Why does the p-value increase when I add more observations to my t-test?

You seem to have made a miscalculation in your t-values

If you apply

$$t = \frac{x_1-x_2}{\sqrt{sd_1^2/n+sd_2^2/n}}$$

then your second result seems to have not been using $n=30$ (but instead the value $n=15$).

That aside

I expected that adding more observations would make the result more statistically significant, but instead the p-value increased and the result is no longer significant at α = 0.05.

P-values do not necessarily decrease with increasing observations. (that's only true when there is truly an effect, and even then due to statistical variations the values will fluctuate and can also rise)

What primarily changes is the accuracy of the estimate that you make.

Confidence intervals can illustrate this very well.

• With n=15 you got the estimated mean difference A-B is 4.2 with a 95% confidence interval of $[0.45 , 7.94]$.

• With n=30 you got the estimated mean difference A-B of 3.6 with a 95% confidence interval of $[0.91 , 6.29]$.

(so your second result was still significant if you change this $n$ in the formula, but say that we got an effect of 2.6 with interval $[-0.09 , 5.29]$)

So, more observations will make a result more accurate. Typically the confidence interval, the error of the estimate will decrease. As you see in the figures above, the interval got smaller.

But at the same time the estimate can shift.

Significance (in null hypothesis testing) doesn't mean whether your result is accurate or not but whether 'zero effect' is within the range of accuracy or not.

I used these calculations in r to get the intervals

(52.3-48.1)+
(sqrt(4.8^2+5.2^2)/sqrt(15))*
qt(0.025,28)*c(1,-1)
# 0.4571466 7.9428534


(52.6-49.0)+
(sqrt(5.0^2+5.4^2)/sqrt(30))*
qt(0.025,58)*c(1,-1)
# 0.9104385 6.2895615

The t-test boils down to comparing the separation between groups (i.e., the difference of the means) to the spread within groups (the standard deviations).

In this particular case, adding more data

• brought the means closer together (52.3 - 48.1 = 4.2, but 52.6 - 49.0 = 3.6)
• increased the standard deviations (4.8 -> 5.0, 5.2 -> 5.4)

Thus, the resulting p-value is a bit larger because the groups are "harder" to distinguish. How should you interpret this?

P-values often decrease with larger samples because that data allows more precise estimates of the mean and standard deviation. That didn't quite happen here. If the sample sizes and differences were larger, I might wonder whether your initial data only came from part of the population, but I think this is likely just random sampling error. The P-values themselves are random variables and are thus affected by that sampling. You could try to convince yourself of this by running t-tests on sub-samples of 15 observations from the larger dataset. You'll find some that are close to 0.03, some that are close to 0.07, and some that are larger and smaller.

It is also important to be aware that "The Difference between Significant and Non-Significant is not Itself Statistically Significant", as the paper of the same title points out. Intuitively, imagine I told that one number was between 1-3 ("different from zero") and another was between 0-5 (not). Could you reliably say which is likely to be larger? Nope. Thus, I would not read much of anything into the difference between 0.03 and 0.07.

The simple answer is that you made a computation error.
I used a Welch t-test, because one should always use a Welch t-test.
For the sample of 15, I obtain $p=0.029$, and a CI of the difference of means of $[0.451, 7.949]$.
For the sample of 30, I obtain $p=0.01$, and a CI of the difference of means of $[0.909, 6.291]$

So as you see, the p-value went down, the CI is further away from $0$, and the width of the CI has been narrowed. So nothing to wonder about...

Note that in your case, the p-values are virtually the same for a Student t-test, as you have balanced sample sizes, and very similar variances. So the error is some other data entry. And there must be multiple errors.
E.g., for the sample size of 30, you report $t=1.81$, when it should be $t=2.68$; but then you also report that $p=0.075$ for $t=1.81$. That is also incorrect as $p=0.81$ for $t=1.81$. I am not sure which software, tables, calculator, etc. you are using, so it is difficult to dig further.
If you want to check for yourself, I can recommend this calculator for the Student t-test, or this calculator for the Welch t-test. They are both quite didactic, show the various aspects of the test, the formulas, etc.

Now, should one always expect a lower p-value when increasing the sample size? Usually yes, but not always. It will depend on the change in the difference of means, and the change in standard deviations. In your case, these are not very large, so yes, you should have expected this, and indeed, properly computed, that is what the data says.