Exploratory Analysis and Interpretation: Quantitative Examples

R. Schwartz

1.      Interrogate the historical source:

*What information does it contain?

*What can the information reveal or indicate?

*What are the limitations of the source, i.e., what is it unlikely to indicate or reveal?

2.      Frame a question to explore.

3.      Generate a hunch or hypothesis about the likely results.

4.      Carry out the analysis and generate results.

5.      Interpret the results:

*explain the meaning, the significance, and the likely implications of the results;

*clearly indicate the limits of the interpretation by stating qualifications.

6.      Report the results and interpretation:

*identify the source from step one;

*re-state the original or revised question from step 2 and explain why it’s important to ask and answer;

*re-state the original or revised the hypothesis from step 3;

*present the results from step 4;

*present the interpretation, with connections to other works when possible and with needed qualifications.

1. A village census

If the census is a full enumeration, then it reveals much about the households making up the village, including the occupation of the head and the number of children residing in the household.

The census doesn’t reliably indicate the total number of children in a family because some children may be absent, having gone to live elsewhere for schooling, for work, and so forth.

2. Did farming families tend to have more children than other, non-farming families?  Did the number of residing children depend on the occupation of the household head?

Reasoning: looking through the census gives the impression that cultivateurs (land owning farmers) had more residing children than other households.  It’s likely that farming households that owned land were better off than other households and that they needed labor to help work the farm.  For both reasons they had more residing children.

3. Hunch:  For the reasons stated, farming did tend to have more residing children than other households.

4.  Calculate the mean number of residing children within different occupational groups; OR calculate the mean number of residing children in two groups: farming vs. non-farming families

The first procedure has the advantage of preserving possible differences among households with differing economic and occupational characteristics. 

The second procedure is easier to carry out when doing calculations by hand; but it has the disadvantage of simplifying the results and possibly generating some misleading results because of the lumping together of all other occupations into one composite group.  So qualifications are in order.

Another way of presenting the results is to use a graph.

Figure 1. Mean Number of Residing Children by the Occupational Group of Household Heads for Tart-le-Bas, Tart-le-Haut, and Tart l’Abbaye in 1836.

5. Table 1 shows landowning farming families, on average, had a greater number of residing children than families in all other occupational groups. The mean number of residing children was greater also than the general mean for all groups, being 2.79 compared to 2.04.

Qualification in more advanced work would include a statistical test to determine whether the differences in the observed means are large enough to reject the possibility that differences of this size could have occurred merely by chance.

Qualification without significance testing: Although it is possible that these results could have occurred merely by chance, the size of the difference between the mean for the cultivateurs and the landless peasants or petty merchants suggests that the hypothesis is correct.

Conclusion (qualifications underlined): As the above table and graph show, the number of residing children varied, on average, according to the head of household’s occupation. In particular and compared to other groups in the village, substantial farmers had, as a rule, a larger number of children living with them at home. This pattern likely reflected the economic circumstances of landowning farming families: they had a greater need for labor and the greater wealth needed to feed more mouths at the table. Although we can’t be sure that these results would hold true in all villages, it is likely that the pattern existed earlier in Sacy where Edme Rétif was a large landowning farmer with an unusually large number of residing children.

Another implication concerns the family of Célestine in Chassignolles during the 1840s and 1850s.  There, substantial farmers were worried that their sons and daughters would leave the village and go elsewhere, leaving them without the labor and heirs needed to continue the family farm.  This concern was less apt to bother families who earned their livings in commerce or as craftsmen or wageworkers. In the case of Célestine’s family, for example, keeping the inn did not require as many hands as running a farm. Hence Célestine worked for her father and lived on in the village, while her brothers left in their teens and never returned.  In sum, the chances of children remaining in their home villages into their adult lives were probably greater for the children of farmers than for children born of fathers in other trades and situations.

One further implication arises and suggests another interesting question. Because children of farming families were more likely to live on in their home villages, it would be interesting to see if farming families tended to persist over more generations than families of artisans or wage workers.  Using the census over an extended period, one could examine this possibility by tracing families, much as Tindall did for the Chaumette family in Chassignolles.

Example 2: What was the typical size of a rural household?  Was the average size of household around 6 people?  Or 12 people, as with the case of Edme Rétif in Sacy during the 1760s?  Or as many as 15 as portrayed in the painting by Boilly of 1810, Cow’s Hoof?

This question is examined on my web site:

http://www.mtholyoke.edu/courses/rschwart/encounters/representing_the_family.htm

Example 3: Was there a relationship between economic standing and village office holding? Or, in the terms of Nicolas Restif, were villages like Sacy governed like the republics of old in which power and office holding was shared?

