I have two columns of data that show the values for R1, R2, R3, R4, R5, R6 and R7. Among these two columns, values in one column is always fixed and the values in the other column vary. Please note that the fixed values are the desired values always. In addition the values are less than 10 always.
My questions are
1. Is this data enough for statistical analysis
2. If yes, what is the best method
3. What can be my null hypothesis
1. How much replications do you have for "R"? If you have at least two replications of "R" you can do statistical analysis, but maybe you have problems with power analysis (insufficient replications)
2. You can use the generalized and mixed linear models
3. H0: R1 = R2 = R3 = R4 = R5 = R6 = R7.
H1: al least one "R" are different from the others
If you explain me more details maybe I can help you more. I believe you can't to compare the two columns, both are differents. One is the factor and the other one is the response. It´s correct?
Test for equality of variance (F test): H0: the two datasets have equal variances
test for equality of means (t test): H0: the two datasets have equal means
Would the "fixed" data be x-values in a regression, with the other data being the corresponding y-values??? Then you might be looking at the variances of the prediction errors?? A residual analysis perhaps?
If you just had two samples and wanted to compare means, I'd suggest a confidence interval around the difference in the estimated means, but you seem to have some complication. At any rate, I'd warn against the idea of so-called "significance," as it is an incomplete concept. (You might research the terms "power," "type II error," and "effect size.")
Best wishes.
I have one set as R1=3, R2=1, R3=4, R4=4, R5=3, R6=3, R7=2 . The other set of values is fixed, i.e., R1=10, R2=9, R3 = 5, R4=5, R5=7, R6=8, R7=5 (reference standard). The values in the first set can be either above or below the reference standard. I think this will help you to get a clear picture to suggest possible statistical analyses.
@ Amin, thank you for the information. As Mr. Knaub suggested, is there any possibility to do confidence interval around the difference in the estimated means.
I agree with Raid. It sounds like you only have one datum for each of seven different experiments.
You might see if there is some way to graphically plot your data, if that makes any sense to your application, to see if anything stands out.
If there is some kind of overall meaning to your data ... that is, there is some overarching principle ... you might try letting the "reference standard" (not my field ... I don't know what that means) be x and the other data y in a scatterplot ... if that makes any sense.
But if each pair of observations (and I am assuming that a "reference standard" is paired with a single observed value) is unique, then you do not have enough information for inference, as Raid noted.
Best wishes.
You could create a bar chart in which you use two different colors for each bar, representing actual score in one color and standard score in the second color. You can order the seven bars according to maximum difference between standard and actual scores. This will be similar to following the Pareto Principle.
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