# Error in books formula concerning the log-rank test?

I am currently reading the following book:

On page 243-244 there is an example about the log-rank test.

The log-rank test statistic is denoted by the chi square symbol and calculated in the following way:

and further on it is given:

and

I do not want to focus on the idea behind these formulas and what each symbol stands for. I give you the following table, so you do not need to calculate the $d_j$ and the $n_{1j}$ resp. $n_j$.

It is maybe difficult to read, but the Treatment A colmuns are referred to index 1 and the Treatment B columns are reffered to index 2.

In my opinion the given formula to calculate the $e_{1j}$ is wrong.

E.g. let's consider the first 2 j's:

$e_{11}=\frac{n_{11}-d_1}{n_1}=\frac{17-1}{34}=0.47$ and this is $!=0.5$

$e_{12}=\frac{n_{12}-d_2}{n_2}=\frac{16-1}{31}=0.484$ and this is $!=0.5161$

In my opinion, the correct formula is:

$e_{1j}=\frac{d_j}{n_j}*n_{1j}$

I check this for Time (months) =23 (j=7) and 27 (j=8):

$e_{17}=\frac{d_7}{n_7}*n_{17}=\frac{1}{20}*13=0.65$

$e_{18}=\frac{d_8}{n_8}*n_{18}=\frac{1}{19}*13=0.6842$

And indeed, these are the values given in the table.

What do you say?

EDIT: Of course, I should say that the table is from the book.