curve fitting1

8/3/2019 Curve Fitting1

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EXAMPLE 1

Actual Actual f=Observed Estimated

# Boys # Girls # Families # Families

5 0 14 104 1 56 50

3 2 110 100

2 3 88 100

1 4 40 50

0 5 12 10

Total 320 320n = 5

p = 0.5

q = 0.5

EXAMPLE 2

X = Actual O=Observed XiOi

# Events # Frequency #

0 305 0 0

1 365 365 365

2 210 420 840

3 80 240 7204 28 112 448

5 9 45 225

6 2 12 72

7 1 7 49

2

ii XO


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Total 1000 1201 2719

= 1.2010

2

= 1.2766

EXAMPLE 3

X = # Dice O=Observed

Showing 1,3,0r 5 # Frefquency r=Successes s=Failures0 10 0 4

1 25 1 3

2 40 2 2

3 30 3 1

4 7 4 0

Total 112

p = 0.5000

q = 0.5000

n = 4

EXAMPLE 4

Cured Conditioned No

Worsened Effect

Given the Drug 200 40 60

Not Given the Drug 120 30 50

Total 320 70 110

300 patients were administered the new drug and 200 other patients were not given

the drug. The patients were monitored and the results were obtained as follows:

Since = 2, actual observed frequencies follow Poisson Distribution.

Since = 2, actual observed frequencies follow Poisson Distribution.

Four dice were thrown 112 times and the number of times 1, 3, 5 was thrown

were as under: Find Chi-square presuming that all the dice were fair.

To test the efficiency of a new drug a controlled experiment was conducted wherein


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Worsened Effect

Given the Drug 200 40 60

Not Given the Drug 120 30 50

Total 320 70 110


Worsened Effect

Given the Drug 192 42 66Not Given the Drug 128 28 44

Total 320 70 110

O E O-E (O-E)2

200 192 8 64

120 128 -8 64

40 42 -2 4

30 28 2 4

60 66 -6 36

50 44 6 36

2 =

is less than that of the table value, the effect of the drug is not significant. So, we a

d.f. = (2-1)(3-1) = 2, Tabulated Value of 2 for 2 d.f. = 5.99. Since computed val

Observed Frequencies

Expected Frequencies

Expected frequency for each cell =

We set Ho: There is no effect of drug; H1: There is effect of drug, i.e. the drug is e

Computation of 2 (Chi-Square)

Use 2

(Chi-Square) Test for finding the effect of the drug.

Solution:

Totali.e.GrandSize,Sample

TotalColumnTotalRow


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Example:

