# What an experimental design is this?

I collect blood from one human (donor), separate leukocytes and put $2\times10^6$ of them per each well of five:

• well 1: $2\times10^6$ Lk (leukocytes)
• well 2: $2\times10^6$ Lk
• well 3: $2\times10^6$ Lk
• well 4: $2\times10^6$ Lk
• well 5: $2\times10^6$ Lk

(Lk consists of a mix of different sets of cells and one of them are lymphocytes (Lph)).

Then I incubated the cells under different conditions (with the following substances in the same concentration (with the exception of well #1, of course)):

• well 1: saline (serves as a zero control)
• well 2: substance A (is a native compound)
• well 3: substance B (is a chemically modified analogue of A)
• well 4: substance C (is a chemically modified analogue' of A)
• well 5: substance D (is a chemically modified analogue'' of A)

Then I incubate the leucocytes for 24 hours.

Then I run FACS and get percentages of lymphocytes expressing a receptor (CD69) of interest (Lph') (where the percentages is the ratio of Lph' to all Lph).

Then I repeated the experiment 7 times: i.e. totally I collected blood from 8 different donors (so $n = 8$).

With this experiment I want to know:
Does a structure of a molecule affect the percentage/proportion of activated lymphocytes (Lph') (i.e. Lph bearing CD69 molecule)?

My example data (in percentages, %) are:

DonorID  cntrl  substanceA  substanceB  substanceC  substanceD
20       5.1    12.42       10.10       9.58        8.54
21       4.07   9.96        14.12       10.79       12.24
22       3.94   4.92        13.04       15.96       9.37
25       0.60   3.24        8.94        0.61        3.62
26       1.72   13.96       2.48        3.44        3.12
27       0.53   3.36        1.40        4.00        0.81
28       0.97   3.88        2.33        3.77        3.31
31       0.15   4.05        1.45        2.44        1.47
32       0.58   1.92        2.47        2.33        4.92
33       1.02   6.03        4.40        4.80        3.88

SUMMARY:

So the experimental design can be characterized by the following terms:

• ANOVA as more than 2 groups are tested;
• RM as the statistical/experimental unit ("Lph") for every case is under different conditions;
• one-way there is one fixed (within-subject) factor / independent variable ("conditioins") with 5 levels; if I'm not mistaken in the light of linear mixed models the "DonorID" might be interpreted as an additional random factor ("donor").

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@stan: If I understand correctly, your sample size was 8, that is, you collected sample from eight humans? I would also like to ask if substances A, B, C, D effect Lph in the same way ? I would think of them as different treatments. I think you experiment seems like a split-plot design of which repeated measures is a special case. Please clarify; it would help us answer your question in a better way. –  suncoolsu Jun 14 '11 at 2:27
@suncoolsu: Q1: "...you collected sample from eight humans?" A1: yes, i collected blood eight times from eight different people (given that 1 collection per 1 donor). Q2: "if substances A, B, C, D effect Lph in the same way ?" A2: well, i wanted to know it that's why i run the tests. but looking at the numbers, yes the substances affect Lph differently. Please note: we modified substance A to obtain its B, C, D derivatives and tested all substances all together with untreated cells to find (if any) the role of different chemical groups in substance A looking at the biological activity of its c –  stan Jun 14 '11 at 5:27
Yes within subject designs are repeated measures. This might help you see why this experiment follows that design. It sounds like you don't have to worry about carryover effects since you tested the samples ex vivo (unless I misunderstood the description of your experiment) so you get all of the advantages with apparently none of the potential concerns of the procedure. Here is an example of how to do this sort of analysis and interpret the results from SAS. –  Chris Simokat Jun 14 '11 at 13:48
@suncoolsu: thanks a lot for your response :). @Chris Simokat: thanks a lot for your links:) –  stan Jun 14 '11 at 23:40
@stan repeated measures seems appropriate for your design. –  Chris Simokat Jun 18 '11 at 1:27