Yeomen, Sharecroppers, and Socialists: Plain Folk Protest in Texas, 1870-1914

Appendix C

(APPENDIX C) MethodsforChapter3 Household Wealth Distribution and the Farm Family in Hunt County, Texas, 1870–1910 Tax Rolls, 1870–1910 I determined the sample sizes from the Hunt County Tax Rolls for the years 1870, 1880, 1890, 1900, and 1910 through the initial use of a pilot sample of twenty-five cases per year. I used the pilot samples to determine variance for the variable “wealth,” which I then used as an estimate of the real variance of wealth in the entire population. This figure (variance) governs the size of the statistically valid sample. The higher the variance (the greater the variation from around the mean), the larger the sample must be in order to render results within desired confidence levels. The ultimate size of the sample can be raised or lowered to reasonable levels by changing the confidence level (not recommended), changing the confidence interval (which can make more sense depending on the value of the mean), and by applying the formula for correction for finite population size found in R. S. Schofield, “Sampling in Historical Research,” in E. A. Wrigley, Ed., Nineteenth Century Society: Essays in the Use of Quantitative Methods for the Study of Social Data (Cambridge: Cambridge University Press, 1972), 146–90. After the variance within the pilot sample was determined using the formula mentioned above (sum of squared deviation divided by size of pilot sample minus 1) provided by Schofield (actually, letting the software program Statistical Program for the Social Sciences X figure the 230 Appendix C variance of the pilot sample), this variance then determined the size of the actual sample when used in “Formula 8” provided by Schofield, which takes into account the decisions made regarding confidence level and confidence interval (see “Formula 8” in Schofield, 163). The level of confidence for all five samples is 95 percent for the given confidence interval. The confidence intervals, however, had to be varied to offset the wildly fluctuating levels of variance in the pilot samples in order to maintain some control over the sample sizes. Finally, in cases where the indicated sample size represented a significantly large portion of the total population, at Schofield’s suggestion I corrected for finite population (see “Formula 6” in Schofield, 162). Finally, the samples, population counts, confidence intervals, confidence levels, and wealth means for each year are listed below: Table A1. Hunt County Tax Roll Samples, 1870–1910 1870 1880 1890 1900 1910 Total Population (households) 1,337 4,064 6,809 10,345 11,996 Sample size 100 100 200 250 350 Confidence interval ±$100 ±$50 ±$100 ±$200 ±$300 Confidence level 95% 95% 95% 95% 95% Mean wealth $1,446 $825 $841 $1,088 $1,385 All sample sizes have been rounded to a number divisible by ten in order to allow for decile tables. Further, the ± confidence interval refers to a 95 percent certainty that the sample mean is within ½ of the value of the confidence interval’s value (above or below) of the true population mean. For example, in 1910 this sample size ensures that the average from the sample has a 95 percent chance of being no less than $150 of the true mean or no more than $150 of the true mean. Systematic sampling “A systematic sampling is most like a random sample when the population to be sampled is listed in a random order. This can effectively be so for the purposes of the sample when the items are ordered by some characteristic, say alphabetically by surname, which has no relation to the characteristic under investigation in the sample” (Schofield, 153–54). Such was the case in the tax rolls. Methods for Chapter 3 231 1870 The 1870 sample size was 100 from a total population of 1,337 contained in 46 pages of tax rolls. By taking two cases per page (first and last entry) I could get 92 cases; I then started over and took one case (middle entry) per page from the pages 1, 8, 15, 22, 29, 36, 43, and 3. 1880 The 1880 sample size was 100 from a total population of 4,064 contained in 137 pages. I took the tenth case from the top of the page of every other page starting on page two. When I arrived at the last page I started over and took the tenth case from the top of every other page starting on page one. I used the...