0.252 0.599 0.630 0.415

0.853 0.704 0.222 0.0030.213 0.505 0.337 0.821

0.470 0.150 0.996 0.674

0.840 0.858 0.988 0.116

0.051 0.344 0.978 0.575

0.365 0.817 0.491 0.5160.978 0.527 0.160 0.054

0.791 0.837 0.586 0.700

0.230 0.436 0.410 0.702

0.897 0.417 0.378 0.779

0.983 0.492 0.164 0.3580.588 0.873 0.405 0.400

0.860 0.400 0.276 0.663

0.595 0.833 0.450 0.928

0.661 0.308 0.196 0.992

0.012 0.929 0.895 0.243

0.741 0.921 0.877 0.998

0.107 0.328 0.062 0.476

0.108 0.837 0.539 0.845

0.162 0.565 0.612 0.636


5/20

0.282 0.268 0.689 0.129

0.984 0.422 0.812 0.329

0.218 0.470 0.912 0.954

0.945 0.422 0.751 0.8520.209 0.820 0.721 0.113

0.158 0.147 0.280 0.723

0.951 0.210 0.947 0.603

0.394 0.940 0.251 0.476

0.917 0.436 0.700 0.9290.380 0.383 0.771 0.597

0.940 0.840 0.785 0.694

0.513 0.360 0.382 0.766

0.963 0.606 0.638 0.856

0.223 0.135 0.674 0.1590.506 0.854 0.062 0.702

0.429 0.775 0.373 0.045

0.127 0.495 0.400 0.725

0.041 0.493 0.382 0.647

0.135 0.129 0.543 0.2070.232 0.953 0.855 0.518

0.904 0.223 0.848 0.000

0.301 0.591 0.103 0.138


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0.613 0.416 0.756 0.688

0.763 0.484 0.336 0.983

0.294 0.873 0.070 0.458

0.124 0.079 0.895 0.2340.571 0.625 0.335 0.558

0.025 0.151 0.217 0.602

0.844 0.567 0.745 0.731

0.073 0.634 0.365 0.724

0.695 0.462 0.041 0.5340.151 0.980 0.594 0.007

0.639 0.788 0.826 0.302

0.662 0.636 0.595 0.038

0.960 0.345 0.564 0.307

0.011 0.132 0.942 0.3920.142 0.083 0.171 0.056

0.199 0.192 0.453 0.320

0.318 0.754 0.463 0.462

0.789 0.257 0.305 0.124

0.904 0.785 0.346 0.5370.805 0.465 0.193 0.228

0.477 0.198 0.352 0.284

0.062 0.882 0.232 0.742


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0.357 0.397 0.426 0.276

0.339 0.615 0.336 0.415

0.302 0.829 0.210 0.717

0.101 0.954 0.887 0.1540.115 0.120 0.646 0.386

0.047 0.760 0.981 0.532

0.715 0.825 0.300 0.362

0.947 0.819 0.177 0.492

0.564 0.461 0.523 0.5680.290 0.378 0.776 0.064

0.846 0.233 0.702 0.744

0.621 0.443 0.251 0.638

0.110 0.377 0.501 0.832

0.870 0.407 0.804 0.3780.464 0.566 0.709 0.863

0.021 0.574 0.414 0.444

0.402 0.295 0.195 0.027

0.122 0.655 0.605 0.383

0.405 0.260 0.583 0.6220.101 0.549 0.837 0.112

0.924 0.489 0.103 0.185

0.851 0.243 0.403 0.625


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0.141 0.586 0.091 0.977

0.131 0.837 0.951 0.035

0.084 0.570 0.219 0.530

0.207 0.967 0.062 0.9980.389 0.584 0.122 0.787

0.961 0.887 0.275 0.411

0.270 0.402 0.057 0.812

0.669 0.101 0.788 0.201

0.633 0.871 0.959 0.6180.607 0.197 0.511 0.381

0.077 0.822 0.137 0.219

0.039 0.480 0.118 0.425

0.537 0.889 0.529 0.525


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Chi-

Square

1.6000.720

1.000

1.440

2.000

0.400

7.160

stimatedFrefquency

300.893 0.0560533

361.373 0.0364093

217.004 0.2260797

86.874 0.543921326.084 0.1407496

6.265 1.1935862

1.254 0.4436129

0.215 2.8626466

0

20

40

60

80

100

120

1 2 3 4


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999.963 5.5030589

Estimated

# Frefquency7

28

42

28

7

112

Total

300

200

500


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Total

300

200

500

Total

300200

500

(O-E)2/E

0.3333

0.5000

0.0952

0.1429

0.5455

0.8182

2.4351

cept Ho.

e 2 of

fective.


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Observed Expected

0.928 0.000 0

0.466 0.100 43 500.058 0.200 59 50

0.934 0.300 48 50

0.649 0.400 57 50

0.726 0.500 54 50

0.867 0.600 50 500.415 0.700 43 50

0.626 0.800 39 50

0.809 0.900 57 50

0.176 1.000 50 50

0.040 0 5000.101 500

0.022 0.744

0.983 0.360

0.526

0.098

0.244

0.651

0.347

0.378


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0.007

0.520

0.080

0.2470.238

0.365

0.334

0.758

0.1220.514

0.130

0.136

0.377

0.0440.189

0.084

0.306

0.074

0.7250.193

0.850

0.288


14/20

0.410

0.998

0.857

0.3130.691

0.777

0.905

0.939

0.2850.585

0.397

0.260

0.513

0.3320.955

0.131

0.199

0.334

0.3600.856

0.806

0.610


15/20

0.966

0.058

0.821

0.8980.433

0.018

0.353

0.870

0.5730.993

0.033

0.244

0.370

0.8660.708

0.481

0.646

0.677

0.3840.393

0.998

0.306


16/20

0.941

0.583

0.417

0.2790.238

0.490

0.977

0.838

0.8210.169

0.538

0.782

0.563


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5 6

Series1


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19/20


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2

0.9801.620

0.080

0.980

0.320

0.0000.980

2.420

0.980

0.000

8.360

curve fitting1

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