What's the difference between an ecological study and a cross-sectional study? What's the difference between an ecological study and a cross-sectional study? And could you provide an example?
 A: An ecological study is one where you take values of a variable for an entire population, the outcome from that population, and use that to draw inference. A cross-sectional study is where you look at individuals within a population at a single point in time.
Examples:
Ecological Study: Consider a study where you find the average number of years of education each of the 50 states in the U.S., as well as their rate of teenage pregnancy, and drew a correlation between them.
Cross-Sectional Study: You recruit people in Montana, and ask them about a number of biological, sexual and behavioral variables and their HPV status, and examine whether particular variables are associated with having (or not having) HPV.
A: DEFINITIONS
An ecologic study is a study that uses at least one measurement made at the group level.
A cross-sectional study uses measurements all of which are made on individuals.
https://www.ctspedia.org/do/view/CTSpedia/StudyUnit
ECOLOGIC STUDY EXAMPLES
Many good examples of ecologic studies are studies that assess disease rates according to population measures of nutrient consumption for countries across a wide range of consumption levels.
EXAMPLE 1
An often-cited and classical study is Armstrong and Doll’s comprehensive assessment of various dietary factors and cancer mortality and incidence by country.  In the study, information about the incidence and mortality for 27 cancer sites and a large number of population measures of diet was obtained from public sources for 37 countries.  A graphical depiction of the results of the analysis of colon cancer incidence in women according to per capital daily mean consumption in the 23 countries with data on colon cancer incidence and meat consumption in women is shown.
Armstrong B, Doll R. Environmental factors and cancer incidence and mortality in different countries, with special reference to dietary practices. Int J Cancer. 1975 Apr 15;15(4):617-31. PubMed PMID: 1140864.  FIGURE 2.  Correlation between incidence of colon cancer in women and per caput daily meat consumption in 23 countries.

https://onlinelibrary.wiley.com/doi/abs/10.1002/ijc.2910150411
EXAMPLE 2
Another ecologic study of cancer and diet, with an excellent graphical presentation of the results (FIGURE 1), is a study that assessed the relationship between stomach cancer mortality and dietary salt and nitrate in 24 countries.  In this study, population-level data from 24-hour collections of urine that measured dietary salt and nitrate were used in conjunction with data on stomach cancer mortality for 24 countries to assess the relationship between stomach cancer mortality and dietary consumption of salt and nitrate.
Joossens JV, Hill MJ, Elliott P, Stamler R, Lesaffre E, Dyer A, Nichols R, Kesteloot H. Dietary salt, nitrate and stomach cancer mortality in 24 countries. European Cancer Prevention (ECP) and the INTERSALT Cooperative Research Group. Int J Epidemiol. 1996 Jun;25(3):494-504. doi: 10.1093/ije/25.3.494. PMID: 8671549.
https://academic.oup.com/ije/article/25/3/494/756987
CROSS-SECTIONAL STUDY EXAMPLE
This is a cross-sectional study of the association of dietary intake of calcium, sodium, and potassium with blood pressure.
Morikawa Y, Nakagawa H, Okayama A, Mikawa K, Sakata K, Miura K, Ishizaki M, Yoshita K, Naruse Y, Kagamimori S, Hashimoto T, Ueshima H. A cross-sectional study on association of calcium intake with blood pressure in Japanese population. J Hum Hypertens. 2002 Feb;16(2):105-10. PubMed PMID: 11850767.
https://www.nature.com/articles/1001314
In the study, 476 men and women age 20-59 years were included.  Blood pressure was measured and dietary calcium intake was estimated from a 1-day 24-hour recall in the 476 individual participants.  Dietary intake of sodium and potassium was measured using 24-hour urine collection in the 476 individual participants.  Individual-level data were analyzed to examine the association of dietary calcium intake with systolic blood pressure after adjustment for dietary potassium and sodium separately in men and women.
