I have a sample size of 23, with 11 and 12 participants in each group. I conducted t-tests for several continuous dependent variables. All of them are non-significant, but some of them have quite high Cohen's d values (for example 0.6 or above). In addition, the confidence intervals in these cases, while still spanning zero, usually have one case which is very very close to zero.
As an example, one of the tests has a Mann-Whitney U value of 41, a p-value of .11, CIs of -0.00004 and 1.2, and cohen's d of 0.75. How should I interpret this finding? Intuitively I would say it is a power problem, but with medium-large effect sizes I am not sure, since even small samples would theoretically be enough to detect such effects.
I used the jamovi package in R to conduct the tests
ttestIS(data = dat, vars = vars(variable_1, variable_2, variable_3, variable_4, variable_5), group = condition, students = FALSE, mann = TRUE, meanDiff = TRUE, desc = TRUE, effectSize = TRUE, ci = TRUE, plots = TRUE)
Update: I went off the effect size interpretations specified by Cohen (0.2 = small, 0.5 = medium, 0.8 = large). The dependent variables are self-report questionnaire items on a 5 point likert scale. The responses were non-normally distributed, hence the use of Mann-Whitney U tests.