Generalized linear model of the binomial family (aka "logit model", "logistic model" or "logistic regression").

see for instance:

http://www.sagepub.com/sites/default/files/upm-binaries/21121_Chapter_15.pdf

http://data.princeton.edu/wws509/notes/c3.pdf

https://onlinecourses.science.psu.edu/stat507/node/18

Generalized linear model of the binomial family (aka "logit model", "logistic model" or "logistic regression").

see for instance:

http://www.sagepub.com/sites/default/files/upm-binaries/21121_Chapter_15.pdf

http://data.princeton.edu/wws509/notes/c3.pdf

https://onlinecourses.science.psu.edu/stat507/node/18

You can use a Chi2 test to evaluate if there is a significant difference between the proportions of positive responses across the 5 treatments (2x5 contingency table) (e.g. see http://www.itl.nist.gov/div898/handbook/prc/section4/prc46.htm)

You can complete your analysis by using the Marascuilo procedure to simultaneously test the differences of all pairs of proportions (e.g. see http://www.itl.nist.gov/div898/handbook/prc/section4/prc474.htm).

(Check the application conditions of the Chi2 test)

if treatments quantative or ordinally qualitative, you may use multi-logistic; howerer, if  treatments simplely qualitative, you may employ non-parameteric. 

you can try non-parameteric, such as Wilconox Test

Indeed, it seems like a case for using logistic regression.

The question is not fully complete. You have a binary outcome which means that you need a model that models probabilities or odds -> logistics regression as Jochen pointed at. You talk about 5 treatments: do you actually mean one factor in five levels? I think you do. Then you write 12 replications per treatment: do you actually mean 12 independent observations for each level of the factor. If yes, then Jochen's and Christine's suggestions are both fine (and rather similar, although Christine indicate a way of ranking the treatments which you asked for). However, if your observations are dependent because e.g. repeated observatiions on the same unit, then you need a method to deal with the dependence. This would be the extension to GLM that Jochen pointed at, namely GLMM (Generalized Linear Mixed Model).

Okay Here i have attached my data set.

1/ All treatments are independent.

2/ Response (1/0)  measured as Positive or Negative

my objective is which treatment is the effective when considering the Positives(1)

Are these time-series (i.e. is the information of the time-points relevant for your reserch question)? Would it make a difference when the rows in the table were re-ordered? Or is it only the proportion of 1's withing these 12 time-points, no matter if they occur "earlyer" or "later"?

Before starting analysis I would recommend tidying your data first. See https://cran.r-project.org/web/packages/tidyr/vignettes/tidy-data.html

So I copied your data and restructured it in to a column with the positive/negative as 1/0 and a column with the factor with five levels (0=A, 1=B and so on) and ran a logistic regression (see below, sorry for the ugly output). Basically, the results suggest it to be a statistical difference between the levels (p-value=0.002) and the point estimates indicate level A to be associated with the greatest odds for a positive value on the response variable. Treatment A appears also to differ statistically significant from the other treatment levels (this statement does not follow immediately from the print out below).

However, seeing the pattern of the data over time I very much wonder if the observations per treatment level are genuinly independent. I think it would be useful to explain (as asked by Jochen) the meaning of hour and the time-series characteristics in your data.

****

Variable Value Count

Y  1 29 (Event)

0 31

Logistic Regression Table

Predictor Coef SE Coef Z P Ratio Lower Upper

Constant 2.39790 1.04445 2.30 0.022

L

1 -3.49651 1.23908 -2.82 0.005 0.03 0.00 0.34

2 -2.73437 1.19738 -2.28 0.022 0.06 0.01 0.68

3 -2.06142 1.19738 -1.72 0.085 0.13 0.01 1.33

4 -3.49651 1.23908 -2.82 0.005 0.03 0.00 0.34

Log-Likelihood = -33.239

Test that all slopes are zero: G = 16.634, DF = 4, P-Value = 0.002

And here is the plot to Kenneth' analysis showing the means and the (approximate) 95% confidence intervals for the "proportion of events" (an "event" is where you gave "1").

Hello Jochen Wilhelm. I want to reproduce a graph like the one you made above, but I'm having trouble doing it. My dataset is composed of a binary variable (0 = no capture, 1 = capture) and a categorical variable (bait) grouping 5 levels (bait1, bait2, up to 5). To check which bait was most effective, I performed a logistic regression. Now I want to make a graph visually representing this difference between the baits. If you could give me some advice, I would be very grateful.

I attached the script to reproduce the plot for Ranga's data in "Result.docx".

PS: Note that I did not consider the time - I just took the data from all 10 hours as independent.