Ecological Correlation

An ecological correlation is a correlation based on group means, rather than measurements from individuals. For example, if we are interested in the relationship between urbanization and national prosperity, we might look across countries to see if there is a correlation between the percentage of people living in urban areas and GDP per capita. This is an ecological correlation because it is based on data about groups of people, i.e. countries, rather than individuals. If our interest is in national economies, then it’s appropriate to look at ecological correlations based on aggregate data for countries. However, if we find a correlation at the country level, we cannot assume we will find a similar correlation at the individual level or even for groups within countries. We cannot assume, for example, that people who live in urban areas are more prosperous on average than those who do not. Nor can we assume that urban areas within countries will be more prosperous than non-urban areas.

Consider another example. Suppose we find a positive correlation at the national level between life expectancy and Internet use. Can we conclude from this that individuals who use the Internet live longer than those who do not? No, we cannot.

Assuming equivalence between correlations derived from group means and correlations derived from individual data leads to the ecological fallacy.

From Wikipedia:

The term comes from a 1950 paper by Robinson (1950). For each of the 48 states in the US as of the 1930 census, he computed the literacy rate and the proportion of the population born outside the US. He showed that these two figures were associated with a positive correlation of 0.53 — in other words, the greater the proportion of immigrants in a state, the higher its average literacy. However, when individuals are considered, the correlation was −0.11 — immigrants were on average less literate than native citizens. Robinson showed that the positive correlation at the level of state populations was because immigrants tended to settle in states where the native population was more literate. He cautioned against deducing conclusions about individuals on the basis of population-level, or “ecological” data.

Wikipedia also notes that, according to a book by Gelman, Park, Shor, Bafumi, & Corina (2008), in recent elections wealthier states were more likely to vote Democratic and poorer states Republican.  At the individual level, however, wealthier voters are more likely to vote Republican, and poorer voters more likely to vote Democratic. This illustrates the need to be careful about what we conclude from ecological correlations.

As Lubinski & Humphreys (1996) have advised, however, there are times when an ecological correlation is the proper way to look at the relationship between two variables.  For example, to understand the impact of smoking on public health, looking at group-level relationships between smoking and lung cancer is more useful than looking at correlations based on data from individual smokers.

References

Gelman, Andrew; Park, David; Shor, Boris; Bafumi, Joseph; Cortina, Jeronimo (2008). Red State, Blue State, Rich State, Poor State. Princeton University Press. ISBN 978-0-691-13927-2.

Lubinski, D., & Humphreys, L. G. (1996). Seeing the forest from the trees: When predicting the behavior or status of groups, correlate means. Psychology, Public Policy, and Law, volume 2, pages 363-376.

Robinson, W.S. (1950). “Ecological Correlations and the Behavior of Individuals”. American Sociological Review 15: 351–357

Cookies & Candy

Dan and I have been making cookies for over 35 years now.  We especially enjoy making cookies at Christmas time to share with family and friends.  In the early years, we kept with a few tried and true recipes: pressed spritz, brandy balls and Dan’s famous chocolate chip cookies.  After tiring of these, we began taking chances on new recipes we’ve found or invented. The photo above shows our 2013 Christmas cookies, which included red velvet with cream cheese frosting, peppermint chip, chocolate chip with walnuts, chocolate mounds (dusted with powdered sugar), and sugar cookies with various flavors of icing (cherry, creme de menthe, cinnamon, and orange).

We’ve also branched out into making chocolate truffles. These are fun because you can experiment with various flavors and additions in micro batches. The photo below shows the truffles I sent to my Mom for Valentine’s day in 2011.

Chocolate truffles in a variety of flavors

Paris in 1976

Dan and I first visited Paris in 1976, arriving at Gare de l’Est on May 31. Our first day was stressful because our lodging arrangements made in advance by correspondence somehow fell through. On a limited budget, we were unable to afford a hotel. Fortunately, people at the Society of Friends office in Paris were able to arrange a room for us at guest house in a convenient location on the left bank.

Years later, I recall walking along the Avenue des Champs Élysées from the Place de la Condorde to Charles de Gaulle-Étoile, and I remember how hair-raising it was at that time to be a pedestrian trying to reach the Arc de Triomphe.

Image by Anton Lovász from Pixabay

The Arc is surrounded by a traffic circle that’s typically filled with fast-moving cars. The technique for getting across was to wait until a large group had gathered so that everyone could venture forth together.

