Introductory statistical inference texts and courses treat the point estimation, hypothesis testing, and interval estimation problems separately, with primary emphasis on large-sample approximations. Here, I present an alternative approach to teaching this course, built around p-values, emphasizing provably valid inference for all sample sizes. Details about computation and marginalization are also provided, with several illustrative examples, along with a course outline. Supplementary materials for this article are available online.

In over 100 years of blood donation practice, INTERVAL is the first randomised controlled trial to assess the impact of varying the frequency of blood donation on donor health and the blood supply. It provided policy-makers with evidence that collecting blood more frequently than current intervals can be implemented over two years without impacting on donor health, allowing better management of the supply to the NHS of units of blood with in-demand blood groups. INTERVAL was designed to deliver a multi-purpose strategy: an initial purpose related to blood donation research aiming to improve NHS Blood and Transplant’s core services and a longer-term purpose related to the creation of a comprehensive resource that will enable detailed studies of health-related questions.

Approximately 50,000 generally healthy blood donors were recruited between June 2012 and June 2014 from 25 NHS Blood Donation centres across England. Approximately equal numbers of men and women; aged from 18-80; ~93% white ancestry. All participants completed brief online questionnaires at baseline and gave blood samples for research purposes. Participants were randomised to giving blood every 8/10/12 weeks (for men) and 12/14/16 weeks (for women) over a 2-year period. ~30,000 participants returned after 2 years and completed a brief online questionnaire and gave further blood samples for research purposes.

The baseline questionnaire includes brief lifestyle information (smoking, alcohol consumption, etc), iron-related questions (e.g., red meat consumption), self-reported height and weight, etc. The SF-36 questionnaire was completed online at baseline and 2-years, with a 6-monthly SF-12 questionnaire between baseline and 2-years.

All participants have had the Affymetrix Axiom UK Biobank genotyping array assayed and then imputed to 1000G+UK10K combined reference panel (80M variants in total). 4,000 participants have 50X whole-exome sequencing and 12,000 participants have 15X whole-genome sequencing. Whole-blood RNA sequencing has commenced in ~5,000 participants.

The dataset also contains data on clinical chemistry biomarkers, blood cell traits, >200 lipoproteins, metabolomics (Metabolon HD4), lipidomics, and proteomics (SomaLogic, Olink), either cohort-wide or is large sub-sets of the cohort.

Statistics for the comparisons of the most commonly occurring melodic interval sizes in tone and non-tone language music databases; n1 and n2 refer to the sample sizes of tone and non-tone language music databases. (All comparisons were made with the two-tailed independent samples t-test, α-level adjusted using the Bonferroni method).

There are surveys that gather precise information on an outcome of interest, but measure continuous covariates by a discrete number of intervals, in which case the covariates are interval censored. For applications with a second independent dataset precisely measuring the covariates, but not the outcome, this paper introduces a semiparametrically efficient estimator for the coefficients in a linear regression model. The second sample serves to establish point identification. An empirical application investigating the relationship between income and body mass index illustrates the use of the estimator.

Companion data for the creation of a banksia plot:Background:In research evaluating statistical analysis methods, a common aim is to compare point estimates and confidence intervals (CIs) calculated from different analyses. This can be challenging when the outcomes (and their scale ranges) differ across datasets. We therefore developed a plot to facilitate pairwise comparisons of point estimates and confidence intervals from different statistical analyses both within and across datasets.Methods:The plot was developed and refined over the course of an empirical study. To compare results from a variety of different studies, a system of centring and scaling is used. Firstly, the point estimates from reference analyses are centred to zero, followed by scaling confidence intervals to span a range of one. The point estimates and confidence intervals from matching comparator analyses are then adjusted by the same amounts. This enables the relative positions of the point estimates and CI widths to be quickly assessed while maintaining the relative magnitudes of the difference in point estimates and confidence interval widths between the two analyses. Banksia plots can be graphed in a matrix, showing all pairwise comparisons of multiple analyses. In this paper, we show how to create a banksia plot and present two examples: the first relates to an empirical evaluation assessing the difference between various statistical methods across 190 interrupted time series (ITS) data sets with widely varying characteristics, while the second example assesses data extraction accuracy comparing results obtained from analysing original study data (43 ITS studies) with those obtained by four researchers from datasets digitally extracted from graphs from the accompanying manuscripts.Results:In the banksia plot of statistical method comparison, it was clear that there was no difference, on average, in point estimates and it was straightforward to ascertain which methods resulted in smaller, similar or larger confidence intervals than others. In the banksia plot comparing analyses from digitally extracted data to those from the original data it was clear that both the point estimates and confidence intervals were all very similar among data extractors and original data.Conclusions:The banksia plot, a graphical representation of centred and scaled confidence intervals, provides a concise summary of comparisons between multiple point estimates and associated CIs in a single graph. Through this visualisation, patterns and trends in the point estimates and confidence intervals can be easily identified.This collection of files allows the user to create the images used in the companion paper and amend this code to create their own banksia plots using either Stata version 17 or R version 4.3.1

