Testing the Census Reports
A warning that testing had not been carried out is included in my famine index page.
This page records tests and comments on the Census Data, to examine internal consistency.

The Census reports referred to were published in 1856 as Parliamentary Papers. With care, further information can be deduced from the Reports.. This can give an insight into the progress of the famine between 1845 and 1850, and to provide information on, for example, the probable numbers of births and deaths prior to 1850. I have published my deductions on several web pages in the current directory.

The Census Reports and other data on Web pages are of little value unless it can be shown that :
there are no errors in transcribing data from the source;
that there are no arithmetic errors; and
that the methods used are sound.
Further, the data should be internally consistent and externally consistent.
 

One method of testing is to publish the information on the web, in order to invite criticism.
Below is one of the more coherent responses to my post in soc.culture.irish newsgroup under:
"famine statistics revisited":

>Sir,
>I find it remarkable that you seem to have discovered statistics which
>have evaded historians like Churchill, Lyons, Porter, and the dozen-odd
>mentioned in an earlier post. In the face of this fact there are three
>possiblities:

>1. You have uncovered rock-solid sources of information that were
>previously unknown, and have discovered a sinister papist-republican
>plot to distort history.(You should publish as soon as possible, because
>there are a bunch of academic awards coming your way if you do.)

>2. You are a blatant revisionist attempting to minimise one of the
>nastier episodes in Britain's past by blowing it up into a republican
>plot.

>3. You are an idiot who should check the reliability his sources before
>making wild statements.

>I am inclined to discount the first possiblity.

>The parlimentary record is not really the most reliable record,
>understandably enough. If you think the figures were rigged I would
>recommend O'Brien's "The Economic History of Ireland from the Union to
>the Famine", or O'Rourke's "The history of the great Irish famine of
>1847 : with notices of earlier Irish famines"; both published
>pre-independence. Better still just read the bibliography to Cecil
>Woodham-Smith's "The Great Hunger, Ireland 1845-1849" and stop annoying
>us.

The reliability of the Census Report is entirely relevant, the remainder of the post is insubstantial nonsense.

Quoting Cecil Woodham-Smith, "The Great Hunger", Chapter 1
"... though the practice of taking a ten-yearly census began in 1821 the first figures considered reliable are those of 1841"

but I shall not be selective...

"By 1841... the population had reached 8,175,124," [ch 1]

"He had it [the census] tested in Co Clare and found the population to be one third greater than had been recorded, therefore in 1845 when the famine came the population might well have been above nine millions." [ch 1]

"For this closely packed and rapidly increasing people, ......" [ch 1]

1846.... "yet thanks to the relief scheme the people in many districts had been better off than usual.  Trevelyan, with whom John Ball agreed, wrote, 'In the first failure  the people suffered less than in ordinary years, owing to the pains taken to prevent them from feeling want'" [ch 4]

I see a measure of ambiguity and inconsistency in this revered work, but ambiguity is what makes life tolerable, and inconsistency makes life interesting.
Cecil Woodham-Smith does not provide the quality of information needed to immediately test the Census Report, or to improve it.

I cannot improve the Census Report  by adding information of lesser quality, however good the source. To improve the quality of information provided by the Report data added should include age, sex, and location at the time of the Census. Material from other sources can be used to test the reliability of the Census Report, and can enable speculation on the true populations from which the Census Data was drawn, but without evidence it remains speculation.

Before that can take place the Report and my calculations must be tested for internal consistency, that is that the figures in one part of the report agree with other parts. That will allow testing of external consistency,  i.e. testing against other information on the famine, to begin.

INTERNAL CONSISTENCY:

1. Ages of population.
The graphs showing ages of the population  [A] [B] in the Census Report showing the raw data contain alarming peaks at ages 10, 20, 30 and 40, etc for the population in 1851.
Smoothing the peaks is necessary to produce accurate estimates of the population, but it also removes some information. For example on the ability to remember facts and how those people saw themselves. A simple low-pass filter is a recognised method of removing transient noise and improving a lower frequency signal. I used this method to ensure that subjective bias was not present in carrying out the necessary step of producing corrected data on the ages of the population. The Census Report also provided smoothing for these peaks, however, and the figures given in the tables of figures for the Ages of Populations do not agree with the figures I used to produce graphs of the population, nor apparently with the Report's own graphs.
The potential error is of the order of 37,500 [about five percent] for those children aged between 5 years and less than ten years. The raw Data appears to be accurate for children up to approximately seven years of age, but the child's appearance may have assisted recall. The numbers of 8, 9, and 10 year olds in 1851 are shown as 170,000, 155,000 and 192,500 respectively,  and I believe such a large fluctuation in population to be most unlikely. The errors between my corrected data and the smoothed figures in the  graphs in the Census are small, but not small enough to be discarded, at least for the present. As the totals for the entire population are within one percent, the difference in the figures is in the apportionment of fluctuations in the raw data to various ages of the population. Please note the peak at Age 13, shown in the graph of population for 1851; the numbers aged between 60-70 1n 1841 and 70-80 in 1851; and the figures recorded for infants in 1841 and 1851.

