1.1 The Two Branches of Statistics

The statistical genius and research of Snow not only saved lives, it anticipated the two main branches of modern statistics: descriptive statistics and inferential statistics.

Descriptive Statistics

A descriptive statistic organizes, summarizes, and communicates a group of numerical observations.

Descriptive Statistics Summarize Information It is more useful to use a single number to summarize many people’s weights than to provide a long, overwhelming list of each person’s weight.
U.S. Air Force photo by Staff Sgt. Shawn Weismiller

Descriptive statistics organize, summarize, and communicate a group of numerical observations. Descriptive statistics describe large amounts of data in a single number or in just a few numbers. Here’s an illustration using familiar numbers: body weights. The Centers for Disease Control and Prevention (CDC, 2004, 2012) reported that people in the United States weigh more now than they did four decades ago. The average weight for women increased from 140.2 pounds in 1960 to 166.2 in 2010. For men, the average weight went from 166.3 to 195.5 pounds in the same time span. These averages are descriptive statistics because they describe the weights of many people in just one number. A single number reporting the average communicates the observations more clearly than would a long list of weights for every person studied by the CDC.

MASTERING THE CONCEPT

1.1: Descriptive statistics summarize numerical information about a sample. Inferential statistics draw conclusions about the broader population based on numerical information from a sample.

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Inferential Statistics

An inferential statistic uses sample data to make general estimates about the larger population.

Inferential statistics use sample data to make general estimates about the larger population. Inferential statistics infer, or make an intelligent guess about, the population. For example, the CDC made inferences about weight even though it did not actually weigh everyone in the United States. Instead, the CDC studied a smaller representative group of U.S. citizens to make an intelligent guess about the entire population.

Distinguishing Between a Sample and a Population

A sample is a set of observations drawn from the population of interest.

The population includes all possible observations about which we’d like to know something.

A sample is a set of observations drawn from the population of interest. Researchers usually study a sample, but they are really interested in the population, which includes all possible observations about which we’d like to know something. For example, the average weight of the CDC’s samples of women and men were used to estimate the average weight for the entire U.S. population, which was the CDC’s interest.

Samples are used most often because we are rarely able to study every person (or organization or laboratory rat) in a population. For one thing, it’s far too expensive. In addition, it would take too long. Snow did not want to interview every family in the Broad Street neighborhood—people were dying too fast! Fortunately, what he learned from his sample also applied to the larger population.

CHECK YOUR LEARNING

Reviewing the Concepts

  • Descriptive statistics organize, summarize, and communicate large amounts of numerical information.
  • Inferential statistics use sample data to draw conclusions about larger populations.
  • Samples, or selected observations of a population, are intended to be representative of the larger population.

Clarifying the Concepts

  • 1-1 Are samples or populations used in inferential statistics?

Calculating the Statistics

  • 1-2a If your professor calculated the average grade for your statistics class, would that be considered a descriptive statistic or an inferential statistic?
  • 1-2b If that same class average is used to predict something about how future students might do in statistics, would it be considered a descriptive statistic or an inferential statistic?

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Applying the Concepts

  • 1-3 Researcher Andrew Gelman wrote about his research in the New York Times (February 18, 2013): “The average American knows about 600 people. How do we know this? Researchers led by my Columbia colleague Tian Zheng posed a series of questions to a representative sample of 1,500 Americans.”
    1. What is the sample?
    2. What is the population?
    3. What is the descriptive statistic?
    4. What is the inferential statistic?

Solutions to these Check Your Learning questions can be found in Appendix D.