For example, a comparison needs to be performed between the means of 2 populations. I have two values from each group. I want to check the significance. Which test can be used? Mann Whitney?
Mann-Whitney is not a test for difference in means. Further, it can't become significant for less than 4 values per group.
If the assumptions are not violated you can perform a t-test. The problem (here as well as with any other test, no matter if "parametric" or not) is that you can not check if this data might violate the assumptions. So any argument for this must come "from outside", from other data, similar data, scientific reasoning. And you will have to hope that the reader/reviewer will follow you and believe that the assumptions won't be (severely) violated.
[edit: typos]
Regardless of distribution of the two populations you need to have minimum necessary information to compare both of them and mean alone without standard deviation being mentioned (either equal or not) may not be enough to test the significance in difference of mean. students t-test will suffice if you describe the means, slandered deviations and the number of sample-size for each group on which the mean is based.
Dear Rajpal, Statistics is a tool and a language. If we want to speak in a language we need enough words, in statistics, we need enough repetitions to speak around a subject.
Rajpal. Even though "significance" is not important in my opinion,we may also asume that each one has a frequence p=1/N=1/2 as it is used with bigger samples. Let's suppose that your two X variables are 15 and 5, so you obtain total media, T=10. This means that the tall sector has an average of U1=15/10=1.5 medias and the lower sector of U2=5/10=0.5 medias. In this cases always U1+U2=2 and Standard Deviation, SA= {(0.5)^0.5]/2 or SD=0.717068...
But if you have U1+U2 > 2 immediately the fractions P1,P2 are not equally split, so the distribution can not be symetrical at all. Gauss premises are broken and loose relevance; other distributions may be observed and if we build the 3 possible points of Lorenz Curve we obtain:
(0;0); (0.5;0.75); (1;1). we´ll find that X1
Lets suppose I have treated cells with a drug but experiment was done only twice (no duplicates). now I want to see the difference between treated and untreated cells. is it possible? if not minimum how many data points I need?
I understand you measure twice each treated individual, so you obtain an average Xi. I imagine you also measure twice a non treated individual, so you obtain another average X2 i.The two cases refer to two different contexts, if you analyse each context for more individuals, let's say n=10, each data set will show its own media and its own distribution structure. Then you may compare the two medias, the two structures and their graphs in order to interpret them according to your own experience in the field. If there is only one individual in each group I see quite difficult to arrive to a general conclusion that includes other persons different to your two studied ones and it would be better to include more persons in each contextual group. Even with your one individual case per group there is a gain of experience and information as a preliminar research test, perhaps not as precise as you need but good as a starting reference. Once you do it with more persons included, you may observe the position of your one person results in the new distribution obtained, for treated and untreated cases. Ok, good luck, emilio
If I understand clear you have done two experiments such a kind: put some drug into cell population, and after some time (let say Tg) count total amount of cells (Nd1 and Nd2). And now the question is what is the uncertainty of the results (delta Nd1 and Nd2)? If so, I think you have a possibility to evaluate the uncertainty using clear cell population. Just try to prepare M initial cell populations as you done for your experiments before, let them grow during time Tg and after that count the number of cells in each sample again (Ni). After that using simple base of statistic one can obtain mean (sum of Ni divided by M) and standard deviation (sum of differences: (mean square - square mean) divided by M). The standard deviation will be the measure of uncertainty your experiments.
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