2. Births in the population
There is no comprehensive record of births available for the famine period. The Census Reports record the number of infants alive at the time the Census was taken, and infant mortality could be added to this figure to gain an approximation of the number of births. This addition has not been made to the figures quoted, in order to simplify calculations. While the shape of the population graph would suggest that births peaked around 1837 and fell from that time onward, my calculations assume that the number of births remained constant until 1846.  It would appear that the number of births declined proportionally to the numbers of the fertile population of the time. The figures for birth rates would suggest 27 and 21 respectively for the number of births per thousand [births per person of  40 and 49] in 1841 and 1851. The figures for these years are low and should be increased to include infant mortality in order to estimate the number of births. Increases of about two point five and five percent would give a better estimate of the number of births in those years. Note that the Ages of populations graphs show that the numbers of the fertile population fell disproportionally. It would appear that social change and starvation impacted on the birth rate prior to the start of the famine.
The Census Report quotes, for England and Wales, one birth for every 31 population members, per year.

3. Death in the Population
As stated on my "deaths" page, the Census in 1841 and 1851 required householders and others to record details of those who had died in the previous ten years [ see copy of 1851 form]. [FormA][FormB]Nobody believes that the returns accurately recorded all deaths. The difficulty, therefore, is in defining the causes of any errors, and estimating their effect. The information available is considerable. Year on year totals for deaths, an overall profile of mortality during the Census period, breakdowns of mortality by city and district, and information from the previous census, especially for the years 1840 and 1841. Sources of error are; failing human recall, the effects of emigration and migration; the deaths of whole households; and a failure to obtain a full census return. Taking, first of all, the returns for 1840 and 1841 made in 1841, only a failure to obtain full census returns might have a aignificant impact, for example an error in excess of ten percent for that year. While mindful of that possibility, we can say that the returns for the first few months of 1841 are accurate, while those for the later months of 1841, returned in 1851, are subject to the maximum effects of all possible sources of error. Similarly, we can expect that the returns for the months immediately prior to the Census in 1851, to be accurate, and that reasonable corrections can be made for deaths, emigration and migration, for about the previous twelve months. Further, we have within the Census Report, a complete record of deaths in Dublin, by age, sex, month and year of occurrance, from 1841 to 1851 complete. Suffice to say I have used the data from Dublin to estimate corrections to the annual mortality recorded in the Census Report.
A crucial test of the method is the estimate of deaths in 1845. If there were no significant changes in the population between 1841 and 1845 then we would expect mortality levels to be similar. Deaths in 1840 were 141536, recorded deaths in 1845 were  86900 and my correction to this figure gives an estimate of deaths in 1845 as 147842. The Census Report quotes a figure of one death per 45 persons per year, for England and Wales, on average from 1837 to 1853. The equivalent figure for Ireland in 1840 is 55, a twenty percent lower mortality. Part of the difference in these rates may be due to higher child mortality in urban and civic districts.
I would contend that this figure of 147842, although 41 percent higher than the recorded mortality, is a reasonable and fair correction to deaths during 1845, and accurately compensates for errors. Following this, we would expect a progressive reduction in error up until 1851. Successive error figures are, from 1845, -41%, -27%, +1%, +27%, -8%, 0%. It would appear that using the Dublin figures as a bench mark has introduced a new error into the calculations. I had assumed that the increase in fever deaths in urban areas would balance the increased mortality from all causes in rural areas, during the famine years. It would appear that a linear reduction in error may give a better estimate of the number of deaths. Values of -41%, -32%, -24%, -16%, -8%, and 0% will give figures of: 147842,  180719, 328072, 247919, 261735, 164093, giving a total of 1182538, for the years 1846-50 inclusive. My estimated total for the previous five years is 718623, the apparent increase is 463915, but this estimate does not include all instances where a whole family died during the famine. Total deaths 1840-1850 are 1901161, or one death per 37 persons per year.
I should point out that the figure for 1845, showing an error of 41% is a significant problem. The fall in population is less than 25 percent and it would be reasonable to expect the error to be of that order or less. Deducing an explanation may provide a useful insight.
Examining the deaths recorded for 1830 through to 1841 [ 148539, 94713, 96623, 101961, 123114, 141688, 130222, 140239, 141536, 68739, note that the first figure is for 1.56 years and the last for 0.44 years] suggests that memory plays a greater part in errors than demographic change. The likely values of errors appear to be distributed along an 'S' shaped curve, rather than a linear progression as the years pass, with recollection in 1841 being much more accurate for the most recent five years. However comparing the results in 1841 and 1851, the likely error for 1832 is significantly smaller at about 33 percent than that for 1842 at 46 percent. My estimates of likely errors for using a highly subjective method  1845-1850 is -39%, -24%, -12%, -8%, -4%, -1%, and 0%. There is, however, so little scientific basis for this opinion that I will not trouble the reader with calculate figures. If you wish to pursue this avenue of enquiry, email me an I will forward what photocopies I have of the Report pages relating to years 1830-1841, or publish on these pages.
I conclude that he likely range of "excess" deaths due to the famine is therefore 290,000-470,000; from my reading of the Census Report.