Today there are two pedestrian tunnels that go under the traffic circle, but the technique for crossing still applies for other busy streets where there are lights to stop traffic while pedestrians cross.

In 1976, Paris was a great place for students on a tight budget. One of the best bargains was the Metro, which provided quick and convenient transportation.

Image by Rayman78 via Wikimedia Commons, distributed under a CC-BY-SA 4.0 license

Although the buses routes were more difficult to understand, we had a memorable ride that took us through the Bois de Boulogne which appeared to be under the protection of a large tribe of cats.

Photo by Nick Zefish, distributed under a CC-BY-SA 3.0 license

We stayed in Paris for about two seeks. Although full summer had not arrived, the midday heat was sometimes oppressive. So we adopted the habit of lounging under a cafe table umbrella and sipping anise-flavored pastis diluted with cold water.

For breakfast we’d visit a cafe for a croissant or brioche and strong, hot coffee. Lunch was usually a snack from a boulangerie (bakery) or street vendor. One day we visited the MacDonald’s restaurant on the Champs Elysee to see how if the hamburgers that chain served in Paris were better than those served in the USA (they were). Another day we purchased attractive saffron-colored Moroccan pastries that turned out to be so intensely sweetened with honey that we were unable to eat more than a few bites.

By carefully conserving our centimes and francs during the day, we were able to splurge on dinners at neighborhood restaurants where waiters used creative methods, including making sketches on table coverings, to explain the prix fixe menu choices.

Until 202, when the Euro was adopted, centimes and francs were the currency of France. I still remember the look and feel of those earlier coins. I was also stuck by the colorful banknotes.

Coins of France prior to adoption of the Euro

We were not able to afford notable vintages, but we enjoyed the house wines served with our meals. Coming from California, though, we were partisans of Napa Valley. As it turned out, even French experts gave high marks to California wines in the famous tasting that’s come to be known as The Judgement of Paris that was held on May 24, 1776. Decades later, however, I have a growing preference for French wine. Competition can be a good thing.

For those interested in further exploring the Paris of 1976, I’ve embedded some YouTube videos from the period.

This first video below, has accompanying music but no commentary. Jumping from place to place, it gives glimpses of what Paris looked like in 1976, but it doesn’t provide an organized tour or overview.

Archival footage shot by a filmmaker while visiting France in 1976.

The next video below is a documentary made in 1975. It focuses on the changes that were occurring at the time. The dialog is in French.

1975: The old Paris that is disappearing

The next video below focuses on markets in Paris. The dialog is in French.

1975: The markets of Paris

The first minute of this video will give you idea of the Metro experience, both in 1976 and still today. Once caveat I’d offer is that many older Metro stations have only stairs rather than the more modern escalators. The video continues with more in-depth information about the Metro. The dialog is in French.

Behind the scenes of the Metro in 1975

This video has no dialog, just the sounds of the car from which the video was taken during a fast and furious drive across Paris.

This video focuses mainly on historic conservation work, but it has some footage from working bakeries of 1978. The dialog is in French.

1978: In the historic bakeries of Paris

Cath’s Notes

I’m in the process of redesigning and reorganizing this website. In the coming months, the layout, navigation, and overall look-and-feel of the website may change. I’ll also be removing some old information that is no longer up-to-date. As time permits, I will update and repost articles that may still be of interest. Please bear with me during these changes.

Rome in 1992

I first visited Rome with my mother in October of 1992. Soon after we checked into our hotel, we were met by cousins and taken to a birthday party. We’d gotten off a plane mere hours before and had not slept for over 24 hours. To stay awake, I drank many cups of espresso. When the party ended, sometime after midnight, our cousin asked as we walked to his car what sights we particularly wished to see in Rome. After I described our wish list, he declared that he would take us on a tour right then, as it was absolutely the best time for driving in Rome. As I recall, it was about 2 am. So the photos I’ve selected for my slideshow, courtesy of other photographers, are an attempt to capture my first experience of Rome while in a somewhat altered state of consciousness.

I returned to Rome in December of 1993, accompanied by my husband Dan. We were once again embraced by my Italian cousins, who welcomed us into their home and organized another party. The wonderful staff at our hotel then helped us to organize a party of our own so that we could say farewell to everyone before returning to the USA to celebrate Christmas with family.

For many years, we’ve wanted to return to Italy. We were scheduled to do so in May of 2000. At that time, however, the world was in the grip of a pandemic that hit Italy especially hard. So until I’m able to visit Rome again, I’ll enjoy my memories of that amazing city.

