IME 301

Example on Goodness-of-Fit Test Using Data from Height of People

By: Dr. Parisay

Refer to the previous example on height of 36 people in Cm. The collected data is in the table below:

153 / 163.5 / 174 / 178 / 155.5 / 165.6
152 / 168.2 / 167 / 159 / 156.4 / 168.3
180 / 171 / 164.6 / 168 / 177.3 / 154.4
152.5 / 173.5 / 168.5 / 157 / 158.9 / 168
169 / 181.2 / 154.5 / 156 / 158 / 162
155 / 179 / 171 / 155 / 170 / 161.5

We obtained a histogram with 6 cells for this data using “Arena” software (it is simulation software) as below:

We changed number of cells of histogram to 20 and obtained the following graph.

Experiment 5:

Using “Input Analyzer” moduleof “Arena” software an exponential distribution is fitted to the histogram with 6 cells as below:

Distribution Summary
Distribution:
Exponential Expression: 152 + EXPO(12.6)
Square Error:0.051038 / Chi Square Test
Number of intervals= 4
Degrees of freedom = 2
Test Statistic = 19.2
Corresponding p-value
<0.005 / Kolmogorov-Smirnov Test
Test Statistic= 0.168
Corresponding p-value> 0.15

Experiment 6:

Using “Input Analyzer” moduleof “Arena” software a normal distribution is fitted to the histogram with 6 cells as below:

Distribution Summary
Distribution:
Normal Expression:NORM(165, 8.61)
Square Error:0.060880 / Chi Square Test
Number of intervals= 4
Degrees of freedom = 1
Test Statistic = 4.85
Corresponding p-value= 0.0286 / Kolmogorov-Smirnov Test
Test Statistic= 0.203
Corresponding p-value= 0.0911

Experiment 7:

Using “Input Analyzer” moduleof “Arena” software a uniform distribution is fitted to the histogram with 6 cells as below:

Distribution Summary
Distribution:
Uniform Expression:UNIF(152, 182)
Square Error:0.041667 / Chi Square Test
Number of intervals= 6
Degrees of freedom = 5
Test Statistic = 9
Corresponding p-value= 0.114 / Kolmogorov-Smirnov Test
Test Statistic= 0.156
Corresponding p-value> 0.15

Experiment 8:

Using “Input Analyzer” moduleof “Arena” software an exponential distribution is fitted to the histogram with 20 cells as below:

Distribution Summary
Distribution:
Exponential Expression:152 + EXPO(12.6)
Square Error:0.031922 / Chi Square Test
Number of intervals= 5
Degrees of freedom = 3
Test Statistic = 9.19
Corresponding p-value= 0.0276 / Kolmogorov-Smirnov Test
Test Statistic= 0.168
Corresponding p-value> 0.15

Experiment 9:

Using “Input Analyzer” moduleof “Arena” software a normal distribution is fitted to the histogram with 20 cells as below:

Distribution Summary
Distribution:
Normal Expression:NORM(165, 8.61)
Square Error:0.035213 / Chi Square Test
Number of intervals= 5
Degrees of freedom = 2
Test Statistic = 11.8
Corresponding p-value< 0.005 / Kolmogorov-Smirnov Test
Test Statistic= 0.203
Corresponding p-value= 0.0911

Experiment 10:

Using “Input Analyzer” moduleof “Arena” software a uniform distribution is fitted to the histogram with 20 cells as below:

Distribution Summary
Distribution:
Uniform Expression:UNIF(152, 182)
Square Error:0.030247 / Chi Square Test
Number of intervals= 6
Degrees of freedom = 5
Test Statistic = 9.84
Corresponding p-value= 0.0834 / Kolmogorov-Smirnov Test
Test Statistic= 0.156
Corresponding p-value> 0.15

Analysis of experiments:

Complete the following table using the information from the experiments above:

Histogram / Exponential / Normal / Uniform
P-value
For 6 cells
For 20 cells
Square error
For 6 cells
For 20 cells

Analyze the completed table (above) and write your conclusion.

Prepared: Sept. 2005

1