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