I am having trouble comparing two percent values to show the change in one compared to the change in another.
For all stores looking at all sales:
The average sales growth for week 1 this year compared to last year = 8%
The average sales growth for week 2 this year compared to last year = 7%
Change:
$\frac{7\%}{8\%}-1=-12\%$
For all stores looking at only food sales:
The average sales growth for week 1 this year compared to last year = 25%
The average sales growth for week 2 this year compared to last year = 32%
Change:
$\frac{32\%}{25\%}-1=27.8\%$
So these values are the average total sales growth and total food sales growth this year compared to last for all stores. I want to compare a specific store to these averages:
For Store A looking at all sales:
The average sales growth for week 1 this year compared to last year = 33%
The average sales growth for week 2 this year compared to last year = 41%
Change:
$\frac{41\%}{33\%}-1=22.5\%$
For Store A looking at only food sales:
The average sales growth for week 1 this year compared to last year = 21%
The average sales growth for week 2 this year compared to last year = 47%
Change:
$\frac{47\%}{21\%}-1=122.5\%$
To summarize this all
All sales growth
Store A: 22.5%
All stores: -12%
Food sales growth
Store A: 122.5%
All stores: 27.8%
How do I compare the growth of store A compared to all stores for all sales and only food sales? What percentage of food sales make up all sales?
My first approach is the relative change formula: (new value - old value)/|(old value)
$\frac{22.5\%-(-12\%)}{\left |-12\% \right |}$ but since the base percent is negative the signs don't make sense
What about, $-(\frac{22.5\%}{-12\%})+1 = 2.8x$?
The values for food only
$\frac{122.5\%}{27.8\%} = 4.4x$
Does this make sense? Is the growth of food at this store compared to other stores 4.4x more? Is the growth of all sales 2.8x more at store A compared to other stores? Knowing this information, is it possible to look at what percentage of food makes up all sales?