Advances in technology allow the acquisition of data with high spatial and temporal resolution. These datasets are usually accompanied by estimates of the measurement uncertainty, which may be spatially or temporally varying and should be taken into consideration when making decisions based on the data. At the same time, various transformations are commonly implemented to reduce the dimensionality of the datasets for post-processing, or to extract significant features. However, the corresponding uncertainty is not usually represented in the low-dimensional or feature vector space. A method is proposed that maps the measurement uncertainty into the equivalent low-dimensional space with the aid of approximate Bayesian computation, resulting in a distribution that can be used to make statistical inferences. The method involves no assumptions about the probability distribution of the measurement error and is independent of the feature extraction process as demonstrated in three examples. In the first two examples Chebyshev polynomials were used to analyse structural displacements and soil moisture measurements; while in the third, principal component analysis was used to decompose global ocean temperature data. The uses of the method range from supporting decision making in model validation or confirmation, model updating or calibration and tracking changes in condition, such as the characterisation of the El Niño Southern Oscillation.

Supporting documentation on code lists, subject definitions, data accuracy, and statistical testing can be found on the American Community Survey website in the Data and Documentation section...Sample size and data quality measures (including coverage rates, allocation rates, and response rates) can be found on the American Community Survey website in the Methodology section..Tell us what you think. Provide feedback to help make American Community Survey data more useful for you..Although the American Community Survey (ACS) produces population, demographic and housing unit estimates, it is the Census Bureau''s Population Estimates Program that produces and disseminates the official estimates of the population for the nation, states, counties, cities and towns and estimates of housing units for states and counties..Explanation of Symbols:An ''**'' entry in the margin of error column indicates that either no sample observations or too few sample observations were available to compute a standard error and thus the margin of error. A statistical test is not appropriate..An ''-'' entry in the estimate column indicates that either no sample observations or too few sample observations were available to compute an estimate, or a ratio of medians cannot be calculated because one or both of the median estimates falls in the lowest interval or upper interval of an open-ended distribution..An ''-'' following a median estimate means the median falls in the lowest interval of an open-ended distribution..An ''+'' following a median estimate means the median falls in the upper interval of an open-ended distribution..An ''***'' entry in the margin of error column indicates that the median falls in the lowest interval or upper interval of an open-ended distribution. A statistical test is not appropriate..An ''*****'' entry in the margin of error column indicates that the estimate is controlled. A statistical test for sampling variability is not appropriate. .An ''N'' entry in the estimate and margin of error columns indicates that data for this geographic area cannot be displayed because the number of sample cases is too small..An ''(X)'' means that the estimate is not applicable or not available..Estimates of urban and rural population, housing units, and characteristics reflect boundaries of urban areas defined based on Census 2010 data. As a result, data for urban and rural areas from the ACS do not necessarily reflect the results of ongoing urbanization..While the 2016 American Community Survey (ACS) data generally reflect the February 2013 Office of Management and Budget (OMB) definitions of metropolitan and micropolitan statistical areas; in certain instances the names, codes, and boundaries of the principal cities shown in ACS tables may differ from the OMB definitions due to differences in the effective dates of the geographic entities..Industry codes are 4-digit codes and are based on the North American Industry Classification System 2012. The Industry categories adhere to the guidelines issued in Clarification Memorandum No. 2, "NAICS Alternate Aggregation Structure for Use By U.S. Statistical Agencies," issued by the Office of Management and Budget..Data are based on a sample and are subject to sampling variability. The degree of uncertainty for an estimate arising from sampling variability is represented through the use of a margin of error. The value shown here is the 90 percent margin of error. The margin of error can be interpreted roughly as providing a 90 percent probability that the interval defined by the estimate minus the margin of error and the estimate plus the margin of error (the lower and upper confidence bounds) contains the true value. In addition to sampling variability, the ACS estimates are subject to nonsampling error (for a discussion of nonsampling variability, see Accuracy of the Data). The effect of nonsampling error is not represented in these tables..Source: U.S. Census Bureau, 2016 American Community Survey 1-Year Estimates

