What is a Chi-Squared Test Against Weighted Mean?

[majormuss]

Hi all,
I was reading a paper and I wasn't sure how they performed their statistic analysis. What do they mean by a chi-square test against the weighted mean? Is it a chi-square test between the actual data points and the weighted mean? If so, why do they us the function P(X^2,v)? I thought that was a function for Poisson distribution.

This is the paragraph describing the statistics and the graph below is figure 3:
"Lightcurves were produced in 10-day (Figure 3) and 28-day (not shown) bins over the 10-month LAT dataset. Considering the limited statistics, it was necessary to fix the photon index to the (average) fitted value in order to usefully gauge variability in the flux. Considering only statistical errors of all the binned data points with T S ≥ 1 (1σ), a χ 2 test against the weighted mean fluxes of the 10-day and 28-day lightcurves resulted in probabilities, P(χ 2 ,ν) = 22% and 70%, respectively, indicating plausible fits to the tested hypothesis. We conclude that there is no evidence for variability over the period of observations. A radial profile of the γ-ray source counts (not shown) was extracted for the total energy range (>200 MeV). The profile is consistent with that of a point source simulated at energies 0.2 − 200 GeV using the fitted spectral parameters above with a reduced χ 2 = 1.04 for 20 degrees of freedom. The total ∼0 ◦ .2 extent of the 10’s kpc-scale radio lobes of M87 (Figure 1; Owen et al. 2000) is comparable to the LAT angular resolution, θ68 ≃ 0 ◦ .8 E −0.8 GeV (Atwood et al. 2009). Therefore, from the presently available data, we can not disentangle (or exclude) a possible contribution of the extended radio features to the total γ-ray flux. "

Figure 3.

 

[Dr. Courtney]

That is a bit tricky to unravel.

Have you consdered writing the corresponing author?

 

[WWGD]

Hi all,
I was reading a paper and I wasn't sure how they performed their statistic analysis. What do they mean by a chi-square test against the weighted mean? Is it a chi-square test between the actual data points and the weighted mean? If so, why do they us the function P(X^2,v)? I thought that was a function for Poisson distribution.

This is the paragraph describing the statistics and the graph below is figure 3:
"Lightcurves were produced in 10-day (Figure 3) and 28-day (not shown) bins over the 10-month LAT dataset. Considering the limited statistics, it was necessary to fix the photon index to the (average) fitted value in order to usefully gauge variability in the flux. Considering only statistical errors of all the binned data points with T S ≥ 1 (1σ), a χ 2 test against the weighted mean fluxes of the 10-day and 28-day lightcurves resulted in probabilities, P(χ 2 ,ν) = 22% and 70%, respectively, indicating plausible fits to the tested hypothesis. We conclude that there is no evidence for variability over the period of observations. A radial profile of the γ-ray source counts (not shown) was extracted for the total energy range (>200 MeV). The profile is consistent with that of a point source simulated at energies 0.2 − 200 GeV using the fitted spectral parameters above with a reduced χ 2 = 1.04 for 20 degrees of freedom. The total ∼0 ◦ .2 extent of the 10’s kpc-scale radio lobes of M87 (Figure 1; Owen et al. 2000) is comparable to the LAT angular resolution, θ68 ≃ 0 ◦ .8 E −0.8 GeV (Atwood et al. 2009). Therefore, from the presently available data, we can not disentangle (or exclude) a possible contribution of the extended radio features to the total γ-ray flux. "
View attachment 86285Figure 3.

I think the author is referring to a $(\chi^2, v)$ goodness-of-fit test, where v is the number of degrees of freedom. http://stattrek.com/chi-square-test/goodness-of-fit.aspx?Tutorial=AP , where 22%, 70% are pretty far from most choices of significance level.