0.090.46410.3973
0.100.46010.3970
0.110.45620.3965
0.120.45220.3961
0.130.44820.3956
0.140.44430.3951
0.150.44030.3945
0.160.43640.3939
0.170.43250.3932
0.180.42850.3925
0.190.42460.3918
0.200.42070.3910
0.210.41680.3902
0.220.41290.3894
0.230.40900.3885
0.240.40510.3876
0.250.40130.3867
0.260.39740.3857
0.270.39350.3847
0.280.38970.3836
0.290.38590.3825
0.300.38210.3814
0.310.37820.3802
0.320.37440.3790
0.330.37070.3778
0.340.36690.3765
0.350.36310.3752
0.360.35940.3739
0.370.35570.3725
0.380.35190.3712
0.390.34820.3697
0.400.34450.3683
0.410.34090.3668
0.420.33720.3653
0.430.33360.3637
0.440.32990.3621
0.450.32630.3605
0.460.32270.3589
0.470.31910.3572
0.480.31560.3555
0.490.31200.3538
0.500.30850.3521
0.510.30500.3503
0.520.30150.3485
0.530.29800.3467
0.540.29460.3448
0.550.29110.3429
0.560.28770.3410
0.570.28430.3391
0.580.28090.3372
0.590.27760.3352
0.600.27420.3332
0.610.27090.3312
0.620.26760.3292
0.630.26430.3271
0.640.26110.3251
0.650.25780.3230
0.660.25460.3209
0.670.25140.3187
0.680.24820.3166
0.690.24510.3144
0.700.24190.3123
0.710.23880.3101
0.720.23570.3079
0.730.23270.3056
0.740.22960.3034
0.750.22660.3011
0.760.22360.2989
0.770.22060.2966
0.780.21770.2943
0.790.21470.2920
0.800.21180.2897
0.810.20890.2874
0.820.20610.2850
0.830.20320.2827
0.840.20040.2803
0.850.19760.2780
0.860.19490.2756
0.870.19210.2732
0.880.18940.2709
0.890.18670.2685
0.900.18400.2661
0.910.18140.2637
0.920.17880.2613
0.930.17620.2589
0.940.17360.2565
0.950.17100.2541
0.960.16850.2516
0.970.16600.2492
0.980.16350.2468
0.990.16110.2444
1.000.15860.2420
1.010.15620.2396
1.020.15380.2371
1.030.15150.2347
1.040.14910.2323
1.050.14680.2299
1.060.14450.2275
1.070.14230.2251
1.080.14000.2227
1.090.13780.2203
1.100.13560.2179
1.110.13350.2155
1.120.13130.2131
1.130.12920.2107
1.140.12710.2083
1.150.12510.2059
1.160.12300.2036
1.170.12100.2012
1.180.11900.1989
1.190.11700.1965
1.200.11510.1942
1.210.11310.1919
1.220.11120.1895
1.230.10930.1872
1.240.10750.1849
1.250.10560.1826
1.260.10380.1804
1.270.10200.1781
1.280.10030.1758
1.290.09850.1736
1.300.09680.1714
1.310.09510.1691
1.320.09340.1669
1.330.09170.1647
1.340.09010.1626
1.350.08850.1604
1.360.08690.1582
1.370.08530.1561
1.380.08380.1539
1.390.08220.1518
1.400.08070.1497
1.410.07930.1476
1.420.07780.1456
1.430.07630.1435
1.440.07490.1415
1.450.07350.1394
1.460.07210.1374
1.470.07080.1354
1.480.06940.1334
1.490.06810.1315
1.500.06680.1295
1.510.06550.1276
1.520.06420.1257
1.530.06300.1238
1.540.06180.1219
1.550.06060.1200
1.560.05940.1182
1.570.05820.1163
1.580.05700.1145
1.590.05590.1127
1.600.05480.1109
1.610.05370.1092
1.620.05260.1074
1.630.05150.1057
1.640.05050.1040
1.650.04950.1023
1.660.04840.1006
1.670.04750.0989
1.680.04650.0973
1.690.04550.0957
1.700.04460.0940
1.710.04360.0925
1.720.04270.0909
1.730.04180.0893
1.740.04090.0878
1.750.04010.0863
1.760.03920.0848
1.770.03840.0833
1.780.03750.0818
1.790.03670.0804
1.800.03590.0790
1.810.03510.0775
1.820.03440.0761
1.830.03360.0748
1.840.03290.0734
1.850.03220.0721
1.860.03140.0707
1.870.03070.0694
1.880.03000.0681
1.890.02940.0669
1.900.02870.0656
1.910.02810.0644
1.920.02740.0632
1.930.02680.0620
1.940.02620.0608
1.950.02560.0596
1.960.02500.0584
1.970.02440.0573
1.980.02380.0562
1.990.02330.0551
2.000.02270.0540
2.010.02220.0529
2.020.02170.0519
2.030.02120.0508
2.040.02070.0498
2.050.02020.0488
2.060.01970.0478
2.070.01920.0468
2.080.01880.0459
2.090.01830.0449
2.100.01790.0440
2.110.01740.0431
2.120.01700.0422
2.130.01660.0413
2.140.01620.0404
2.150.01580.0396
2.160.01540.0387
2.170.01500.0379
2.180.01460.0371
2.190.01430.0363
2.200.01390.0355
2.210.01350.0347
2.220.01320.0339
2.230.01290.0332
2.240.01250.0325
2.250.01220.0317
2.260.01190.0310
2.270.01160.0303
2.280.01130.0297
2.290.01100.0290
2.300.01070.0283
2.310.01040.0277
2.320.01020.0270
2.330.00990.0264
2.340.00960.0258
2.350.00940.0252
2.360.00910.0246
2.370.00890.0241
2.380.00870.0235
2.390.00840.0229
2.400.00820.0224
2.410.00800.0219
2.420.00780.0213
2.430.00750.0208
2.440.00730.0203
2.450.00710.0198
2.460.00690.0194
2.470.00680.0189
2.480.00660.0184
2.490.00640.0180
2.500.00620.0175
2.510.00600.0171
2.520.00590.0167
2.530.00570.0163
2.540.00550.0158
2.550.00540.0154
2.560.00520.0151
2.570.00510.0147
2.580.00490.0143
2.590.00480.0139
2.600.00470.0136
2.610.00450.0132
2.620.00440.0129
2.630.00430.0126
2.640.00410.0122
2.650.00400.0119
2.660.00390.0116
2.670.00380.0113
2.680.00370.0110
2.690.00360.0107
2.700.00350.0104
2.710.00340.0101
2.720.00330.0099
2.730.00320.0096
2.740.00310.0093
2.750.00300.0091
2.760.00290.0088
2.770.00280.0086
2.780.00270.0084
2.790.00260.0081
2.800.00260.0079
2.810.00250.0077
2.820.00240.0075
2.830.00230.0073
2.840.00230.0071
2.850.00220.0069
2.860.00210.0067
2.870.00210.0065
2.880.00200.0063
2.890.00190.0061
2.900.00190.0060
2.910.00180.0058
2.920.00180.0056
2.930.00170.0055
2.940.00160.0053
2.950.00160.0051
2.960.00150.0050
2.970.00150.0048
2.980.00140.0047
2.990.00140.0046
3.000.00130.0044