U.S. Census Bureau 2020 block groups within the City of Seattle with American Community Survey (ACS) 5-year series data of frequently requested topics. Data is pulled from block group tables for the most recent ACS vintage. Seattle neighborhood geography of Council Districts, Comprehensive Plan Growth Areas are also included based on block group assignment.The census block groups have been assigned to a neighborhood based on the distribution of the total population from the 2020 decennial census for the component census blocks. If the majority of the population in the block group were inside the boundaries of the neighborhood, the block group was assigned wholly to that neighborhood.Feature layer created for and used in the Neighborhood Profiles application.The attribute data associated with this map is updated annually to contain the most currently released American Community Survey (ACS) 5-year data and contains estimates and margins of error. To see the full list of attributes available in this service, go to the "Data" tab, and choose "Fields" at the top right. Vintages: 2023ACS Table(s): Select fields from the tables listed here.Data downloaded from: Census Bureau's Explore Census Data The United States Census Bureau's American Community Survey (ACS):About the SurveyGeography & ACSTechnical DocumentationNews & UpdatesThis ready-to-use layer can be used within ArcGIS Pro, ArcGIS Online, its configurable apps, dashboards, Story Maps, custom apps, and mobile apps. Data can also be exported for offline workflows. Please cite the Census and ACS when using this data.Data Note from the Census:Data are based on a sample and are subject to sampling variability. The degree of uncertainty for an estimate arising from sampling variability is represented through the use of a margin of error. The value shown here is the 90 percent margin of error. The margin of error can be interpreted as providing a 90 percent probability that the interval defined by the estimate minus the margin of error and the estimate plus the margin of error (the lower and upper confidence bounds) contains the true value. In addition to sampling variability, the ACS estimates are subject to nonsampling error (for a discussion of nonsampling variability, see Accuracy of the Data). The effect of nonsampling error is not represented in these tables.Data Processing Notes:Boundaries come from the US Census TIGER geodatabases, specifically, the National Sub-State Geography Database (named tlgdb_(year)_a_us_substategeo.gdb). Boundaries are updated at the same time as the data updates (annually), and the boundary vintage appropriately matches the data vintage as specified by the Census. These are Census boundaries with water and/or coastlines erased for cartographic and mapping purposes. For census tracts, the water cutouts are derived from a subset of the 2020 Areal Hydrography boundaries offered by TIGER. Water bodies and rivers which are 50 million square meters or larger (mid to large sized water bodies) are erased from the tract level boundaries, as well as additional important features. For state and county boundaries, the water and coastlines are derived from the coastlines of the 2020 500k TIGER Cartographic Boundary Shapefiles. These are erased to more accurately portray the coastlines and Great Lakes. The original AWATER and ALAND fields are still available as attributes within the data table (units are square meters). The States layer contains 52 records - all US states, Washington D.C., and Puerto RicoCensus tracts with no population that occur in areas of water, such as oceans, are removed from this data service (Census Tracts beginning with 99).Percentages and derived counts, and associated margins of error, are calculated values (that can be identified by the "_calc_" stub in the field name), and abide by the specifications defined by the American Community Survey.Field alias names were created based on the Table Shells file available from the American Community Survey Summary File Documentation page.Negative values (e.g., -4444...) have been set to null, with the exception of -5555... which has been set to zero. These negative values exist in the raw API data to indicate the following situations:The margin of error column indicates that either no sample observations or too few sample observations were available to compute a standard error and thus the margin of error. A statistical test is not appropriate.Either no sample observations or too few sample observations were available to compute an estimate, or a ratio of medians cannot be calculated because one or both of the median estimates falls in the lowest interval or upper interval of an open-ended distribution.The median falls in the lowest interval of an open-ended distribution, or in the upper interval of an open-ended distribution. A statistical test is not appropriate.The estimate is controlled. A statistical test for sampling variability is not appropriate.The data for this geographic area cannot be displayed because the number of sample cases is too small.

