How do I calculate a t-score from a p-value (gain scores and N also available) I have this problem that only the gain scores with the p-value of a t-test are given in a scientific article. The authors neglected to report the t-test statistic and I'm stuck on figuring out how to calculate a t-test statistic from a p-value. The gain scores (difference in scores before and after an intervention) are given and the sample size is also known. 
How can I calculate this t-score? 
 A: I'm guessing (hoping) this is a one-sided one-sample t test, where the 'gain' for
the $i$th subject is a difference $d_i$ and the test statistic is
$t = \bar d \sqrt{n}/S_d,$ in which $\bar d$ and $S_d$ are the mean
and standard deviation, respectively, of the $n$ differences.
Let $\delta$ be the population mean of $d_i$. Then one would reject $H_0: \delta = 0$ against $H_a: \delta > 0,$ for sufficiently large $t.$
The P-value, would be the probability under the density curve of
Student's t distribution with $n -1$ degrees of freedom beyond
the observed $t$ statistic. If $T$ is a random variable with
that distribution then the P-value $p$ is $P(T > t)$. That is,
$1 - p = P(T \le t).$  
The value $t$ you wish to reclaim from the reported $p$ is then
the inverse CDF (quantile) function of $1 - p$.
For example, if $n = 16,$ and $p = 0.037,$ then we could use
statistical software to obtain $t = 1.92$.  In R, the
code qt(1-.037, 15) returns 1.920596.  
A difficulty may be that P-values are not reported to many decimal
places, especially when $p$ is too large to lead to rejection of
$H_0$ at some significance level such as 5%. As a 'reality check', in my example,
the critical value for a 5% level test (separating acceptance
and rejection regions) is given by R code qt(.95, 15) which
returns   1.753050 (probably 1.753 in a printed
t table).
Possible difficulties: (a) Your retrieved values of observed
$t$ might be only approximate if $p$ is rounded.
In the example above, if the P-value is reported as $p = .04$,
my suggested procedure gives $t = 1.88$. (b) You must know $n$ to get the degrees
of freedom. Or, if $n$ is very large, you might get a useful
approximation from standard normal tables. (c) If the
alternative is the two-sided $H_a: \delta \ne 0$, then that alternative
will be rejected for large $|t|$ and you won't be able to
know whether the observed $t$ is positive or negative.
(d) If this is a two-sample t test, you can still retrieve $t$,
provided you know the degrees of freedom. (For the pooled version
of the test $DF = n_1 + n_2 - 2$, but for the Welch (separate-variances)
version you would need to find $DF$ via a formula that involves
both the two sample sizes $n_1$ and $n_2$ and the standard
deviations of the two samples, which I'm guessing will not be
reported if $t$ isn't. 
A: Why not just look it up a T Table or just punch the numbers in excel? I get the elaborate explanation above and good job at it but feels a bit overkill. In excel you can use T.INV. Just that you need degrees of freedom (which for the t distribution is n-1) for the second argument in T.INV(). And then just adjust based on what test it was upper, lower, two tailest test etc
