7.5: Sampling Examples

7.5.1: Measuring Unemployment

Unemployment, for the purposes of this atom, occurs when people are without work and actively seeking work. The unemployment rate is a measure of the prevalence of unemployment. It is calculated as a percentage by dividing the number of unemployed individuals by all individuals currently in the labor force.

Though many people care about the number of unemployed individuals, economists typically focus on the unemployment rate. This corrects for the normal increase in the number of people employed due to increases in population and increases in the labor force relative to the population.

As defined by the International Labour Organization (ILO), “unemployed workers” are those who are currently not working but willing and able to work for pay, those who are currently available to work, and those who have actively searched for work. Individuals who are actively seeking job placement must make the following efforts:

• be in contact with an employer
• have job interviews
• contact job placement agencies
• send out resumes
• submit applications
• respond to advertisements (or some other means of active job searching) within the prior four weeks

There are different ways national statistical agencies measure unemployment. These differences may limit the validity of international comparisons of unemployment data. To some degree, these differences remain despite national statistical agencies increasingly adopting the definition of unemployment by the International Labor Organization. To facilitate international comparisons, some organizations, such as the OECD, Eurostat, and International Labor Comparisons Program, adjust data on unemployment for comparability across countries.

The ILO describes 4 different methods to calculate the unemployment rate:

1. Labor Force Sample Surveys are the most preferred method of unemployment rate calculation since they give the most comprehensive results and enable calculation of unemployment by different group categories such as race and gender. This method is the most internationally comparable.
2. Official Estimates are determined by a combination of information from one or more of the other three methods. The use of this method has been declining in favor of labor surveys.
3. Social Insurance Statistics, such as unemployment benefits, are computed base on the number of persons insured representing the total labor force and the number of persons who are insured that are collecting benefits. This method has been heavily criticized due to the expiration of benefits before the person finds work.
4. Employment Office Statistics are the least effective, being that they only include a monthly tally of unemployed persons who enter employment offices. This method also includes unemployed who are not unemployed per the ILO definition.

Unemployment in the United States

The Bureau of Labor Statistics measures employment and unemployment (of those over 15 years of age) using two different labor force surveys conducted by the United States Census Bureau (within the United States Department of Commerce) and/or the Bureau of Labor Statistics (within the United States Department of Labor). These surveys gather employment statistics monthly. The Current Population Survey (CPS), or “Household Survey,” conducts a survey based on a sample of 60,000 households. This survey measures the unemployment rate based on the ILO definition.

The Current Employment Statistics survey (CES), or “Payroll Survey”, conducts a survey based on a sample of 160,000 businesses and government agencies that represent 400,000 individual employers. This survey measures only civilian nonagricultural employment; thus, it does not calculate an unemployment rate, and it differs from the ILO unemployment rate definition.

These two sources have different classification criteria and usually produce differing results. Additional data are also available from the government, such as the unemployment insurance weekly claims report available from the Office of Workforce Security, within the U.S. Department of Labor Employment & Training Administration.

The Bureau of Labor Statistics also calculates six alternate measures of unemployment, U1 through U6 (as diagramed in the following images), that measure different aspects of unemployment:

• U1: Percentage of labor force unemployed 15 weeks or longer.
• U2: Percentage of labor force who lost jobs or completed temporary work.
• U3: Official unemployment rate per the ILO definition occurs when people are without jobs and they have actively looked for work within the past four weeks.
• U4: U3 + “discouraged workers”, or those who have stopped looking for work because current economic conditions make them believe that no work is available for them.
• U5: U4 + other “marginally attached workers,” “loosely attached workers,” or those who “would like” and are able to work, but have not looked for work recently.
• U6: U5 + Part-time workers who want to work full-time, but cannot due to economic reasons (underemployment).

7.5.2: Chance Models in Genetics

Gregor Mendel is known as the “father of modern genetics. ” In breeding experiments between 1856 and 1865, Gregor Mendel first traced inheritance patterns of certain traits in pea plants and showed that they obeyed simple statistical rules. Although not all features show these patterns of “Mendelian Inheritance,” his work served as a proof that application of statistics to inheritance could be highly useful. Since that time, many more complex forms of inheritance have been demonstrated.

In 1865, Mendel wrote the paper Experiments on Plant Hybridization. Mendel read his paper to the Natural History Society of Brünn on February 8 and March 8, 1865. It was published in the Proceedings of the Natural History Society of Brünn the following year. In his paper, Mendel compared seven discrete characters (as diagramed in ):

1. color and smoothness of the seeds (yellow and round or green and wrinkled)
2. color of the cotyledons (yellow or green)
3. color of the flowers (white or violet)
4. shape of the pods (full or constricted)
5. color of unripe pods (yellow or green)
6. position of flowers and pods on the stems
7. height of the plants (short or tall)

Mendel’s work received little attention from the scientific community and was largely forgotten. It was not until the early 20^th century that Mendel’s work was rediscovered, and his ideas used to help form the modern synthesis.

