Statistics: Hypothesis testing to find p-value I am currently writing a thesis in machine learning and I am trying to use t-test to show that my model is better than the current state of the art. The dataset I used has 16 different tasks and each of the mean performance and the number of dataset for each task are as below:

dataset =
[2690,76,55,898,3758,69,787,392,1547,451,202,184,283,66,152,5271]
comparison1=
[84.6,86.3,87.2,81.1,91.1,76.5,92.6,88.4,82.7,96.2,78.1,95.8,85.4,69.0,82.0
,83.6]
proposed =
[85.8,87.2,90.8,81.4,91.4,81.5,92.8,88.2,84.9,96.4,77.9,96.5,84.8,69.1,
78.2,84.1]

I would like to find out whether my model has improved or not using t-test and so far I calculated it by creating a new list that repeats or replicate the mean performance by the corresponding number of dataset.

(e.g. full_comparison1 = [comparison1[0]]*dataset[0]+[comparison1[1]]*dataset[1]+[comparison1[2]]*dataset[2]...

Then, I used scipy from python to calculate p-value:

scipy.stats.ttest_ind(full_proposed , full_comparison1 , equal_var=True)
Ttest_indResult(statistic=13.868700994408345,
pvalue=1.2916487642703654e-43)

This result tells that the difference is significant, but it seems that p-value is way too small. Could somebody please let me know whether I have done it correctly or not?
Thank you so much!!
 A: I have no idea from your description whether
samples comp and prop both of size $n = 16$
are intended to be independent samples, or paired
element-by-element.
Both comp and prop pass Shapiro-Wilk tests as
consistent with sampling from normal distributions.
And normal Q-Q plots are suitably linear. So it seems
safe to do t tests.
However, both have sample means near $85$ and in R neither a 2-sample Welch t test
nor a paired t.test gives a significant result.
summary(comp)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  69.00   81.78   85.00   85.04   89.08   96.20 
summary(prop)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  69.10   81.47   85.35   85.69   90.95   96.50

The high correlation between comp and prop seems
to indicate paired data---as does the scatterplot.
cor(comp, prop)
[1] 0.9649813

stripchart(list(comp, prop), ylim=c(.5,2.5), pch="|")


plot(comp, prop, pch=20)
 abline(a=0, b= 1, col="blue")


The P-value $0.1914 > 0.05 = 5\%$ does not show
a significant difference.
t.test(comp,prop, pair=T)

        Paired t-test

data:  comp and prop
t = -1.368, df = 15, p-value = 0.1914
alternative hypothesis: 
 true difference in means is not equal to 0
95 percent confidence interval:
 -1.6627189  0.3627189
sample estimates:
mean of the differences 
                  -0.65 

The t-statistic $T=-1.368,$ can also be
found as shown in the R code below:
d = comp-prop
mean(d)/(sd(d)/sqrt(16))
[1] -1.368042

For the record, a two-sample Welch t test also gives non-significant P-value $0.799.$
t.test(comp,prop)$p.val
[1] 0.799499

Bottom line: From what you show, I cannot figure out how you
did which t test nor explain your P-values. Please
edit your question for clarity if I have missed
something.
