To elaborate a little: you need to generate a boxplot where x-axis = samples, y-axis = intensities. Quantile-normalized data has approximately equal medians, upper and lower quantiles.
Hi,
I have miRNA microarray expression data. It's claimed that it's quantile normalized, but I'm are not sure about it. is there any method to check this?
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This depends on the answer to jobinv's question in the comments on your post, but I suspect you just mean "has (any) normalization been performed?". To simply determine if a normalization procedure has been run, just dump the values and assess the data yourself:
Raw data ...

... is background corrected ...

... and then quantile normalized

You can also just assess the average expression of all probes/probesets for each array - any large deviance would suggest you're not looking at processed data.
great. let's consider a case, where data is normalized, but we don't know which normalization method are used . how I can detect it ?
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Do you mean as opposed to having been normalized by other methods than quantile, or as opposed to having been normalized at all?