First some advice: NEVER collect data without considering the statistics of the situation. I believe that you will see why in a minute. I am hopeful that we can do something with your data. Let's see. We'll begin by making a rough data table of the experiment you described.

day 0 cmpd added Variables DV-not mentioned so

we assume a Growth curve was done on all DAYS Values

DAYS control treatment cell type

0 no trt trt w/ cmpd w/o cmpd 1,2

4

7

10

Now my friend you appear to be a PhD student so I will treat you exactly like I treated my students

Comments 1. you didn't even say what you measured, that's your DV. how do you expect anyone to help you if you didn't tell them what you measured in your experiment. Now I assumed you measured cell concentration (bacteria, Phage, yeast, N. crassa, whatever)

2. you measured at 4, 7, 10 days these are not enough to make two growth curves. I know because I spent 4 undergrad years doing these(TMTC) in mutagen solutions

in Herman Brockman's lab. Perhaps you did a growth curve on each day that would be better. However you said you did not do it on day 0-THAT WOULD BE YOUR CONTROL.

So you now have an uncontrolled exper w ino base line measure.. The major variable here is treatment time-this is a repeated measure or longitudinal design. The other major variables are treatment and cell type. you should have sent a table like the one I tried to make based on your description. You notice if you do that the errors become clear. PROPER PRIOR PLANNING PREVENTS POOR PERFORMANCE

After doing all of this you would have a correct version of the table I tried to make.

Now you THINK ABOUT Collecting data. Suppose you do what I described. BTW

you don't have a research question which would have told the DV which would be a real help.

3. Lets suppose you made the above corrections and I was right about your DV

Further let's suppose a decent growth cure was done on all four days for the treated flask and flask with no treat compound the experiment is the same for both treatments.

4. now the first day I I was in Prof. Brockman's lab I dropped a 12 liter Florence flask. Suppose such a thing happened to you.. on day 7. You apparently have a compound treated flask and and a non- compound flask. Then your experiment is, using a technical term, Kaput. Wouldn't it be wise to a backup? now you're growing cells so I assume they are in something like a water bath held at constant temp. Is temp effect important? I don't know and we aren't going to find out from your experiment. Think about it. Do you want to know that? Or any similar issue?

5. Now the growth curves. You want to compare trt vs no trt under the 4 day growth times. How do you do that? well fortunatley one of the great Biostatisticians, C R Rao took up this problem. His paper and a number of others can be found at this link: https://www.bing.com/search?q=How+do+you+statistically+compare+growth+curves&pc=U528&form=QBLH&sp=-1&ghc=1&pq=how+do+you+statistically+compare+growth+curves&sc=1-46&qs=n&sk=&cvid=B31667C492E744D5B42EF661354EE496

Now you have a lot of growth curves to compare. Now you haven't decided on a DV. What are you going to use from the growth cure analysis for your DV? Statistics is all about decisions so read the the GC papers. Now you need a longitudinal linear model. The type depends on what DV you select. see: https://www.bing.com/search?q=How+do+you+choose+a+type+of+regression&qs=n&form=QBRE&sp=-1&ghc=1&pq=how+do+you+choose+a+type+of+regression&sc=0-38&sk=&cvid=2A94D413EAB244D99E362683D6A67BB2

Now you must build your model. We know this experiment is longitudinal. One of the best of modern day biostatisticians literaly wrote the books on longitudinal models in order to follow drug treatments for AIDS here are the notes from her course:

https://www4.stat.ncsu.edu/~davidian/st732/notes.html

Now how do you build the RHS of your model. Well these notes will guide you, as will a good Design of experiments book. The best I've found is at this link: https://www.bing.com/search?FORM=U528DF&PC=U528&q=Montgomery+D+C+design+and+Analysis+of+experiments

Now you should have 1 or more regression models to analyze, depending on the choices you still need to make. How do you do that? Go to more links. I have attached a recent paper of ours which may give you an idea of how such an analysis goes. Very different problem of course. I hope you now have some idea of how to design, execute and analyze such an experiment. I would expect my research students to have something like this in their notebook. We want good, reproducible experiments that we can be proud to write up and submit. This is an example of some the things you might do to improve your experiment. this type of approach leads to good reproducible research. Good science takes lots of time and effort but is one of the most rewarding things in your life. Give it the treatment it deserves. Best wishes for a good career, David E. Booth

Adrian, Prof David Booth has actually given you much more than you requested including appropriate research design that will help you to carry out a good Ph.D. research.

