# How to compare increase in price from different samples?

#### e_man64

##### New Member
I have data samples of home sales of N different cities, and I want to find the city with the biggest increase in average prices between 2012 and 2015.

How could I compare these cities while taking into account the difference in number of transactions?

City 1 Sample:
Year, Average Price, # of Transactions
2012, 10000, 100
2013, 14000, 120
2014, 15500, 140
2015, 13500, 50

City 2 Sample:
Year, Average Price, # of Transactions
2012, 90000, 80
2013, 95000, 120
2014, 12500, 180
2015, 15000, 30

City N .. etc

Thanks

#### Junes

##### Member
Well, since you have the average, you can compare it quite directly.

You can't add confidence intervals (error bars), because you have no date on the variation. However, confidence intervals are kind of unnecessary anyway, since you have sampled the entire population of houses sold each year (we could argue there is still a hypothetical population). You could estimate them if you have data on typical variance.

Note that the type of houses sold might differ (between each year and each city) so what the differences actually mean is up for interpreation.

What I would do is make a simple line graph with indexed house prices for each city (100=2012). As long as you have a decent number of transactions each year (say, >20), that should give you a relatively stable measure.

#### e_man64

##### New Member
Okay. Since I wan to find the city with the biggest price increase, can I calculate the percentage change for each city by finding the difference between the base year, and the last year divided over the base year?

In that case would it even be necessary to calculate the index?

#### Junes

##### Member
Okay. Since I wan to find the city with the biggest price increase, can I calculate the percentage change for each city by finding the difference between the base year, and the last year divided over the base year?

In that case would it even be necessary to calculate the index?
Well, that's kind of what I mean by indexing - the calculation you describe gives you the indexed price. The base year is indexed at 1. If you want it indexed at 100, just multiply your result by 100.