A Chi-Squared Analysis of the Measurements of Two Cosmological Parameters over Time

Round 1

Reviewer 1 Report

Referee's report for "Chi-Squared Analysis of Measurements of Two Cosmological Parameters Over Time" by Faerber and Lopez-Corredoira

 

I find the paper to be straightforward and extremely clear in its methods. The findings are both timely and interesting, and I recommend that the paper be published. There are two very minor points below which should be addressed, as well as a handful of typographical errors.

 

(a) In the paragraph below equation (1) it is stated that  "In any case, adding a term for covariance to Equation  (1) would make the probability of higher deviations even lower, so our simplistic approach can be considered a conservative calculation." I am confused by this statement. As ane example, if data were all perfectly correlated, the probablility of a high deviation would be the same as a for a single data point, which is obviously lower than for a number of independent data points. The authors should reevaulate this statement, or make it clearer if I have misinterpreted it.

(b) Figures 2 and 4, and 3 and 5 contain the same information, except with the addition of some best fit lines. It would make the paper clearer if Figures 2 and 3 were not included.

(c) There are a few typos:

"indenpendence" in paragraph below equation 1.

line 170 of page 8 "reinforce" -> "reinforces"

last paragraph "surprise" -> "surprised"

Author Response

REFEREE:
This paper describes a some-what pedagogical analysis of the measurements of two cosmological parameters over time: sigma_8 and H_0. It has some intrinsic interest, but it should be reviewed in the light of making it less qualitative.
In many cases the paper is a little didascalic and explains too much in a "text-book" way.

OUR REPLY:
The paper gives numerical quantification of the statistics, it is not just "qualitative". Certainly, the plots already show the trends that we describe in the paper, but the plots were accompanied by chi^2 analyses that give "quantitatively" how much is their statistical significance.
We agree that our paper may be a little disdascalic in a textbook way, though we do not think this is something that must be avoided. Nonetheless, we change or remove some sentences that may sound too pedagogical with well-known facts or observations.

REFEREE:
-Caption of Figure 1: it should be extended and made more clear; same applies for all figures;

OUR REPLY:
We have extended the caption of all figures.

REFEREE:
-The "Croft and Dailey" reference is wrong. I had to look for it but I think that the correct reference is the following: arXiv:1112.3108;

OUR REPLY:
Yes, we substitute arXiv:1112.3107 for arXiv:1112.3108 in the reference of Croft & Dailey

REFEREE:
-On section 1.4 there are other papers like for instance this (The Astrophysical Journal, Volume 598, Issue 2, pp. L75-L78.) and others that are not cited in Croft and Dailey. Also, referring to Croft and Dailey and reference therein seems a little unusual for the main part of the paper;

OUR REPLY:
For the years 1990-2010, we have taken the compilation of Croft & Dailey. Certainly, there may be some missing references, but anyway the sample is large enough for our statistical purposes.
Croft & Dailey is an unusual paper, yes, but it is the most complete paper we have found in the present topic of evolution of cosmological parameters.

REFEREE:
-On section 2: it there a claim that there is a trend with time. Is B value not consistent with 0? This should be discussed more as it does not seem wright looking the figure. For instance, the authors may want to consider to add other statistical tests.

OUR REPLY:
We have revised our statistical calculations about the error of the slope B and we found an error: in the application of Avni (1976) method, we had not taken into account that the reduce chi^2 in our case is larger than one (due to an underestimation of the error bars, as pointed out in the paper). We correct this by a factor equivalent to make reduced chi^2=1, i.e. equivalent to make the error bars statistically compatible with the fit. Also, we add statistical calculation of the degree of correlation of H_0 with time.
Still we see a very significant non-zero slope of H_0 with time. Nonetheless, we have also checked the significance of the evolution through the calculation of the correlation factor, and we only find a 2-sigma significance, so the referee was correct to find an error there.
These numbers and others throughout the paper are now corrected in the new version.
We also add a new figure (Fig. 4 in the present version).

We remove in the conclusions the comparison with Millikan's case (since now the correlation is not significant enough to claim it). The rest of the conclusions of the paper remain as previously.