Embedding a Google Doc

I’ve recently been experimenting with Google Docs. If you have Internet access and a Google account (and who doesn’t?), Google Docs is a pretty handy way to create a document you can store on Google Drive, and also print or download if you wish. Because a Google Doc can be shared with others in various ways, it’s an ideal tool for collaborative editing.


A Google Doc can also be embedded into a website. What you see below is an example of that. What’s really nice about this is that you can update what a visitor sees on the webpage simply by editing the Google Doc. The embed is dynamic and shows the current version of the Doc.

Sacred Harp Music

What you see above is a video of Quire Cleveland performing a song called Sherburne, sung to music written by the 18th century American composer Daniel Read. This music first appeared in The American Singing Book (New Haven, CT, 1785), a hymnal published and sold by Read himself. [1] In that publication, the song is shown with “Words by unknown.”[2] However, according to some modern sources, the words are attributed to Nahum Tate, having first appeared in 1700 in a supplement to the New Version of the Psalms of David (1696), authored by Nahum Tate and Nicholas Brady and published in England. [3]


I first heard Sherburne sung by The Boston Camerata as part of the album Sing We Noel: Christmas Music from England & Early America (Joel Cohen, director) recorded in 1978. I found the sound of the music to be unique and hauntingly beautiful. It came to mind recently when I heard music that seemed to have a similar unique sound. I’ve since learned that Sherburne is part of a body of early American music that’s sometimes referred to as Sacred Harp music. There are a number of YouTube videos that provide additional information and various performances of this music. Here are links to some of the videos that have contributed to my understanding of this music:

Sacred Harp Singing
The Sacred Harp of Hoboken
“Soar Away” (Sacred Harp 455) Cades Cove Primitive Baptist Church
Coming Again, White Hill AME Zion Church, Rock Hill, SC
Quire Cleveland sings Shiloh by Williams Billings
Anonymous 4 sings Bethleham by William Billings


[1] Rhoades, Mark D. Anthology of The American Hymn-Tune Repertory. Retrieved from https://people.bethel.edu/~rhomar/index.htm.

[2] ibid. Retrieved from https://people.bethel.edu/~rhomar/TunePages/Sherburne.html.

[3] See Wikipedia article While shepherds watched their flocks.

1757 – Richard Marshall

This Richard Marshall was born ~1757, probably in Virginia, and was part of Virginia regiments during the American Revolutionary War. According to his wife, Keziah, she and Richard were married in Virginia in 1784, probably in Spotsylvania.

He came to Ohio, probably before 1809, and spent the rest of his life in or around Muskingum County, Ohio.

Information about his military services comes from the Pension Application of Richard Marshall, kindly transcribed by Will Graves, who maintains a website for Southern Campaigns Revolutionary War Pension Statements & Rosters.
Census records of 1800 and 1810 for Ohio were mostly destroyed in a fire, so it’s difficult to track those who came to Ohio during the critical period of settlement from 1790 to 1820. I infer that Richard Marshall came to Ohio before 1809 because there is a record of the marriage of his daughter Frances “Franky” Keziah in that year. That’s the only record of Frances that I’ve been able to find, but I am confident that she’s Richard and Keziah’s daughter based on a variety of records establishing that Marshal and Elizabeth Stults are Richard Marshal’s grandchildren.

U. S. Census records for Muskingum County, OH place Richard there from 1820 until his death in 1841.

1770 – Moses Marshall

Moses first wife, Lydia Lamborn, wrote letters that have been preserved. These provide information and details of a kind often missing for those who lived in the frontier regions of North America in the 17th century. On the other hand, the origins of Moses are a bit of a mystery to me. Some family trees have him as the son of a Thomas Marshall (1745-1819 and Ann Cox (1745-1798) who lived in Chester County, PA and were members of the New Garden Quaker Meeting. Other accounts, however, indicate that Moses was born in Germany and spent his early years there.

