The descriptive statistics can be used to determine the inferential statistics.
> lapply(list(Outcome1, Outcome2), function(x) c(length(x), mean(x), sd(x)))
[[1]]
[1] 4.00000 2.00000 2.44949
[[2]]
[1] 4.00000 6.00000 2.44949
The descriptive statistics are calculated separately for each instance (which are shown as separate variables).
The inferential statistic shows the key elements to be calculated.
> t.test(Outcome2, Outcome1, paired = TRUE)
Paired t-test
data: Outcome2 and Outcome1
t = 3.266, df = 3, p-value = 0.04692
alternative hypothesis: true mean difference is not equal to 0
95 percent confidence interval:
0.1023152 7.8976848
sample estimates:
mean difference
4
Here, t = 3.266 and p = .047. This would be considered a statistically significant finding.
Using the confidence interval, the researcher estimates that the true population mean difference is somewhere between 0.102 and 7.898 (knowing that the estimate could be wrong).
Cohen’s d is not shown here, but can be calculated from the available information (d = -1.633). Given Cohen’s heuristics for interpreting effect sizes, this would be considered an extremely large effect.
For this analysis, the differences between two measurements on one set of people are being compared. Thus, the summary and the inferential statistics focus on that difference.
A paired samples t test showed that the difference in Outcome scores (N = 4) between the first time point (M = 2.00, SD = 2.45) and second time point (M = 6.00, SD = 2.45) was very large and statistically significant, t(3) = 3.27, p = .047, 95% CI [0.10, 7.90], d = 1.63.
Alternatively, the means, standard deviations, and confidence intervals could be presented in a table or figure associated with this text.