Calculate the chi-squared probability for the fit

In summary, an experiment was conducted to test the linearity of displacement produced by a piezoelectric drive with applied potential voltage. Data was collected and a linear fit was displayed in Excel, with a chi-squared probability calculated to determine the degree of fit. There was uncertainty in the voltage setting, but it was negligible, while the displacement measurements had an uncertainty of +-5um. The equation y=474.82x+8.3818 was used for the fit, but there were questions about whether the values for V(subscript theory) should be taken from this equation or if the graph should go through the origin.
  • #1
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Homework Statement



an experiment is performed to test whether the displacement D produced on a piezoelectric drive behaved linearly with the potential voltage V applied across it. The following data are obtained:

V (volts) D (um)
0.1 50
0.2 101
0.3 151
0.4 198
0.5 249
0.6 298
0.7 346
0.8 393
0.9 438
1 181
1.1 521

the uncertainty on the voltage setting can be considered negligible. While the displacement measurements are performed with a linear encoder with an uncertainty of +-5um

calculate the chi-squared probability for the fit

The Attempt at a Solution


when I plotted the graph the equation Excel displayed was:
y=474.82x+8.3818

I have thought about two possibilities:

when calculating chi-squared, the values of V(subscript theory) be taken by using the equation on the least-squared-fitted graph on Excel?

y=474.82x+8.3818

or does one assume that V is supposed to be proportional to D and that the graph is meant to go through the origin?

Should I use the above equation to work out what Dis supposed to be in theory when working out chi-squared? or should I assume it's supposed to go through the origin?
 
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  • #2
by the way, I had trouble getting the values in the table to look presentable on the screen, but I'm sure you can guess what I meant
 

FAQ: Calculate the chi-squared probability for the fit

What is chi-squared probability?

Chi-squared probability is a statistical measure that calculates the likelihood that the observed data fits a given model. It is used to determine the goodness of fit between the observed data and the expected data.

How is chi-squared probability calculated?

Chi-squared probability is calculated by dividing the difference between the observed data and the expected data by the expected data, squaring the result, and then summing all of these values together. This calculation results in a chi-squared value, which is then compared to a chi-squared distribution table to determine the probability.

What does a low chi-squared probability indicate?

A low chi-squared probability indicates that there is a high likelihood that the observed data does not fit the expected model. This could mean that there is a significant difference between the observed and expected data, and the model may need to be revised.

What is a good chi-squared probability value?

A good chi-squared probability value is typically considered to be greater than 0.05, which indicates that the observed data fits the expected model well. However, the significance level can vary depending on the specific research question and the field of study.

What are some limitations of using chi-squared probability?

One limitation of using chi-squared probability is that it assumes the data is independent and normally distributed, which may not always be the case. Additionally, it can only determine the likelihood of fit, not causation. Furthermore, it may be affected by sample size, so larger sample sizes may result in a lower chi-squared probability even if the fit is not significantly different.

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