# Comparing distribution of two dependant binary variables different sample size

#### MoEco

##### New Member
Hello everyone,

I have been searching for solution for my problem but keeps running into more questions so decided to finally ask for a bit of help. I am working with a dataset in which I want to compare efficiency of two detection techniques. Detection using both techniques are expressed as binary outcomes (1=detection, 0=no detection) but carried out on the same observation so no independant. For this, if I understood correctly different posts I have read, I should use McNemar test. But here are some problem I'm not sure still allow me to perform it :
• Sample are different size (time on effort is different), basically one technique is carried out twice as often as the other which I read can lead to unequal variances.
• Response variable are dependant, as both techniques sometimes carried out on the same observation (being minutes of a time series here). This is the reason why I selected McNemar test
• Observation are not independant either because one observation is likely to influence the following one (time series)
Moreover both techniques are sometimes carried out together or alone. I organized the dataset so that I have 0 ; 1 as detection but NA when the effort is off for the technique. Which results in something looking like this (with way more observations though) :

Code:
    Observation Effort_tech1 Effort_tech2 Detection1 Detection2
1            1            1            0          1         NA
2            2            0            0         NA         NA
3            3            0            0         NA         NA
4            4            0            1         NA          0
5            5            1            0          1         NA
6            6            1            0          0         NA
7            7            1            0          0         NA
8            8            1            1          1          1
9            9            0            0         NA         NA
10          10            1            1          1          1
My question is comparing detection efficiency of both techniques, so what I am looking to test, I guess, is if there is a significant difference in distribution of detection. But I am not sure it is even possible anymore with my dataset... Can I still use McNemar test ? If not do you have any tips on what other test I could use ?
Hope I am clear enough, sorry if this case was answered somewhere else but I couldn't find it...
Thanks for any advice, Have a nice day !