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I am testing cell cultures. I grow cells in a "control media" for 2 weeks. During these 2 weeks, the cells produce an antibody, and at the end of the 2 weeks, I measure the levels of the antibody. I also measure cell growth (the number of living cells).

The problem is, because it is a biological living system, if I do the experiment 5 times (in exactly the same manner as described above), I will have substantially different numbers for cell growth and antibody production. For example, in 5 experiments I found cell growth: 46, 59, 50, 77 and 74, and antibody production: 2558, 3089, 3498, 2115 and 1958. These variations can even be higher, depending on my test sample.

Can anyone suggest, how can I correct for this kind of inter-experimental variation.

thanks.

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If there is a physical/biological/experimental way of improving the precision and reducing this natural variability, then it is possible. If not, then you have to deal with this. This is, depending on your goals, you have to include this characteristic in your statistical model. What are you planning to do with these data? – user10525 Jun 12 '12 at 10:45
Interesting question. When i perform the above experiment with a test sample- i see variability and that's exactly what i study! so, i would like to separate the variability due to "inter-experiment variation" and variability due to "variation in test samples". for e.g. the variation in test samples is like if you have 10 biscuits of same quality of brand A- they slightly differ in their quality due to production process, raw material etc.. hope it is clear...if you have any ideas.. thanks. – abhishek Jun 12 '12 at 10:53

2 Answers

up vote 4 down vote accepted

If the high variability in cell culture tests is just random variation there is nothing special that can be done about it other than the reduction in variance that averaging provides. However, if there are differences among the tests that can be explained through explantory factors, a linear model could be used to reduce the uncertainty. Regarding your comment above about separating the inter-experiment variability from the intra-experiment variability you can perform a simple one-way ANOVA with experiment as a factor.

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thanks for your input...may be you can refer to my comment above..and if you have any ideas about it? thanks a lot... – abhishek Jun 12 '12 at 10:57
+1 For one-way ANOVA – user10525 Jun 12 '12 at 11:39
thanks Michael and Pro...I will check this out. – abhishek Jun 12 '12 at 12:14

It may be useful to distinguish between "repeats" and "replicates" in this case. The terminology is definitely not standardized, though.

In this case, your description might be interpreted as a single study with five "repeats". That is, the five experiments were all conducted during the same two weeks, perhaps on the same lab bench. No experimental intervention was performed (for example, dosing the cells with some chemical, or changing the type of media, or varying the temperature, etc.). In this case, there is not much to be done other than to calculate the variation (e.g., by using the sample standard deviation). The sources of variability here are probably primarily biological.

Or, your description might be interpreted as a set of serial studies, with each study taking two weeks. In each study, you may or may not have had multiple repeat experiments. I would call this situation "replicates" in this case, because you have replicated the entire study. It would be reasonable to call these "blocks", also.

If you only had one repeat in each replicate, then it is more or less the same situation as before --- simply calculate the sample standard deviation. However, in addition to the biological variability, the variability now includes anything else that may have changed across the replicates, including both "random" variation and any systematic effects happening over time.

If you had more than one repeat per replicate, then you can think in terms of partitioning the variance between repeats and replicates. This is the situation in which the one-way analysis of variance would be useful, though you would probably wish to think of replicates as a random effect rather than as a "fixed" effect. This has gone under the name of variance components analysis in the past. Here, the two components would be repeat-to-repeat variance (presumably mostly biological and assay related) and replicate-to-replicate variance (presumably relating to experimental set-up or any other time effects).

To be honest, though, this is all probably not of major interest to you. Most likely what you will be doing down the road is applying experimental treatments of some sort, such as varying the media, varying the cell types, or doing things to the cells. You will then want to know the effects of these experimental treatments upon antibody production and cell growth.

But, at that point, you will be able to use the data from these preliminary experiments to decide how to structure your studies. The choices you will have to make are things like: How many repeats should you allocate per experimental treatment? How many replicates should I perform?

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