Hello Danilo,

First question : what is exactly your response ? what is exactly your factor (groups I presume... but you talk also about time) ? what hypothesis are you testing ?

If your data are not normal, you can try data transformation prior going through singular test....

Regards

Hi Cyril,

thanks for your answer.

So my response is a %of luminescence used to establish viability of bacteria(i used other methods to confirm it). i incubated same drug at different concentration and exsposed to 24 h of treatmet. samples has been taken every 30 min up to 6h and then at time 12 and 24. so my groups will be a different drug concentration and my x axes will be the time. Basically my would be a time response and not a dose-response. I'm interested in actual time where a specific drug concentration is effective.

Having a look to the curve graph i clearly show which are the controls and which are the treatment. So my idea is to do it using statistics to show it.

I'm not a big fan of data transformation unless i have to. I think that transforming the data is like making up new data to be able to use tests that in normal condition cannot be used. In my case Dunnett test (compair one control to the other treatment) should do the work but it assume that i have normal distributed data and ugual variance ad also is fitting a linear model......my data are absolutaly not linear, not normal and not ugual variance. This is not because the data are not good (similar result after i did the experiment 3 times and every time using 3 independent sample) but because the biological response often is different from what in "theory" should be.

So what i described in my original post is a logic thought (in my opinion) of what i can statisticly doing using this data without transforming them. For instance, i'm using the Dunnett t3 test that do a pairwise compairison of all treatment when you have not normal distributed data and not ugual variance.

Hope i was more clear this time, and please let me know what you think.

Regards

Danilo

Hello Danilo,

So clearly (to me) you have two factors : groups and time. So you can't ignore time in your model.

"Having a look to the curve graph i clearly show which are the controls and which are the treatment. So my idea is to do it using statistics to show it." -> How do you see it exactly ? Change in global mean ? Change in inflexion point ?

Can you provide two curve ? Control vs treatment ?

(Maybe you should implement a model on your curve ? And extract your response from it -- such as we can extract inflexion point from logistic curve).

"Data transformation is makin up new data"  -> No, it is wanting to get means which mean something. If your data are not normal, well the mean doesn't represent something useful. Most of the time, we are interested in the effect (p-value) but we are also interested in the amplitude of the effect (difference in means). So data transformation to get "real" mean is sometime more than useful !

"what i can statistically doing using this data without transforming them" -> Response is simple : nothing. Because, you can't use parametric test because they are not normal. So you'll use non-parametric test (Dunnett t3 should be one) which, somehow, transforms your data by ordering them and you will compare the "median" of your data. This lead to the increase of type I and type II errors...

Finally, I don't know Dunnett t3 test, but if where you, I would try to perform an ANOVA following this model :

anova(lm(response~groups*time,data=your_table))

Hoping the response is close to be linearly decreasing function of time.

Please check ANOVA assumptions first following this link : http://www.statmethods.net/stats/anovaAssumptions.html

This will also help you in knowing better your data.

And if it's suit well your data, try to perform standard Dunnett test with it.

Regards

Hi Cyril,

Thaks for your explanation,

i attached an example of my curves to give you an idea.

And below  there is a result from the ANOVA

Analysis of Variance Table

Response: Response

Df Sum Sq Mean Sq F value Pr(>F)

Treatment 5 111879 22376 36.3462

Hello Danilo,

Having a look to your figure, it seems that your data follow a logistic digressive curve.

response=K(-1/(1+a*exp(-rt))+1)

So I suggest you to fit your curve response(t) to this model and then extract the inflexion point of each curve :

Inflexion_Point (ln(a)/r,K/2).

You can then compare the abscissa of this point. I'm pretty sure that it will be normaly distributed.

And other and more simple (but also more "coarse") method, is to take (graphically) the time when 50% of the response is reach and compare this time.

Concerning the importance of normality and homoscedasticity, let me introduce you a simple exemple. You want to know who is the best teacher between two of them. So you give the same test to 2x30 students and look at the results :

1st teacher : 5 students get 11/20, 20 students get 12/20 and 5 students get 13/20

2nd teacher : 20 students get 9/20, 5 students get 17/20 and 5 students get 19/20

So who is the best teacher ? Means tell you that they are the same. Are they really ? Can you really compare this results ?

Regards