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Figure 3 | Journal of Statistical Distributions and Applications

Figure 3

From: Chi-p distribution: characterization of the goodness of the fitting using Lp norms

Figure 3

Possible values of the reduced chi-square and their meaning. (a) Seven data points are fitted by a statistical model, here a straight line. (b) When the errors are too small (underestimation), the calculated reduced Chi-square is χ red 2 > 1 , and the fitted line does not pass through the data points or their error lines. Other more complicated curve can fit better the data (dash line). (c) In the case where the errors are similar to the deviations of the data points from the model, the reduced Chi-square is χ red 2 ~ 1 , and the fitting is good. (d) Finally, when the errors are too large (overestimation), the reduced Chi-square is χ red 2 < 1 . In this case, the fitted line does pass through the data points or their error lines, but the curves of any other model can also pass through these, leading to good fitting; hence, the rate of the fitting is meaningless.

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