The Joy of Maths for Historians?!

Local historians, especially those of us not working in academia, often ignore quantitative history as it can be more challenging, particularly if you are not comfortable with maths or statistics. But we should be bold; it is all too easy to drift into narrative history, especially when focusing locally. Digging about in the numbers can reveal interesting information and can be the springboard for further investigations. Excel and its open-source alternatives have powerful tools for crunching number and producing charts, and there is plenty of help on the internet, Google is our friend! This blogpost is about using quantitative data to reveal trends and spark further investigations.

Back in the 1970s Roger Schofield and Tony Wrigley produced an excellent study of England’s population across the last 500 years using data taken from the parish registers of 404 English parishes. Subsequently, this data was expanded to produce data for baptisms, marriages and burials aggregated into yearly, ten-year and fifty-year totals and made available on CD-ROM via www.localpopulationstudies.org.uk and Hertfordshire University. This vast dataset has the potential to be a handy resource for local historians. For this investigation, I took the parish register aggregate data for Sedgley in Staffordshire for no other reason than that some of my forebears originate there.

Before we can look in any detail at how a historian could use this information, it is worth considering the dataset as a whole. In 1538 Henry VIII’s Vicar-General Thomas Cromwell introduced the requirement that every parish had to enter in a book every wedding, christening and burial in the parish. He also required that the parish information had to be stored in a coffer with two locks, one key being held by the priest and one by the churchwardens. This storage scheme seems like a secure system which would suggest good survival of the records. However, the paper used for early records was poor quality, loose sheets rather than books were often used, while damp, vermin and mismanagement caused sheets and whole books to be lost.

For these reasons, only a small number of parish records are even reasonably complete. This haphazard survival gives us the first problem; the size of the dataset. It totals only 404 parishes in England out of an approximate figure of around 9,000 parishes, i.e. less than 5% of all parishes. Secondly that the dataset is not evenly distributed but random, based on fortuitous survival, leading to uneven geographic representation, even where data is available, it might not be complete for the entirety of the period 1538-1834. So, this means that parish register data can be used for broad demographic trends but rarely for comparisons between neighbouring parishes or counties. Thirdly the data is raw rather than standardised, i.e. it is not contextualised by reference to the local population. The earliest accurate population data comes from the 1801 census, and so before that date, more work needs to be undertaken to gather population estimates. Population information is necessary because, without it, any significant variations that appear have no context.

The parish aggregate dataset does contain a population figure for 1811, but a single data point is not very useful. With increasing urbanisation, many parishes underwent rapid growth in the late 18th and early 19th centuries, especially such as those in rapidly industrialising areas like the West Midlands. So a single point is not helpful and gives no clue as to local trends.

Looking at Sedgley, my first step was to try to increase the population data available so that I could put the figures into some context. Population information can be inferred if not precisely calculated using other records such as hearth tax information, voter registrations and also the early 19th century censuses, so I used these to provide some base data.

Data Source	Recorded No.
Householders in 1563	126
Hearths in 1660	398
Householders in 1665	490
Voters in 1747	753

Table 1 Hearths and households from data held at Dudley Archives

The hearth tax and householder figures needed to be converted to a population, and Campop (The Cambridge Group for the History of Population) suggest multiplying by a factor of around 4.5 (a fixed multiplier representing average household size) to convert these numbers into population figures.[1] Doing this provided the following data:

Date	Population
1563	567
1660	1,791
1665	2,205
1747	3,389
1801	9,874
1811	13,937
1821	17,195
1831	20,577
1841	24,819
1851	29,447
1861	36,637
1871	37,355

Table 2 - Sedgley population 1563-1871

With this data, it became possible to estimate the growth of Sedgley and to standardise the parish datasets.

Figure 1 - Sedgley population growth

The graph shows that the population rises rapidly from 1750 or so, this is consistent with the early industrialisation of the Black Country. The next step was to standardise the data so that I could see real trends, but there are gaps in my population values and to produce meaningful information about how and why the population was changing I needed to fill those gaps. Back to maths, I could interpolate the missing numbers to give me population data for the years where there is no data. Interpolation is a mathematical means of accurately estimating values between two known points, and it has been used for thousands of years; Babylonian priest astronomers used it 3000 years ago when studying star movements.

Given that the period of real interest is 1801 onwards where the rise is almost linear and so estimating will be reasonably accurate, I used a linear interpolation formula to improve my data. The formula I used (with the assistance of an Excel spreadsheet) is:

y=y^1+(x-x^1 ) *( (y^2-y^1) /(x^2-x^1 ))

Where x & y are my known year and population values.

Once I had reasonable population data, I then produced baptism, marriage and burial figures standardised against 1000 people making it easier to identify trends.

Figure 2 - Data per 1000 population

The number of both births and deaths per 1000 population declined in the period under consideration, this is roughly to be expected as life expectancy improves and the community’s average age rises. We can also see that the rate of crude population increase slows but this trend does not tally with the rise in population revealed by voter and census data. Looking at this in more detail, we can see some significant dips:

Figure 3 - Crude population increase in Sedgley 1558-1838

Part of the cause may be the under-recording of births; the period from the late 18^th century tallies with the rise of non-conformism. Parish data was produced by the Church of England and often did not incorporate data from non-conformist churches. Smaller non-conformist chapels and tabernacles often did not have had their own graveyards, so burials were conducted by the Church of England. The details of these were then recorded at the parish church or the cemetery. Baptisms, in contrast, could be carried out relatively easily in chapels or other informal locations and were not necessarily recorded in the Church of England parish registers. This administrative difference can lead to an overall under-recording of baptismal data compared with death data.

