I have done qRT-PCR on 20 genes in 5 groups. qRT-PCR data was analyzed using the 2−ΔΔCt method. No replicates. Suggest analysis test like One-way Anova to find the significant difference among the groups.
Without replicates, your main problem is not with the statistical test but with representation: How do you know that your data are representative of anything?
For two groups:
The t-test (parametric) or Mann Whitney (non-parametric).
For three or more groups:
One way ANOVA (parametric) or Kruskal Willis (non-parametric).
Selecting either parametric or non-parametric test use;
Levene's test to check for equality of variances and
Kolmogorov–Smirnov test or Shapiro–Wilk test to check for normality.
You can clearly see that sample variance is at the centre of these tests, thus you really need replicates to calculate sample variance.
There is a concern with applying statistical tests after you have collected data. The proper way is to;
1. Determine your research question
2. Determine the statistical test suitable for that question.
3. Determine the appropriate sample size with enough power.