Measuring the absolute deviation from a group median with median removal

dear community,

I have multiple groups of numbers, each group has 3, 4 or 5 numbers. I want to analyze the absolute deviation of the numbers from the respective group median over all groups.

Is it allowed to remove the 0 deviation in groups with 3 or 5 members and analyzing the other absolute deviations or should we keep the 0 deviation entries? Here a short data example, the rows are the respective groups

data=[0 1 2 3 4;
    2 4 NaN 2 3;
    4 NaN NaN 5 6;
    5 7 6 2 4;
    NaN 9 10 12 10;
    15 16 18 18 NaN];
data=data-median(data,2,'omitnan');
data=abs(data(:)); % i am only interested in absolute deviation
figure; subplot(1,2,1); boxplot(data); title('with zeros')
subplot(1,2,2); boxplot(data(data~=0)); title('without zeros'); linkaxes()

to the background:

I measured onsets of 5 singers singing under mutiple circumstances (factors). I am interested in the onset spreading of the group under specific conditions while the number of onsets per recording can of course vary between recordings.

so the numbers can be moments in time in which minimum 3 of 5 singers started singing

Of course i have more onsets per recording and maaany different factors, but the principle should be clear.

I hope it is halfway clear what I am asking here. Is it allowed to remove the 0 deviations at small groups sizes. In addition, in the case of 4 onsets, we would end at 4 analyzed onset, when we have 5, wen end also in 4 and if we have 3 onsets, we would end in effective of 2 onsets if we would remove the group median onset member

best regards

Jonas

[Jonas]

anyone?

Answer 1

[Harimurali]

Hi Jonas,

I understand that you wish to know if removing the zero deviation entries is permitted when analyzing the absolute deviation of the numbers from the respective group median over all groups where each group has 3, 4, or 5 numbers.

In the context of examining the absolute deviation of numbers from the corresponding group median, it is often acceptable to remove the 0 deviation entries in groups of 3 or 5 members.

Removing the zero deviation data simplifies the study by focusing on the numbers that differ from the group median, which may be more relevant for your particular investigation.

As your analysis focuses on the onset spreading under certain conditions, it is reasonable to rule out scenarios in which all vocalists begin singing at the same time (0 deviation).

By removing the 0 deviations in groups of 3 or 5 members, you may concentrate on the diversity in onset times, which may provide more significant insights into the group's onset spreading behavior. This method considers the effective onset count based on the number of non-zero deviations.

I hope this helps.

[Jonas]

thank you for the input