According to an unverified online source, Moses was present at the Quaker wedding of George Lamborn and Martha Marshal on December 2, 1790, and there there are meeting notes in which Moses is listed in a way that suggests he was considered a family member. Specifically, he is described as being “listed on the right side.” I don’t know whether this refers to a seating arrangement or to the layout of written notes. Be that as it may, it seems he was “on the right side” along with George & Martha Lamborn, Robert Lamborn, Thomas & Ann (Cox) Marshall, Robert Lamborn Jr., Hannah Marshall, Susannah Marshall, David Lamborn, Lydia Lamborn, Ann Pennock, and Pamela Marshall. In 1791, Moses married Lydia Lamborn, and the ceremony was performed by a magistrate rather than in a Quaker meeting. Records of the New Garden Monthly Meeting show that Moses and Lydia were disowned by that meeting on February 4, 1792. [1]

By 1793 (perhaps earlier) Moses and Lydia had moved west and were living near the Monogahela River in what was then Fredericktown, Washington County, PA. They had two sons, James and John Lamborn. According to The Genealogy of the Lamborn Family, “Judging from old sayings and records we have come to the conclusion that Moses was a blacksmith and followed the trade for a living. For when Lydia Lamborn (24) was being talked to by her father before her elopement with Moses, she said ‘Father, I wouild rather live with Moses Marshall in a corner of his blacksmith shop than with Ennion Cook in a palace.’ This saying is vouched for in Mary Ann Dawson’s (116) statement, who had often heard the expression when quite young, which is conclusive that he was a blacksmith; and when Robert (2) cried out in the night ‘David, David, (20) Tid’s gone!’ he was sending one blacksmith to chase another, as David was also a blacksmith.” [2]

This same source includes transcriptions of letters written by Lydia, which I’ve reproduced below with only one change to correct a date that was obviously wrong.

18th of the Sixth month, 1773
 
Dear Father — I may inform thee we unexpectedly received lines by the hand of our neighbor, Lewis, which was a great satisfaction to us, it being the first we had had since we have been so far seperated. I expect in the course of one or towe years more if I live to see you again, I should have come with Jesse Townsen at this time only we are about building and expected if we have good luck to live in it this fawl. I can say with safety, I beleive we have a prospect of doing very well hear if we are industress and careful. We have now got three prentiss and a very great plenty of work. I believe we might have work for as many more. Sister Parmela lives with us and follows the trade, and as for myselfe I never was heartier in my  life than I have been since I came to this contery, and am very well contented, I wish for my brother George hear, for he might doe so much better hear than he will their; dont think it is because I am hear myselfe, far be it from me to even wish for any of you if I did not think it to your advantage. I conclude with my affectionate love to thee and all my friends and relations, and among the rest Old Eve. This from thy daughter,
 
LYDIA MARSHALL
Our little Sune grows finely; he runs about.
 
Frederick Town, Washington Co.
The 4th of the Eighth month, 1793
 
Dear Sister. — I may inform thee I received thy letter by Cousin Samuel, which they live about eight miles off. I have been much confined at home this some time, for my little boy has been very poorly this some time, but is now giting better, and the rest of the famely is all well; as for myselfe I never was heartier in my life than I have been since I came to this contery. We live in a pleasant place close by the river called Monnongahala, and a great number of boats goes to Caintuck and other places on this river; and I may inform thee that Esther Towsen is married to one of the name of Morgan, and lives in this town, and the keep taverin. She was in hear this morning and desired me to send her kind love to thee and famely. Have not much more to ad at this time. I conclude with my affectionate love to thee and brother, with thy little children. This from thy sister.
 
LYDIA MARSHALL
 
Frederick, Eight month 24th, 1793.
 
Respected Sister — I embrace this opportunity to inform thee we got safe to our journey’s end with much less diffeculty then I expected. The child stude the journey admirable, was very good all the way. I may say I never lost one our’s sleep with it since it was born. Not time to write much more at present. I conclude with my kind love to all my relations as if named. Inform Sister Susanna than I heard from the Widow Nicles, and she is well, and likewise David Grave I seen; they live about eight miles of. Give my kind love to unkel Francis and his famely. I conclude with very kind love to thee. I expect to have another opertunity and shall rite more frely.
 
LYDIA MARSHALL

After Lydia died, Moses married Mary Adams. Between 1799 and 1827, the had 15 known children: Moses, Lydia, Joseph, Robert, Albert, Benjamin, Charles, Lewis, Thomas, Gallatin, William, George, Mary, Eliza and Permelia. Sometime around 1810, Moses and Mary moved to Columbiana County, Ohio. [2]


[1] This information is from a message sent on October 14, 2005 by Allan Gillignham to the RootsWeb PABUCKS mailing list. At the time when this post was first written, that message could be seen at http://archiver.rootsweb.ancestry.com/th/read/PABUCKS/2005-10/1129390536. That URL is no longer valid. However, as of January 2021, that message can be seen at https://mlarchives.rootsweb.com/listindexes/emails?listname=&thread=18453534.

