Dear all,
I have recently conducted an experiment involving the study of how genes respond to varying levels of radiation, and at different time-points after exposure. The experimental conditions are as follow: 4 independent subjects (n = 4), 3 radiation doses, and 4 time-points.
Question: Which statistical test would be most appropriate for use to investigate the dose effect and time-effect on the genes of interest?
Essentially, I would like to understand if:
1. An increase in dose changes the gene expression significantly (dose-effect)?
2. An increase in time post-exposure changes the gene expression significantly (time-effect)?
Would appreciate any advice! Thanks.
In my opinion you can go for T-test or F-test.
https://www.khanacademy.org/math/statistics-probability/significance-tests-one-sample/more-significance-testing-videos/v/z-statistics-vs-t-statistics
https://www.khanacademy.org/math/ap-statistics/estimating-confidence-ap/one-sample-t-interval-mean/v/introduction-to-t-statistics
Hi Elvin,
indeed you have a complicated analysis. I imagine that different pools of 4 subjects receive the different radiation doses. But then the same subjects are analysed at different time-points? This is important.... I also imagine you have a control conditions, such as gene expression of all subjects before the start of the experiments or you have an independent group of subjects for basal gene expression. Also this is important to decide if you need to do paired-tests or not... Anyway, if your data is normally distributed (n=4 is not much, but you can test with a Shapiro-Wilk test), you should apply ANOVA.
If you are interested in the separate effects of dose or time, then a one-way ANOVA with the factor being the dose or the time-points will suffice if subjects are different in every experiment. But is the time-points are taken on the same subjects at every dose, then you should use a repeated-measures ANOVA for the time. As you see, repeated measures represent the pairing of the experiments. So if you have a basal gene expression for the subjects you treat, it complicates a lot, because each subject should be paired with the respective treatment it received. In this case you will have to do individual tests, although I would in general forget the t-test when you have so many multiple comparisons due to type I errors. But you could use corrections such as divide the significance value by the square root of the number of comparisons.
If you are interested in a possible interaction of dose and time then a two-way ANOVA test will be best suited, where the two factors are the radiation dose and the time-points or one factor will be the dose and you will have repeated measures for the time (see above, pairing...).
Of course the ANOVA test will have to be followed by post-hoc tests such as Tukey or Bonferroni. These are sort of t-tests corrected for multiple comparisons to avoid false positives (or type I errors, as I was mentioning previously) and will tell you which pair comparisons are significantly different.
I guess no statistical analysis is perfect, but you can try to be the most reasonably accurate as possible...
Good luck!
Dear Dr Chua
None of the above responses are correct.
The closest to being correct is Dr Hayakawa. The Normal (Guassian/Laplace) distribution does occur in nature but mostly in phyics and chemistry. This is because the data sets there tend to be larger than those in biology.
ANOVA and to a lesser extent the F test is sensitive to departures from normaility.
The t test is relatively insensitive to non normality but this depends on how non normal the data is.
The first thing anyone wants to know is what does the data look like? Is it normal - or reasonably so - or not?
If the data is very non normal non parametric tests - Friedman or similar - may be useful. An alternative may be to use a boostrap.
To comment much further the distribution of data would be to be clarified.
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