One-way ANOVA and Two-sample T-test give different results for two groups

#1
Hello guys,

So i tried conducting a two-sample t-test and i wanted to prove that it will be the same for the one-way ANOVA as i have done before in the past.
The only problem is that i get different p-values. My F-value is equal to t-squared so that is checked out but the p-values are different and i believe this is not suppose to happen. Is this due to small sample sizes? my data is:

before after
11 1
9 0
51 1
16 0
8 0


so N=5 for both groups. It is not possible to do more tests. But the weird part is that the pvalues differ and i cant explain why. I showed the results below


Two-Sample T-Test and CI: before, after

Two-sample T for before vs after

N Mean StDev SE Mean
before 5 19.0 18.2 8.1
after 5 0.400 0.548 0.24


Difference = μ (before) - μ (after)
Estimate for difference: 18.60
95% CI for difference: (-3.95, 41.15)
T-Test of difference = 0 (vs ≠): T-Value = 2.29 P-Value = 0.084 DF = 4


One-way ANOVA: before, after

Method

Null hypothesis All means are equal
Alternative hypothesis At least one mean is different
Significance level α = 0.05

Equal variances were assumed for the analysis.


Factor Information

Factor Levels Values
Factor 2 before, after


Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Factor 1 864.9 864.9 5.24 0.051
Error 8 1319.2 164.9
Total 9 2184.1


Model Summary

S R-sq R-sq(adj) R-sq(pred)
12.8413 39.60% 32.05% 5.62%


Means

Factor N Mean StDev 95% CI
before 5 19.00 18.15 ( 5.76, 32.24)
after 5 0.400 0.548 (-12.843, 13.643)

Pooled StDev = 12.8413
 

Karabiner

TS Contributor
#2
The first is a t-test for dependent samples (n=5 intra-individual differences; the mean intra-individual
difference is compared with zero difference, df=4).

The second is a test for independent samples (n=10).

With kind regards

Karabiner