Populations and Samples

Central Limit Calculation

We want to use the CalEnviroScreen data and the central limit theorem to see how likely it is that a factor influences an outcome in the data.

We can look at the case of asthma and pollution. We can take a sample of census tracts with high pollution and compare the means of those asthma measurements to the overall mean. We then use the central limit theorem to see how likely we were to see that mean at random.

Spreadsheet Implementation

When we have a large data set like the CalEnviroScreen data, we want to use a spreadsheet to compute the data.

We start with the strategy and then move on to the spreadsheet implementation.

Steps

Identify measurement column (the population)
Compute mean and standard deviation of measurement column
Identify criteria for your subpopulation
Select this subpopulation using spreadsheet commands
Determine how many census tracts are in the subpopulation
Use the number of census tracts to find the standard error
Compute the mean of the subpopulation
Compute the effect size from the subpopulation and overall population means
Compare the effect size to the standard error to determine the likelihood

Common functions

Mean or average =average(range)
Gives the percentage of values below value in the range of data =percentrank(range, value)
Gives the value at which percentile of the data is below that value =percentile(range, percentile)
Median median(range)
Standard Deviation stdev(range)
Range of data A1:A10
Range of data (entire column) A:A
Range of data from another sheet SheetName!A:A
={data!A:A} gets an entire column from other sheet/tab from a command in one cell
take average of entire population: average(data!W:W) for column W
take stdev(data!W:W) of entire pop for column W

Selecting the subsample

Here you need to select certain data for computation based on the value of some other piece of associated data.

There are several ways to do this:

you could sort your data (on say, pollution) and then find the range of asthma data corresponding to your area of interest
you can instruct the computer to select data under a certain condition

Google Sheets Query Language

We can select a subpopulation from a column of spreadsheet data in Google Sheets using the query language. Here we tell the computer to give us data from column A according to the value of column B.

=query(data!A:BT, "select A where B < 10")

=query is the command
data! tells the computer to look at the data sheet
- if your sheet name has spaces in it, you’ll need to put the sheet name in single quotes (’’)
A:BT says use columns A through BT
select A says take values from column A
where B < 10 says to take those values from where column B is less than 10
use "&D1$" in the query if you want to use cell value D1 in the condition in your query