Hi, hoping to get some help with whether I can use a paired t-test for this dataset.
An experiment was run under identical conditions, each day, for nine days. On each day cells in a plate were exposed to EITHER control or drug and a measurement made of expression of a fluorescent marker to give the following dataset:
Day 1: Control = 2.5, Drug = 8
Day 2: Control = 1.3, Drug = 1.9
Day 3: Control =1.1, Drug = 1.7
Day 4: Control = 4.3, Drug = 5.3
Day 5: Control = 2.7, Drug = 4.1
Day 6: Control = 11.9, Drug = 14.1
Day 7: Control = 3.3, Drug = 3.9
Day 8: Control = 9.6, Drug = 11.3
Day 9: Control = 10.1, Drug 11.7
I want to test whether there is a significant difference between Control and Drug.
The data from each Day did not come from an individual sample exposed to both the Control (before) and Drug (after), so I initially assumed this was unpaired data, and ran an unpaired t-test: p = 0.42.
However, the data is paired within each day, and if I run a paired t-test: p= 0.01. Clearly, there is variability in the baseline from day to day, so this is not unexpected and I think a paired t-test in this respect may be logical.
Is it appropriate to run a paired t-test on this data?
Thanks for any advice
Yes, you can, and it seems that you should (because there seems to be a major day-to-day variability, so "day" is a relevant source of "common variance", which is controlled for in a paired test).
Note: multiple regression model allows to control for more than only one common source of variance.
Note: Using a random intercept term by "day" (in a mixed model) would be a slightly more modern and way more flexible approach to handle different sources of variance, but in this simple case the results will be identical to that of a paired t-test.
Just following Jochen Wilhelm 's first note, do you know what differences between days there were that may be important? I would think one question to ask is whether the experimental effect (higher for all 9 days) is a similar effect to whatever may be influencing the differences among days.
Daniel Wright , this is data from cultured cells. To my experience, cells grow differently every time you grow and seed them. It's quite common to get read-outs that vary (sometimes a lot) from day to day, for no obvious (or known) reason. But maybe cell biologists know more.
Thank you for your responses!
Jochen Wilhelm - thank you for confirming that Day is a relevant source of common variance, allowing me to legitimately use a paired t-test. I was hoping that this was the case.
Daniel Wright - There are a number of factors that could influence this, but as Jochen Wilhelm noted, cultured cells are sensitive to variability. One possibility is that we have a mixed cell population and the proportion of cells sensitive to the drug is changing from preparation to preparation.
Thanks again.
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