Other figures might illuminate the discrepancy between these figures and the recorded population. One of these is the seasonality of marriage; in arable agricultural areas such as pre-industrial Sedgley, marriages are skewed to the latter half of the year after the harvest. In industrial areas though, there is no particular seasonality to marriage as it makes little difference to the income of the celebrants. If Sedgley were industrialising this would be expected to be shown in the marriage seasonality figures; marriage would occur more evenly across the year as the area became less focussed on farming.

Figure 4 - Seasonality of marriage

The graph above that in the 16^th and 17^th centuries, the pattern of marriage was seasonal with most taking place later in the year and fewer in spring and summer. But from the beginning of the 18^th century, the line flattens, and marriages occur more evenly across the year. And it also shows an intriguing increase in December weddings, peaking in the 1800s which is probably worthy of further investigation. The move towards weddings taking place more evenly across the year is consistent with a move away from agriculture, but the change is less than might have been expected.

So my next question was “why is this change less than might be expected?” perhaps the transition from agriculture to industrial work was piecemeal, with some workers holding more than one job. So I revisited the data, paying particular attention to the occupation data associated with burials and baptisms in the 16th and 17th century. This closer investigation did provide some illumination:

	Baptism Dates			Burial Dates
Occupation (father/self)	1570-1600	1601-25	1675-85	1570-1600	1601-25	1675-85
Agricultural	231	319	65	45	67	16
Metalworking	272	434	478	20	35	64
Mining	29	53	145	4	12	38
Other	46	80	36	13	10	13
total	578	885	724	82	124	130

Table 3 Occupations in pre-industrial Sedgley

Baptism numbers at this time are far higher than burial numbers. This presumably reflects a new younger population moving into the area. Also, in this period, the number of baptisms where the father’s occupation was agricultural declines, and the number whose work is associated with metalworking increases. These figures suggest that a shift in the economic base of the community was taking place. So presumably population growth was caused by migration, as well as the natural increase from the existing inhabitants. This change may at least partially explain the offset between population values and growth rates.

From this data, I went on to look at the information that could be gleaned from the aggregated burial data for Sedgley. I think better visually, so I plotted the data on a graph:

Figure 5 - Deaths per 1000 population in Sedgley

We can see spikes in 1588, 1642, 1728, 1741, 1769, 1810 and 1832 (as well as an increased number of deaths during the Civil War and the Commonwealth period 1640-60). Two possible causes have been suggested for increased deaths; outbreaks of plague (up until 1666) and famine.[1] These figures reveal a possible further project to be undertaken to look at precisely what may have caused these spikes. The spike in 1832 is probably due to the outbreak of cholera which swept England in 1831-32. The deaths in 1832 are concentrated in a single period between August and September, which is entirely consistent with the documented cholera outbreak in the region. That will be the subject of another blogpost later (and how will the COVID data look in a hundred years?).

This exercise was interesting and useful. The data on parish events was a springboard for considering population change, disease and famine, something that is in 2020 still horribly relevant. The death investigation has sent me off to look at Sedgley’s experience of cholera in the 1832 outbreak. Further work beckons on famine disease and the Civil War. So, in conclusion, the parish aggregates are useful datasets which can act as a springboard for further investigation. However, to use them well requires additional material to be found to give the information context. In this instance, the dataset aided the study of the development of Sedgley but was insufficient on its own to produce meaningful data.

As local historians, we shouldn’t let the minimal amount of maths involved put us off. Particularly for those of us working outside academic circles and or squeezing in our historical investigations around other activities, this quantitative work can seem daunting and geeky. But whilst being mindful of the limitations of the data, a little number crunching can add context, provide evidence and enable comparison with other areas which can only add value and strengthen our work.

(originally published 2020)

Bibliography

Anon (1986), Non-conformist chapels and meeting houses Shropshire and Staffordshire

Davenport R.J. (2017), The First Stages of the Mortality Transition in England: A Perspective From Evolutionary Biology, Cambridge Group for the History of Population and Social Structure

Blane, G. (1817), Inquiry into the Causes and Remedies of the Late and Present Scarcity and High Price of Provisions (2^nd edition)

Dickinson, H. T. A. (2002), Companion to Eighteenth-Century Britain. Blackwell Publishing,

Thomas, H.R. (1941), Sedgley All Saints Part 1 1558-1685, Staffordshire Parish Registers Society

Wrigley, E. A. Schofield, R. (1989), The Population History of England 1541-1871 Cambridge University Press

Websites

www.sedgleymanor.com/registers

www.campop.geog.cam.ac.uk/research/projects/transport/data/population1680.html

www.un.org/esa/population/techcoop/DemEst/manual1/chapter5.pdf

www.geog.cam.ac.uk/research/projects/migrationmortalitymedicalisation

www.histpop.org.uk

www.1911census.org.uk/1801

www.nationalarchives.gov.uk/pathways/census/events/census3.htm