[2] Gladden, Sanford Charles (1969) The Durst and Darst Families of America, Vol II. Original publisher unknown. Republished 2013 by the Boulder Genealogical Society. Preview of p. 679 with information about Moses Marshall at https://books.google.com/books?id=lmCiBQAAQBAJ : accessed September 19, 2015.

1786 – Lazarus Marshall

In 1799, outside the small settlement known as Middletown (now Coraopolis), there were 39 documented households in what then comprised Moon Township in Allegheny County, Pennsylvania. One of these was the household of a John Marshal on land that was part of the John Ward grant. Another was the household of a John Marshall on land that was the Henry Bryan grant. [1] Both of these men appear in the 1791 tax rolls for Allegheny County, PA, and I think it very likely that one of them was the father of a Lazarus Marshall, born c. 1786.

By 1824, Lazarus Marshall was residing in Meigs, Muskingum, Ohio, as is evidenced an except from History of Muskingum County regarding the formation of a Methodist Episcopal worship group [2]:

In the year A.D. 1824, Rev. Mordecai Bishop preached in the southeast corner of the township, and formed a class at Lazarus Marshall’s.
 
The members of that class were : Lazarus Marshall and his wife, Mary, David Blackburn and wife, Arthur Ginn and his wife, Mary, James Mitchell and his wife, Mary, James Guy and his wife, Deborah, William and Mary Guy, and Elizabeth Blackburn.

Another source duplicates this information and specifies that Lazarus Marshall’s residence was in the southeast corner of the township. [3]

Looking at the 1820 Census records for Meigs Township, I find nothing that might fit this Lazarus Marshall.

Although I’ve found nothing to connect the ancestry of Lazarus Marshall with that of the Richard Marshall (c. 1757) also living in Muskingum County, they seem to have appeared in Meigs Township around the same time. Marshal Stults, the grandson of Richard Marshall, married Sarah Peirce in 1832. She was the daughter of a Lewellen Peirce who was one of the initial dwellers of Meigs when the township was formed in 1819. The marriage was officiated by John Hammond, who was elected Justice of the Peace (along with Lewellen Peirce) in 1819 and is also listed as a Justice of the Peace (along with Lewellen Peirce) in 1832. [4] Also of interest is that Marshal Stults became a carpenter by trade.

Census records show an Edmund Marshall sometimes living near Lazarus Marshall. A biographical sketch indicates that this Edmund, born in 1817 in Pennsylvania, was the son of Lazarus Marshall, also born in Pennsylvania. This biography also reports that Lazarus was a carpenter who had a family of six children. [5]

There is a record for the grave of Lazarus Marshall at Find A Grave, which gives June 22, 1854 as the date of his death and lists him as buried in Oakland Methodist Church Cemetery. This was the first cemetery in Meigs Township, associated with Hopewell Church 1830-1846, which became a Presbyterian Church 1846-1878, and then several iterations of a Methodist church. In addition to Mary Marshall (wife; b. unknown; d. September 8, 1845), we find in the same cemetery a joint headstone for Albert Marshall (b. August 24, 1842; d. November 27, 1911) and Sarah I Marshall (b. 1844; d. 1913). This suggests that this Albert, son of George Marshall, is a grandson of Lazarus and Mary.


[1] Jockers, Robert A. (2006) Forgotten Past: A History of Moon Township, Pennsylvania. Xlibris Corporation.

[2] Everhart, J. F. (1882). 1794. History of Muskingum County, Ohio: with illustrations and biographical sketches of prominent men and pioneers. Columbus, Ohio: F.J. Everhart & Co.

[3] Biographical and historical memoirs of Muskingum County, Ohio: Embracing an authentic and comprehensive account of the chief events in the history of the county and a record of the lives of many of the most worthy families and individuals. (1892) Chicago: Goodspeed Pub. Co.  Available from Google Books https://books.google.com/books?id=ASBEAQAAMAAJ.

[4] Everhart, ibid.

[5] Commemorative biographical record of the upper Wisconsin counties of Waupaca, Portage, Wood, Marathon, Lincoln, Oneida, Vilas, Langlade, and Shawano. (1895). Chicago: J.H. Beers & Co. Available from Google Books https://books.google.com/books?id=VElEAQAAMAAJ