# Continuous data

#### SafB

##### New Member
If I have daily records (daily average value) of particulate matter pollutant data from an air monitoring station. Is that considered as a continuous data?
If this pollutant value is recorded every 3rd day by the monitoring station, is it continuous data?

Eg:
Day 1: 18.2 microgram per cubic meter
Day 2: 7.1 microgram per cubic meter
Day 3: 23.9 microgram per cubic meter
Day 4: 23.3 microgram per cubic meter
.
.
.
Day 30: 6.3 microgram per cubic meter

Any help will be appreciated!
Thanks

#### GretaGarbo

##### Human
particulate matter pollutant data from an air monitoring station. Is that considered as a continuous data?
Yes.
(Once I heard a somewhat populistic description of continuous as something that you can draw a line on the paper without lifting the pencil from the paper.)

If this pollutant value is recorded every 3rd day by the monitoring station, is it continuous data?
The days would be discrete. You must lift the pencil to do the dot at day 1, 4, 7 etc.

But maybe the question really is if they are ratio scaled variables. They both are ratio scales.
(So it "allowed" to calculate sums and means.)

Out of curiosity, what do you want to do with the air pollution data?

#### hlsmith

##### Less is more. Stay pure. Stay poor.
To get pedantic, if you get small enough everything is granular, even light. I know everything is a bold/strong word.

#### GretaGarbo

##### Human
To get pedantic, if you get small enough everything is granular, even light. I know everything is a bold/strong word.
yes, of course all data a rounded, even if so to tenth decimal. But in principle you can think of many the quantity as a continuous variable. (eg length but it is measured in discrete centimeters, or millimiters or tenth of millimeter, or....)

#### noetsi

##### Fortran must die
I think the point about interval and ratio is important. People tend to confuse the two.

#### Miner

##### TS Contributor
Some technically discrete data begins to behave like continuous data when the numbers get large enough. See the normal approximation to the Poisson and Binomial distributions.

#### noetsi

##### Fortran must die
It is sometimes argued that with likert scale data (which is formally ordinal) once you have 7 or more levels it behaves as in interval level data (it is called interval like).

#### noetsi

##### Fortran must die
I remember learning Poisson regression because I had count data. And Jake pointing out that there was a good chance that the results would essentially be the same lol.

#### SafB

##### New Member
Yes.
(Once I heard a somewhat populistic description of continuous as something that you can draw a line on the paper without lifting the pencil from the paper.)

The days would be discrete. You must lift the pencil to do the dot at day 1, 4, 7 etc.

But maybe the question really is if they are ratio scaled variables. They both are ratio scales.
(So it "allowed" to calculate sums and means.)

Out of curiosity, what do you want to do with the air pollution data?
I want to check if increase in pollutant level impacts hospital visits. Do you have any idea about what kind of statistical analysis would be appropriate. many studies have done this with regression models. But I don't want my analysis to be that complex. Honestly I do not have the background. Help?

#### hlsmith

##### Less is more. Stay pure. Stay poor.
What type of hospital data do you have?

#### GretaGarbo

##### Human
I want to check if increase in pollutant level impacts hospital visits.
A common model in this case is to use the number of hospital visits per day as the dependent variabel, let us call that Y. and that E(Y) = mu and that Y is Poisson distributed. Then the air pollution, the particulate matter (PM) , would be an explanatory variable.

Then you can use Poisson regression:

log(mu) = a + b*PM + other variables

Other variables could be the temperature, the time of the year (a seasonal effect) the number of influensa cases, and so on...

Poisson regression is not that difficult. Most software can do that. Good luck!

#### GretaGarbo

##### Human
you can probably use a t-test
I would guess that a t-test would not fit that well. Since:

I want to check if increase in pollutant level impacts hospital visits
And I think of " hospital visits" as the number of hospital visits per day, so I guess that a Poisson distribution (or a negative binomial) would fit better.

Although:
many studies have done this with regression models. But I don't want my analysis to be that complex.
A linear regression is not that complicated. It is good to try to simplify things. But you should not simplify too much.