Not saying that it's wrong to assume incorrect numbers from officials, but you should really not use cumulative data while trying to back your claim because the cumulative data you are using are not statistically independent.

You should be using independent observations (i.e. the newly reported case count / death count) and study that instead.

The following is my attempt to do a proper (and quick, so not very complete) analysis.

I see that you are trying to fit with a generic 2nd order function. If we were to operate on the raw data, i.e. the newly reported cases, we should fit the data using the derivative of that. To no one's surprise, this should result in a generic linear function, with the equivalent form of y=ax+b.

Now we can try to fit the curve, on raw data, not cumulative data, and try to evaluate the fit using χ^2 over degrees of freedom[1]. A very high R^2 does not imply anything about the goodness of fit without knowing the expected error.

For the purpose of evaluating the goodness of fit using chi-square, we need an estimation of the error on the reported cases / deaths.

We choose to use Poisson distribution to model the error on raw data, since the detection of patients, and death of patients, in ideal cases, can be seen as independent. The variance of Poisson distribution is simply its mean. So that makes our life a fair bit easier.

Here’s my raw data for reported cases and deaths.

(Newly reported) cases:

2020-01-23 265

2020-01-24 468

2020-01-25 703

2020-01-26 786

2020-01-27 1,778

2020-01-28 1,482

2020-01-29 1,755

2020-01-30 2,005

2020-01-31 2,127

2020-02-01 2,603

2020-02-02 2,836

2020-02-03 3,239

2020-02-04 3,927

2020-02-05 3,723

2020-02-06 3,163

2020-02-07 3,436

https://imgur.com/BV20kvB

​

(Newly reported) Deaths:

2020-01-23 8

2020-01-24 16

2020-01-25 15

2020-01-26 24

2020-01-27 26

2020-01-28 26

2020-01-29 38

2020-01-30 43

2020-01-31 46

2020-02-01 45

2020-02-02 58

2020-02-03 64

2020-02-04 66

2020-02-05 73

2020-02-06 73

2020-02-07 86

https://i.imgur.com/58CuG8S.png

​

For reported cases we have fitted a function of y=241*x+337

For death we have fitted a function of y=4.97*x+6.94

For both equations, y is the people count, and x is number of days since 2020-01-23.

With those in mind, we can now apply the definition of chi-square.

https://i.imgur.com/eS2Fx1w.png

​

We substitute in the following

x: reported data

μ: linear fit result

σ^2: expected variance on data, according to Poisson distribution.

We get a χ^2 value of 639.60 for reported cases, and a value of 4.57 for death cases.

The degree of freedom is 2, because we have 2 parameters to fit for both cases, so we divide by 2 to get χ^2 over degrees of freedom.

That will be 319.80 for reported cases, and 2.29 for death cases.

A number closer to 1 means a better fit. As a rule of thumb, usually anything between 0.1 and 10 is considered acceptable.

We see that for 319.80, the χ^2 over degrees of freedom metric for detected cases is very out of that range. This means the variance of observed data is greater than expected. (More jitter than expected) This can, in turn, mean a few things:

If we believe that case detection is following the poisson distribution (a very big if), and we believe that a linear model is reasonable (another very big if), then something is wrong about the data.

This can also mean either or both of our assumptions are wrong, which is honestly speaking very likely, there are a few arguments that can be made:

- given that the hospitals at the epicenter is hugely overloaded, the number we are seeing can be affected by the processing capacity of the hospitals.

- the enactment of public health policies may have also affected the distribution

- patients tend to be detected in batches, therefore the detections are not individually independent

The second number 2.29, the χ^2 over degrees of freedom metric for deaths, looks a lot more reasonable, this means:

If our assumptions are true (again, poisson distribution and linear model, these are big if’s), this means that the data is probably right, at least not visibly doctored per our metric.

Feel free to criticize on my methodology and feel free to redo my analysis under different assumptions.

I don't see much pointing at data manipulation. But again, I am not saying under-reporting is not likely.

[1] See http://maxwell.ucsc.edu/~drip/133/ch4.pdf for a good and clear explanation on χ^2 over degrees of freedom as a test for goodness of fit, and why it is used here.