Normal | Chi Goodness-of-Fit
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A chi-square (χ2) Goodness-of-Fit test is a type of Pearson’s chi-square test. You can use it to test whether the observed distribution of a categorical variable differs from your expectations. A categorical test represents groupings of data, such as a normal chart class.
The formula for this is χ2 = Σ(ƒaf - ƒtf)2 ⁄ ƒtf, where af is the actual frequency and tf is the theoretical frequency.
The resulting value χ2 can be compared against the table below; χ2α,ν where;
α is a predefined level of significance (typically 0.05).
ν is the degree of freedom. ν = m - r - 1
m is the number of classes having a value of 5 or more.
r is the number of parameters of the distribution. For normal distribution, there are 2 parameters; µ and σ
If the value of χ2 is smaller than the table result, then it may be acceptable. A large valuer suggests a larger difference between ƒaf and ƒtf.
| α | ||||||
| ν | 0.5 | 0.1 | 0.05 | 0.025 | 0.01 | 0.005 |
| 1 | 0.455 | 2.706 | 3.841 | 5.024 | 6.635 | 7.879 |
| 2 | 1.386 | 4.605 | 5.991 | 7.378 | 9.210 | 10.597 |
| 3 | 2.366 | 6.251 | 7.815 | 9.348 | 11.345 | 12.838 |
| 4 | 3.357 | 7.779 | 9.488 | 11.143 | 13.277 | 14.860 |
| 5 | 4.351 | 9.236 | 11.070 | 12.833 | 15.086 | 16.750 |
| 6 | 5.348 | 10.645 | 12.592 | 14.449 | 16.812 | 18.548 |
| 7 | 6.346 | 12.017 | 14.067 | 16.013 | 18.475 | 20.278 |
| 8 | 7.344 | 13.362 | 15.507 | 17.535 | 20.090 | 21.955 |
| 9 | 8.343 | 14.684 | 16.919 | 19.023 | 21.666 | 23.589 |
| 10 | 9.342 | 15.987 | 18.307 | 20.483 | 23.209 | 25.188 |
| 11 | 10.341 | 17.275 | 19.675 | 21.920 | 24.725 | 26.757 |
| 12 | 11.340 | 18.549 | 21.026 | 23.337 | 26.217 | 28.300 |
| 13 | 12.340 | 19.812 | 22.362 | 24.736 | 27.688 | 29.819 |
| 14 | 13.339 | 21.064 | 23.685 | 26.119 | 29.141 | 31.319 |
| 15 | 14.339 | 22.307 | 24.996 | 27.488 | 30.578 | 32.801 |
| 16 | 15.338 | 23.542 | 26.296 | 28.845 | 32.000 | 34.267 |
| 17 | 16.338 | 24.769 | 27.587 | 30.191 | 33.409 | 35.718 |
| 18 | 17.338 | 25.989 | 28.869 | 31.526 | 34.805 | 37.156 |
| 19 | 18.338 | 27.204 | 30.144 | 32.852 | 36.191 | 38.582 |
| 20 | 19.337 | 28.412 | 31.410 | 34.170 | 37.566 | 39.997 |
Chi Calculator
To use, enter the actual frequencies as a comma-delimited or new-line-delimited list. The theoretical values field may be a list with size equal to that of the actual frequencies list.
| Degree of Freedom (ν) | Number of Parameters (2 in Normal Distribution) | ||||
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Chi “Test Normality” Calculator
To use, enter the actual frequencies as a comma-delimited list with each sample group on a new-line.
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