REFEREE:
Overall the paper is a little qualitative.

OUR REPLY:
See first point of our replies.

Reviewer 2 Report

This paper describes a some-what pedagogical analysis of the measurements of two cosmological parameters over time: sigma_8 and H_0. It has some intrinsic interest, but it should be reviewed in the light of making it less qualitative.

In many cases the paper is a little didascalic and explains too much in a "text-book" way.

Some comments on the text:

-Caption of Figure 1: it should be extended and made more clear; same applies for all figures;

-The "Croft and Dailey" reference is wrong. I had to look for it but I think that the correct reference is the following: arXiv:1112.3108;

-On section 1.4 there are other papers like for instance this (The Astrophysical Journal, Volume 598, Issue 2, pp. L75-L78.) and others that are not cited in Croft and Dailey. Also, referring to Croft and Dailey and reference therein seems a little unusual for the main part of the paper;

-On section 2: it there a claim that there is a trend with time. Is B value not consistent with 0? This should be discussed more as it does not seem wright looking the figure. For instance, the authors may want to consider to add other statistical tests.

Overall the paper is a little qualitative.

Author Response

REFEREE:
(a) In the paragraph below equation (1) it is stated that "In any case, adding a term for covariance to Equation (1) would make the probability of higher deviations even lower, so our simplistic approach can be considered a conservative calculation." I am confused by this statement. As ane example, if data were all perfectly correlated, the probablility of a high deviation would be the same as a for a single data point, which is obviously lower than for a number of independent data points. The authors should reevaulate this statement, or make it clearer if I have misinterpreted it.

OUR REPLY:
Your example of perfect correlation is correct and in agreement with our statement.
We have rephrased the sentece, so it can be better understood: If the data were not independent, we would have to add a term for covariance to Equation (\ref{Chisquared}). In any case, non-independency of data would make
the spread of the points lower than indicated by the error bars, which would make the probability $Q$ (see subsection 2.3) of higher deviations even lower and the number of points to reject in order to have a distribution compatible the error bars even larger. Therefore, our simplistic approach can be considered a conservative calculation."

REFEREE:
(b) Figures 2 and 4, and 3 and 5 contain the same information, except with the addition of some best fit lines. It would make the paper clearer if Figures 2 and 3 were not included.

OUR REPLY:
We remove Figs. 2 and 3 of the old version of the paper.

REFEREE:
(c) There are a few typos:
"indenpendence" in paragraph below equation 1.
line 170 of page 8 "reinforce" -> "reinforces"
last paragraph "surprise" -> "surprised"

OUR REPLY:
We have corrected these typos.

Reviewer 3 Report

The paper attempts to carry out a statistical analysis of some cosmological parameters. The authors claim that new information can be extracted using simple statistical methods. The results are intriguing, but before I can judge the details of this article I suggest the following major revisions: In many places in the paper, the authors use non-standard nomenclature and notation. The paper itself reads like a lab report, and this unorthodox style makes it difficult to judge the results in the paper. I suggest the authors familarise themselves with the current literature (for example, using inspirehep.net) and then try to rewrite the paper. After this, I will be happy to reconsider it in detail.

Author Response

REFEREE:
The paper attempts to carry out a statistical analysis of some cosmological parameters. The authors claim that new information can be extracted using simple statistical methods. The results are intriguing, but before I can judge the details of this article I suggest the following major revisions: In many places in the paper, the authors use non-standard nomenclature and notation. The paper itself reads like a lab report, and this unorthodox style makes it difficult to judge the results in the paper. I suggest the authors familarise themselves with the current literature (for example, using inspirehep.net) and then try to rewrite the paper. After this, I will be happy to reconsider it in detail.

OUR REPLY:
We are not aware of nomenclature or notation that is non-standard. If the referee can point us out which notation is not appropriate and suggestions of corrections, we will try to improve it accordingly. About the style, we think we have described the problem and the method and results appropriately, with appropriate scientific quantification of the statements. If something is not clear, again, we will be glad to rephrase some paragraph or explain some details that maybe considered missing.

Round 2

Reviewer 2 Report

The paper can be accepted.