5 - Understanding Chi-Squared 2 = reduced 2 = yi f ( xi ;...

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1 Understanding Chi-Squared • Consider 2 situations: – Comparing sampled Data directly with the parent distribution from which it came – Comparing sampled Data with our best estimate of that parent distribution 2 1 2 ) ; ( = = N i i i i i a x f y σ χ 2 1 2 2 ) ; ( 1 reduced = = = N i i i i i a x f y M N DOF Performing a Least-Squares Fit and Understanding the Result A complete example Δ V = 0.05 V for all measurements () 2 1 2 = Δ + = N i i i i y b ax y SUMMARY: Best Fit line with χ 2
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2 Compute Chi-Square for fit () 2 1 2 = Δ + = N i i i i y b ax y χ = 1.95 (for example data on previous slide) DF = Degrees of Freedom P = Probability of exceeding the tabulated value of Chi-square (for a given DF) How do we interpret this value of Chi-Square? • We interpret this the following way: If we were to repeat the same experiment many times, we would expect approximately 96% of those
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5 - Understanding Chi-Squared 2 = reduced 2 = yi f ( xi ;...

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