Interrogations of sources and method of inquiry: Although we lack information on wealth, royal tax assessments can be used as a reasonable estimate of income.  And the data does include information on the kind and number of offices held during the period 1752 to 1789.  Hence, we can take up our historical question by exploring the possible relationship between tax assessments and office holding.  If economic standing was an important consideration in the selection of officers, then we would expect that the likelihood or frequency of holding office was associated with tax assessments:  men with higher tax assessments were more likely to hold office than men with lower assessments.

Hypothesis:  There is an association between tax assessments (low, medium, and high) and officeholding (no vs. yes).

Null Hypothesis:  There is no association between tax assessments (low, medium, and high) and officeholding (no vs. yes)

The results of this question are presented on my web site:

http://www.mtholyoke.edu/courses/rschwart/encounters/village.htm

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Further Food for Thought:  Framing a question and explaining its importance

            In more advanced and sophisticated research, you have to do more than just frame a question; you also need to explain why it is important to answer the question. If you can’t explain why answering a question is important, you’ll have a difficult time writing something that interests you and your readers. Consider the situation. After a long day of research and analysis, you return to your room and speak with a friend. With the help of your friend’s skepticism and curiosity, you eventually discover why your question is significant

You: 

“Wow! Have I been working hard!  I’m trying to determine whether there was a relationship between wealth and power in some Burgundian villages!”

Friend:

“So what?”

You:

“Well, it’s my assignment . . .. And it’s an interesting question, too.”

Friend:

“What’s so interesting about it?”

You:

“Well, I’m using the computer to figure it out.”

Friend:

“So what? We’re all using computers to do our work these days.”

You:

“If you were in the course, you’d understand.”

Friend:

“Maybe I would, maybe I wouldn’t. But I still don’t see why you think the question is interesting. Are you feeling okay? Have you been at the computer too long? You seem spaced out for sure.”

You:

“Okay, look.  We’re reading a book on an 18^th century peasant farmer by his son. The son, Nicolas Restif, says that his father’s village was governed like a republic and not like an oligarchy of a few wealthy men.” 

Friend:

“So?”

You:

“Well, that seems like a big claim. Could it be true that broad participation in local government occurred at that time? Before the French Revolution? This guy makes his father look like a saint, so I think he’s exaggerating about political participation, too. You know, to make this village and the peasants look good.”

Friend:

“I see, sort of.  So you might find out that his father is really the village tyrant?

You

“Well, at least I could see if there was or wasn’t widespread participation. If there wasn’t, I’d have another example for my paper that explains how this book is largely a fabrication by an adoring son. If offices were held by more than just the rich, that would be quite a discovery.  They I could change my paper to show that there was a kind of representative government in villages even before the Revolution.

Friend

“Well, why didn’t you say that in the first place?  By the way, how did you get the information on this one village called Sady?”

You

“Not ‘Sady’. It’s ‘Sacy’. Well, actually I don’t have information for that village but I do have some information on some villages in the same region.

Friend

“Will that be okay? You better explain why.”

Census Records Available for Study

Village

Census on line

Census on photocopies

Tart l’Abbaye

1836, 1841, 1851, 1866, 1896

1836, 1841, 1851, 1856, 1866, 1856, 1872, 1896

Tart-le-Bas

1836, 1851, 1872, 1896

1836, 1841, 1851, 1856, 1866, 1856, 1872, 1896

Tart-le-Haut

1836, 1851, 1866, 1896

1836, 1841, 1851, 1856, 1866, 1856, 1872, 1896

Longecourt

1836, 1851

1836, 1851, 1856, 1872

Thenissey

1836, 1851, 1866, 1896

1836, 1851, 1851, 1856, 1856, 1866, 1872, 1896

Minot

1836, 1841, 1851, 1861, 1866

1851

Summaries of houses, household, age, sex, and marital groups by street or quarter

Summary of individuals by gender, by age, and by marital status (single, married, widowed)

The easiest way to compile an age/sex pyramid in 1851 and over time, using the summaries for 1866 and 1896

Summary of individuals by professional categories: agriculture, industry, and commerce.

Convenient way of studying the distribution of occupations in 1851 and over time using the summaries of 1866, and 1896

1866

Summaries of:

Households by type (one floor, two floors, roof type)

Literacy by gender

Who knew how to read? Who knew how to write?

Individuals by gender, age, and marital status

The easiest way to compile an age/sex pyramid.

Individuals by occupational group

Census of livestock by type: horses, mules, cows, chickens, pigs, and goats

1872

Literacy by gender (Longecourt and Tart-le-Bas only)

1896

Summary of households by street

Summary of houses by type (occupied, vacant; one floor, two floor)

Summary of Households by size

Individuals classified by the region of their birth

Individuals by gender, age, and marital status

The easiest way to compile an age/sex pyramid.

Summary of number of children born by number of years a couple was married