Analysis of two treatments with respect to controls

[ciubba]

For whatever reason, the bio experiment I need to analyze was done with respect to two controls. The "treatment 1" organisms were observed with respect to the control organisms to yield one set of treatment 1 and control data. Then, the "treatment 2" organisms were observed with respect to the control organisms to yield treatment 2 data and a <i>different</i> set of control data. I tried ANOVA, but I didn't know how to account for the fact that two of the treatments were actually the same thing (control).

Can I take the difference between control and treatment for both sets of data and do a two-sample t-test or am I stuck with descriptive statistics?

 

[Bystander]

How many populations? I count five from your post: T₁, T₂, C₁, C₂, and

and a <i>different</i> set of control data.

 

[ciubba]

Sorry, my wording was confusing. I only have T₁, T₂, C₁, C₂. However, the two control groups were organisms drawn from a single test tube subject to the "control treatment," so I assumed it only counted as a single population. If it counts as a separate population, then ANOVA would be a cinch!

 

[Bystander]

If you had to calibrate every physical measurement instrument you own (thermometer, tape measure, stop watch/timer, balance) for each individual measurement you make, and be unable to compare those measurements to one another, would they be useful?

 

[ciubba]

I suppose not. With that in mind, is it more appropriate to treat them as separate populations and do ANOVA or to take the difference of (T1-C1) and (T2-C2) to do a two sample t-test?

 

[Bystander]

You should get the same result, no?

 

[ciubba]

Actually, no. T1=40,40,60; C1=10,12,15; T2=0,0,0; C2=40,12,20

When I tell my calculator to do ANOVA I get p=.00165

When I tell it to do two sample t with (t1-c1) and (t2-c2) and u1>u2, I get p=.00336, which is much higher than the ANOVA one. I'm assuming it is due to different degrees of freedom.

 

[Bystander]

What's the difference you're showing between C₁ and C₂? What's the actual measurement variable?

 

[ciubba]

Number of these organisms eaten. My assumption for why T1 C1 and T2 C2 were examined separately is that they were assumed to be conditional; that is to say, if we put T1 and T2 together with C then it is unlikely any C would be eaten as T1 was the preferred "meal."

 

[Bystander]

Choice/preference between T₁ and C₁ is compared to choice/preference between T₂ and C₂?

My definition of "control" would be more along the lines of a choice/preference of "nothing" and C. Or is T₂ the equivalent of "nothing?"

The choice of "nothing" or T₂ becomes the interesting experiment given the "raw" data.

they were assumed to be conditional;

I'd say "designed" to be conditional, rather than "assumed." Beyond this, other than noting that the "interesting" experiment has not been done, it's not obvious to me what the point of the exercise is supposed to be, or what the statistics should be telling you.

 

[ciubba]

T2 is zero because the t2 organisms were not consumed; instead, the control was preferred. We are trying to sketch a relationship between an independent categorical variable (shape of organism) and a quantitative dependent variable (# of times the organism was eaten). I want to know if I can do a test of some sort to provide evidence towards my claims, such as there is an x% chance of this relationship occurring by chance. Otherwise, I'm just left with descriptive statistics.

Is there a test I can perform is this particular situation?

 

[Bystander]

Looking again at raw data, you may have been undone by the complete zero result for T₂; that leaves you with T₁ and C, and implied but not proven is that your phage would rather starve than eat T₂.

 

[ciubba]

It didn't starve, it just ate the control because the shape of the control was more conducive to eating than the shape of the T2. Is there a test I can perform in this situation?

 

[Bystander]

"Implied." You can compare T₁ and C to the test tubes and get the same results; if no T₂ was eaten, it's the same result as not even offering it, hence my remark that the zero consumption result is unfortunate. There is no statistical test that will yield any information regarding heads or tails when the coin hovers in the air spinning, or more realistically falls down a storm drain into a heavy runoff.

 

[ciubba]

"Implied." You can compare T₁ and C to the test tubes and get the same results; if no T₂ was eaten, it's the same result as not even offering it, hence my remark that the zero consumption result is unfortunate. There is no statistical test that will yield any information regarding heads or tails when the coin hovers in the air spinning, or more realistically falls down a storm drain into a heavy runoff.

Thank you, I now understand why I cannot use standard tests in this situation.

 

[Bystander]

Took me forever to get there, but I think this is the problem --- please find some independent confirmation of what I've sold you --- i.e., do not wager large sums of money on it.