Note, to potential "duplicate" claimants, there is a similar question posted here. However, 1. that post is actually asking a different question and 2. that question has removed the code in the OP and thus is difficult to follow. Either way, it does not answer my question.
Main Question
I have calculated some monthly averages. I want to find out which season has the strongest value for animal presence.
Do I sum the means of each month for each season
summer = jun average + jul average + aug average
Or do I find the average of those averages?
summer = jun average + jul average + aug average / 3
Which method is correct for finding out the season with the highest and lowest values?
Context to aid answering the question is provided below
Details
Say we have a 4×4 square with 16 cells.
We lay this square on the on a beach and measure the presence of animals in each cell.
Weekly Statistics
We fill in each cell with the following rule
- If a animal is present in a cell, cell value = 1
- if the cell is empty (animal does NOT appear), cell value = 0
This results in a cell like so,
Monthly Totals
We repeat this each week of each month. We add up the weekly quadrats to create month summary, where each cell has a number between 0 and 4.
- 0 = no animal present in any of the weeks
- 1 = animal present in 1/4 of the weeks
- 2 = animal present in 2/4 of the weeks
- 3 = animal present in 3/4 of the weeks
- 4 = animal was present in every week
value count
1 0 2
2 1 3
3 2 3
4 3 4
5 4 3
Monthly Statistics
sum = sum of count (i.e. 1+4+2+1+0+1: sum of cells…)
mean = sum / # of rows (i.e. # of weeks + 1)
sum mean
jan 10 2
feb 23 4.6
mar 45 9
apr 15 3
Summary Question
Do I sum the averages of each month for each season?
summer = jun average + jul average + aug average
Or do I find the average of those averages?
summer = jun average + jul average + aug average / 3
Which method is correct for finding out the season with the highest and lowest values?
Desired output…a value showing which season generally has more animals. Should I sum the monthly averages or average the monthly averages?
season value
1 autumn 85
2 spring 40
3 summer 62
4 winter 70
Best Answer
As @lulu pointed it out, as long as your seasons all have the same number of months, it is exactly equivalent to compute the sum of averages or the average of averages.
Example
Let say you compute the two indicators for summer:
And for winter:
Then
strength_sum summer < strength_sum winter
is equivalent tostrength_avg summer < strength_avg winter
(just by multiplying by3
). In both cases, the summer had less animals than the winter.But what if...
If your seasons has a different number of months, or if you want to generalize to other time periods, I think that using the average of averages is more meaningful, regarding your issue.
Imagine you were in the Alps mountains, where the summer and autumn are way shorter than winter. It makes sense to favor the average of averages in order to correctly compare a 2-month long summer with a 5-month long winter.
For example, if you use the sum of average criterion: if
strength_sum summer = 20 * 2 = 40
(n = 20
for each month of summer) andstrength_sum winter = 10 * 5 = 50
(n = 10
for each month of winter), you don't want the winter to "win" simply because it's more than twice as long as summer :strength_sum summer = 40 < 50 = strength_sum winter
, butstrength_avg summer = 20 > 10 = strength_avg winter
. It seems to me thanstrength_avg
makes more sense here.