# Talk:Physics307L:People/Mondragon/Formal Lab Report

## to do

Correct error estimation on lambda values Done, Maybe error lambda is where avg(sqrt(chisquare)) is twice its minimum value No, error on x should be sqrt(lambda)

New Plots for eveything. Smooth plot for poisson fit for comparison to actual data. seperate plots for each run, instead of animation.

comparison of fits obtained lambda from chi square vs lambda from data averaging --Tomas A. Mondragon 14:42, 31 October 2007 (CDT)

plots of what chisquare min looks like

--Tomas A. Mondragon 14:46, 31 October 2007 (CDT)

## error on λ definetly wrong

the error on λ is the interval where $S(\lambda_{best}\pm\Delta\lambda)-S(\lambda)=1$

where $S(\lambda)=\frac{\sum_k{\left(f(\lambda,k)-\tfrac{x_k}{256}\right)^2}}{\sigma^2}$

$\sigma^2=\frac{\sum_{k=0}^{\operatorname{max}\ k}{(f(\lambda_{best},k)-\tfrac{x_k}{256})^2}}{\operatorname{max}\ k}$

## MAIN NOTEBOOK ENTRY

Physics307L:People/Mondragon/Notebook/071003--Tomas A. Mondragon 13:53, 2 November 2007 (CDT)

## RECALCULATED DATA

### 10 ms

• λ from chi-square minimization = 0.0261205
• Average deviation from fit = 0.0013743
• λ from average of data = 0.042969
• Average deviation from fit = 0.0028351
• fit plot

• χ2 plots

• Δλ = 0.0010149

### 20ms

• λ from chi-square minimization = 0.0736898
• Average deviation from fit = 0.0029991
• λ from average of data = 0.10938
• Average deviation from fit = 0.0052407
• fit plot

• χ2 plots

• Δλ=0.0023908

### 40ms

• λ from chi-square minimization = 0.185892
• Average deviation from fit = 0.0082640
• λ from average of data = 0.32422
• Average deviation from fit = 0.015304
• fit plot

• χ2 plots

• Δλ = 0.007938

### 80ms

• λ from chi-square minimization = 0.457154
• Average deviation from fit = 0.0014991
• λ from average of data = 0.70703
• Average deviation from fit = 0.020735
• fit plot

• χ2 plots

• Δλ = 0.022045

### 100ms

• λ from chi-square minimization = 0.468385
• Average deviation from fit = 0.0079525
• λ from average of data = 0.62891
• Average deviation from fit = 0.012870
• fit plot

• χ2 plots

• Δλ = 0.011267

### 200ms

• λ from chi-square minimization = 0.937453
• Average deviation from fit = 0.013170
• λ from average of data = 1.2070
• Average deviation from fit = 0.016055
• fit plot

• χ2 plots

• Δλ = 0.033847

### 400ms

• λ from chi-square minimization = 2.58578
• Average deviation from fit = 0.013153
• λ from average of data = 2.7617
• Average deviation from fit = 0.013404
• fit plot

• χ2 plots

• Δλ = 0.08610

### 800ms

• λ from chi-square minimization = 5.74562
• Average deviation from fit = 0.0074780
• λ from average of data = 6.0234
• Average deviation from fit = 0.0078470
• fit plot

• χ2 plots

• Δλ = 0.08421

### 1s

• λ from chi-square minimization = 7.27233
• Average deviation from fit = 0.0065399
• λ from average of data = 7.3242
• Average deviation from fit = 0.0065502
• fit plot

• χ2 plots

• Δλ = 0.09070

### 10s

• λ from chi-square minimization = 73.9022
• Average deviation from fit = 0.0074556
• λ from average of data = 73.766
• Average deviation from fit = 0.0074574
• fit plot

• χ2 plots

• Δλ = 0.6182

## linefit of λ versus dwell time

Dr. gold's linefit function seems to lend to much weight to the data collected at the beginning. This is understandable because a bunch of datapoints are bunched together there, giving them more credibility, so to speak, than the lonely point at dwell time=10s mark. Polyfit, which dosnt weigh points at all, provides a better fit in my opinion.

• poly fit to line: λ = 0.007411 * dwelltime(ms) − 0.209179