Whats Going On in This Graph? | Free Speech – The New York Times

To adjust the sample to reflect proportionally the composition of the U.S. population for the data used in the Free Speech graph, a sample of the population was taken with weights applied to 8 categories with 26 subgroups. The groups are: gender (2 subgroups), age (4 subgroups), region (4 subgroups), party identification (3 subgroups), political view (3 subgroup), race/ethnicity (4 subgroups), area (3 subgroups) and income (3 subgroups).

BIAS vs. STATISTICAL BIAS

Bias is the tendency to favor one thing over another. Statistical bias is the tendency of a statistic to overestimate or underestimate the actual value of a population characteristic of interest. Statistical bias may be caused by factors involved in the study design and in the data collection.

In the Free Speech graph, the statistical bias relates to how the poll was taken, including the over- or under-sampling of the subgroups, the use of a phone survey, and the wording and ordering of the questions. Statistical bias from the over- or under-sampling was reduced by weighting their responses.

MARGIN OF ERROR (MOE)

Because sample surveys include only some members of a population of interest, surveys are only able to provide an estimate of the actual value. Usually, for a sample, an interval of values that is likely to include the actual value of the population parameter is given, rather than just the value of the sample statistic. This range is determined by the sample statistic plus or minus the margin of error (MOE). (Note that the MOE does not compensate for errors resulting from flawed survey methods, such as using an unrepresentative sample, responders not telling the truth, or faulty wording of the question.) The margin of error is calculated by using a formula that includes the desired confidence level (the confidence that the sample interval includes the actual value) and the sample size. A MOE of 3% is typical in large national polls, using a 95% confidence level and a sample size slightly more than 1,000.

In the Free Speech graph, the sample statistics for the sample of 1,507 have a margin of error of +/- 3.1 percent. Though the confidence level is not stated, it is reasonable to assume that it is the standard 95 percent. Statistically speaking, we are 95% confident that the actual value of each statistic is between the percentages shown in the graph plus or minus 3.1 percentage points. For example, looking at the overall sample with 40 percent of responding that there is a very serious problem with exercising freedom of speech, we are 95 percent confident that the actual value of the share of the overall population who believe that there is a very serious problem with free speech is between 36.9% (40% - 3.1% = 36.9%) and 43.1% (40% + 3.1% = 43.1%).

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The graph for Whats Going On in This Graph? is selected in partnership with Sharon Hessney. Ms. Hessney wrote the reveal and Stat Nuggets with Roxy Peck, professor emerita, California Polytechnic State University San Luis Obispo, and moderates online with Tara Truesdale, who teaches math and statistics at Ben Lippen School in Columbia, South Carolina.

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The graph for Whats Going On in This Graph? is selected in partnership with Sharon Hessney. Ms. Hessney wrote the reveal and Stat Nuggets with Roxy Peck, professor emerita, California Polytechnic State University San Luis Obispo, and moderates online with Tara Truesdale, who teaches math and statistics at Ben Lippen School in Columbia, South Carolina.

More?

See all graphs in this series or collections of 60 of our favorite graphs, 28 graphs that teach about inequality and 24 graphs about climate change.

View our archives that link to all past releases, organized by topic, graph type and Stat Nugget.

Learn more about the notice and wonder teaching strategy from this 5-minute video and how and why other teachers are using this strategy from our on-demand webinar.

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Go to the American Statistical Association K-12 website, which includes teacher statistics resources, Census in the Schools student-generated data, professional development opportunities, and more.

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Whats Going On in This Graph? | Free Speech - The New York Times