4. Emigration and Migration

Emigration: leaving one Country for another, for example from Ireland to Canada
Migration: moving one's abode within a country, for example from Ireland to another location within the United Kindom.

The figures I have calculated for Emigration come from the Census Report, and includes their allowance for error of +ten percent. This suggests that the Emigration figures are known with good accuracy, at least in comparison with the figures for migration. Migration is mentioned twice within the Census report, in 1841, and in 1846. Quoting the 1846 text "" from the 13th of January to the 1st of November, 278,005 immigrants arrived at Liverpool from Ireland, of whom only 122,981 sailed to foreign countries." Unfortunately, the context of this quote makes the exact meaning of this phrase uncertain. If there is little information in the Census Report for Emigration, there is less for Migration. Unfortunately I had to make assumptions for the age profile of presons emigrating, which makes may eatimates of persons migrating less accurate. Before these figures can be reworked, a better profile of emigrants, for example from ship's lists will be needed.

It is clear that there was substantial emigration and migration during the period of the census. Migration is not specifically recorded, and can only be deduced from changes to populations in the most general sense. It may be possible to verify my estimates of numbers migrating by examining growth in British cities.
 

5. General comments

Testing the Census data has endorsed my view of what took place during the famine years. While exteral consistency has still to be tested, the errors found are not yet significant enough to cause me to revise my estimates.

When assessing the change in the population 1841-1851 the reader should note that half the population was below twentyfive years of age, and that that part of the population was declining in numbers before the famine and its emigration began. The decline in the older part of the population was as much due to emigration and migration as to an increase in mortality. There was a massive increase in the deaths of children, together with a falling birth rate as the fertile population declined. Fertility did not fall significantly.

Cities such as Drogheda had apalling rates of child mortality, over twice that of rural areas. This suggests that the mere act of moving from a rural population to an urban location would therefore significantly increase the number of deaths in a population. This problem would also have to be overcome if "excess" deaths were to be kept to the achievable minimum, given that the staple diet of seventy percent of the population had been removed.

And I have to query the meaning of "excess" deaths? For simplicity I have chosen to calculate this as the number of actual deaths estimated less an estimate of the number of deaths which might have occurred if the potato had not been blighted. Other estimates are possible, depending on your definition.

Summarising the surprises found by examining the Census Report
* An anticipated fall in fertility was not found, possibly because birth rates had begun to decline from about 1835 onwards.
* The 1841 data suggests that the population was broadly in balance between births, deaths, emigration and migration.
* Emigration/Migration was substantially from the 20-35 age group and almost half the numbers migrated to England.
* The scale of inaccuracies in reporting some deaths in the early years of the census.
* Peaks and troughs in recorded ages of the population.
* The scale of poverty for years prior to the famine.
* Incompatibility between some comments made by the Census Comissioners when comared with the Census Data.
* The extent to which "excess" deaths were suffered by children.
* The relative levels of mortality in Cities and in England when compared with Ireland generally.

Reconciling these surprises with current vies on the famine will be challenging.
See my external consistencies page
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