Knowledge of the statistical method to use is essential, but it's theoretical basis and assumptions must be compatible with the research design.. You might end up with canonical regression analysi using R package.

Adrian, I would use MANOVA. Post-hoc analysis can be tricky but you might get the information you need (for comparing cell types).

Hope that might help! Best!

David Eugene Booth thank you very much for such a detailed reply!

Harold Chike thanks a lot for the suggestion! Unfortunately I am not familiar with programming language.

Alina Avanesyan, yesterday I re-studied analysis of variance in order to clear my doubts regarding if the "cell type" can be considered as an independent variable in MANOVA design. As I am measuring the same parameter (e.g. metabolic activity) at the same time points, and under the same experimental conditions, although the cells are of different origin, I believe they can be considered as different levels of a discrete variable, and therefore, the 3-WAY ANOVA is the method of choice for my experimental design as I originally thought. However, as you stated, the post-hoc analysis can be tricky, and I am not familiar with it in the case of 3-WAY ANOVA. I am currently using SigmaPlot v12 for statistical analyses, but I am not sure how to perform the post hoc analyses after running the 3-WAY ANOVA. Do you have any suggestion on that?

Thanks a lot in advance,

Adrian

My understanding is that there are at least two options to proceed with such post hoc comparisons:

1. The 'textbook' suggests using the Scheffe Method as a post hoc test for complex comparisons. I've found more details on it here (I haven't done it myself yet): https://www.itl.nist.gov/div898/handbook/prc/section4/prc472.htm

It looks like you would be interested in it ONLY if you have found significant interaction effect in your 3-way ANOVA model.

2. If the interaction effect is not significant OR you are interested in specific pairwise comparisons, then using classic Tukey's test seems to be appropriate.

Yet another option (depending on what comparisons are important for your research question) is, instead of 3-way ANOVA, to proceed with several pairwise comparisons (One-way ANOVA or t-tests) and then do corrections for your p-values (Bonferroni, etc.).

Just a few ideas..

Adrian, you not really need to be familiar with a programming language to use statistical packages. As David Booth advised, all you NEED is obtain appropriate research design from your research objective and research question. These will lead you to the statistical method to use .

As an illustration, your objective is to determine the effect of some independent variables on some dependent variables in your study. As David Booth mentioned, you will be dealing with regression models

Ofcourse, regression models with more than on dependent variable and more than one independent variable are referred to as canonical correlation. Check whether you can find it in R statistical package or any other package.

Harold Chike You are,of course, correct about canonical correlation if Adrian Djalali-Cuevas variables are appropriate. I do think the regression view is easier in this instance but without knowing the variables it is hard to tell. Clearly he has not taken the repeated measure aspect into account at this point and is missing that baseline. He still hasn't mentioned his DV or DVs so the whole question is still up in the air as far as I can see. Thanks for what I consider to be a very helpful comment. Best wishes, David Booth

Adrian Djalali-Cuevas I noticed from your reply to Harold Chike that you are concerned about computer statistical packages. R is free and an easy download. This link should get you started: http://sgpwe.izt.uam.mx/files/users/uami/gma/R_for_dummies.pdf

It would be most helpful if you would tell us your metabolic variable(s) so we could include that in our suggestions. BTW R and SAS can be run online and even from a smartphone with browser. See https://www.bing.com/search?q=running+r++online&qs=n&form=QBRE&sp=-1&pq=running+r+online&sc=3-16&sk=&cvid=64F00E5D7EB44C488C73D33049474641

If your prefer another package just replace R in your query. Hope this helps, David Booth PS if you are concerned about multiple testing I have attached my favorite reference which doesn't require a computer though these are implemented in most packages.