I am finding that there is no significant difference between a number list and another list which has 100*same numbers. The P value is 0.4487. The means are obviously very different (100 times). Why is it so?
Following is code and data in R:
> t.test(vnum, 100*vnum)
Welch Two Sample t-test
data: vnum and 100 * vnum
t = -0.7637, df = 49.01, p-value = 0.4487
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-41.72902 18.74726
sample estimates:
mean of x mean of y
0.1160695 11.6069527
vnum
[1] -0.895220890 0.472985786 -1.153668533 0.299671810 -0.507962145 1.126608614 -1.964113989 -0.102483497 0.869147815
[10] 0.124949840 0.007075569 1.050399452 0.127889864 0.495323100 -1.442668978 -0.617975264 1.142867644 -1.423523025
[19] 0.426532832 -0.186958315 1.648847799 -0.460224243 1.654329219 0.740546166 -0.558588185 2.876850041 0.829542673
[28] -0.409403714 0.226379412 2.722903972 0.664555431 0.661642150 0.479198746 -0.188802783 0.667357712 0.642126933
[37] -1.811820215 -0.117047084 -0.698122450 0.152198274 -0.153932133 -0.344854070 -0.503635532 0.442124918 -0.998293019
[46] 1.219133756 1.178315011 -2.084715497 0.804313978 -1.326328611
>
>
> dput(vnum)
c(-0.895220889527685, 0.472985785738034, -1.15366853263124, 0.299671809636945,
-0.507962145051303, 1.12660861411969, -1.96411398863887, -0.102483497414014,
0.869147815091296, 0.12494983977689, 0.00707556874660856, 1.05039945202467,
0.127889864073583, 0.49532309962209, -1.44266897772691, -0.617975264009241,
1.14286764387227, -1.42352302483503, 0.426532831792985, -0.18695831493576,
1.64884779946544, -0.460224242900372, 1.65432921872007, 0.740546165726594,
-0.558588184596504, 2.87685004055853, 0.829542673396929, -0.409403713666942,
0.226379411797594, 2.72290397151737, 0.664555431373864, 0.661642149516906,
0.47919874642046, -0.188802783058076, 0.667357712376591, 0.642126932641534,
-1.81182021542319, -0.117047083654143, -0.698122449877863, 0.152198273727932,
-0.153932132867208, -0.344854070273716, -0.503635531971558, 0.44212491839201,
-0.998293018734691, 1.21913375551535, 1.17831501135198, -2.08471549710629,
0.804313977822178, -1.32632861087304)
EDIT: As suggested in the answers and comments, I checked "boxplot(vnum, 100*vnum)". It is really impressive:
boxplot(vnum,100*vnum)
$\endgroup$