The Experiment

Mendel discovered that when crossing purebred white flower and purple flower plants, the result is not a blend. Rather than being a mixture of the two plants, the offspring was purple-flowered. He then conceived the idea of heredity units, which he called “factors”, one of which is a recessive characteristic and the other of which is dominant. Mendel said that factors, later called genes, normally occur in pairs in ordinary body cells, yet segregate during the formation of sex cells. Each member of the pair becomes part of the separate sex cell. The dominant gene, such as the purple flower in Mendel’s plants, will hide the recessive gene, the white flower.

When Mendel grew his first generation hybrid seeds into first generation hybrid plants, he proceeded to cross these hybrid plants with themselves, creating second generation hybrid seeds. He found that recessive traits not visible in the first generation reappeared in the second, but the dominant traits outnumbered the recessive by a ratio of 3:1.

After Mendel self-fertilized the F1 generation and obtained the 3:1 ratio, he correctly theorized that genes can be paired in three different ways for each trait: AA, aa, and Aa. The capital “A” represents the dominant factor and lowercase “a” represents the recessive. Mendel stated that each individual has two factors for each trait, one from each parent. The two factors may or may not contain the same information. If the two factors are identical, the individual is called homozygous for the trait. If the two factors have different information, the individual is called heterozygous. The alternative forms of a factor are called alleles. The genotype of an individual is made up of the many alleles it possesses.

An individual possesses two alleles for each trait; one allele is given by the female parent and the other by the male parent. They are passed on when an individual matures and produces gametes: egg and sperm. When gametes form, the paired alleles separate randomly so that each gamete receives a copy of one of the two alleles. The presence of an allele does not mean that the trait will be expressed in the individual that possesses it. In heterozygous individuals, the allele that is expressed is the dominant. The recessive allele is present but its expression is hidden

Relation to Statistics

The upshot is that Mendel observed the presence of chance in relation to which gene-pairs a seed would get. Because the number of pollen grains is large in comparison to the number of seeds, the selection of gene-pairs is essentially independent. Therefore, the second generation hybrid seeds are determined in a way similar to a series of draws from a data set, with replacement. Mendel’s interpretation of the hereditary chain was based on this sort of statistical evidence.

In 1936, the statistician R.A. Fisher used a chi-squared test to analyze Mendel’s data, and concluded that Mendel’s results with the predicted ratios were far too perfect; this indicated that adjustments (intentional or unconscious) had been made to the data to make the observations fit the hypothesis. However, later authors have claimed Fisher’s analysis was flawed, proposing various statistical and botanical explanations for Mendel’s numbers. It is also possible that Mendel’s results were “too good” merely because he reported the best subset of his data — Mendel mentioned in his paper that the data was from a subset of his experiments.

In summary, the field of genetics has become one of the most fulfilling arenas in which to apply statistical methods. Genetical theory has developed largely due to the use of chance models featuring randomized draws, such as pairs of chromosomes.

Attributions

• Measuring Unemployment
  • “Boundless.”
    http://www.boundless.com/.
    Boundless Learning
    CC BY-SA 3.0.
  • “Unemployment.”
    http://en.wikipedia.org/wiki/Unemployment.
    Wikipedia
    CC BY-SA 3.0.
  • “labor force.”
    http://en.wiktionary.org/wiki/labor_force.
    Wiktionary
    CC BY-SA 3.0.
  • “US Unemployment measures.”
    http://commons.wikimedia.org/wiki/File:US_Unemployment_measures.svg.
    Wikimedia
    CC BY-SA.
• Chance Models in Genetics
  • “Boundless.”
    http://www.boundless.com/.
    Boundless Learning
    CC BY-SA 3.0.
  • “Experiments on Plant Hybridization.”
    http://en.wikipedia.org/wiki/Experiments_on_Plant_Hybridization.
    Wikipedia
    CC BY-SA 3.0.
  • “History of genetics.”
    http://en.wikipedia.org/wiki/History_of_genetics.
    Wikipedia
    CC BY-SA 3.0.
  • “chi-squared test.”
    http://en.wikipedia.org/wiki/chi-squared%20test.
    Wikipedia
    CC BY-SA 3.0.
  • “Mendelian inheritance.”
    http://en.wikipedia.org/wiki/Mendelian_inheritance.
    Wikipedia
    CC BY-SA 3.0.
  • “Gregor Mendel.”
    http://en.wikipedia.org/wiki/Gregor_Mendel.
    Wikipedia
    CC BY-SA 3.0.
  • “gene.”
    http://en.wiktionary.org/wiki/gene.
    Wiktionary
    CC BY-SA 3.0.
  • “chromosome.”
    http://en.wiktionary.org/wiki/chromosome.
    Wiktionary
    CC BY-SA 3.0.
  • “Mendel seven characters.”
    http://commons.wikimedia.org/wiki/File:Mendel_seven_characters.svg.
    Wikimedia
    Public domain.