This is the data set behind the Wind Generation Interactive Query Tool created by the CEC. The visualization tool interactively displays wind generation over different time intervals in three-dimensional space. The viewer can look across the state to understand generation patterns of regions with concentrations of wind power plants. The tool aids in understanding high and low periods of generation. Operation of the electric grid requires that generation and demand are balanced in each period.

Computed sample size, estimated expected width, and simulated expected width for 95% confidence interval of standardized contrast when the number of groups G = 3, standardized contrast effect ψ* = 0.5, and covariate disparity θ = 0.25.

This dataset is about: (Table 1) Number of counted pollen samples, intervals and time resolution between samples of ODP SIte 184-1144. Please consult parent dataset @ https://doi.org/10.1594/PANGAEA.738719 for more information.

Supporting documentation on code lists, subject definitions, data accuracy, and statistical testing can be found on the American Community Survey website in the Data and Documentation section...Sample size and data quality measures (including coverage rates, allocation rates, and response rates) can be found on the American Community Survey website in the Methodology section..Although the American Community Survey (ACS) produces population, demographic and housing unit estimates, for 2010, the 2010 Census provides the official counts of the population and housing units for the nation, states, counties, cities and towns..Explanation of Symbols:.An ''**'' entry in the margin of error column indicates that either no sample observations or too few sample observations were available to compute a standard error and thus the margin of error. A statistical test is not appropriate..An ''-'' entry in the estimate column indicates that either no sample observations or too few sample observations were available to compute an estimate, or a ratio of medians cannot be calculated because one or both of the median estimates falls in the lowest interval or upper interval of an open-ended distribution..An ''-'' following a median estimate means the median falls in the lowest interval of an open-ended distribution..An ''+'' following a median estimate means the median falls in the upper interval of an open-ended distribution..An ''***'' entry in the margin of error column indicates that the median falls in the lowest interval or upper interval of an open-ended distribution. A statistical test is not appropriate..An ''*****'' entry in the margin of error column indicates that the estimate is controlled. A statistical test for sampling variability is not appropriate. .An ''N'' entry in the estimate and margin of error columns indicates that data for this geographic area cannot be displayed because the number of sample cases is too small..An ''(X)'' means that the estimate is not applicable or not available..Estimates of urban and rural population, housing units, and characteristics reflect boundaries of urban areas defined based on Census 2000 data. Boundaries for urban areas have not been updated since Census 2000. As a result, data for urban and rural areas from the ACS do not necessarily reflect the results of ongoing urbanization..While the 2010 American Community Survey (ACS) data generally reflect the December 2009 Office of Management and Budget (OMB) definitions of metropolitan and micropolitan statistical areas; in certain instances the names, codes, and boundaries of the principal cities shown in ACS tables may differ from the OMB definitions due to differences in the effective dates of the geographic entities..Occupation codes are 4-digit codes and are based on Standard Occupational Classification 2010..Data are based on a sample and are subject to sampling variability. The degree of uncertainty for an estimate arising from sampling variability is represented through the use of a margin of error. The value shown here is the 90 percent margin of error. The margin of error can be interpreted roughly as providing a 90 percent probability that the interval defined by the estimate minus the margin of error and the estimate plus the margin of error (the lower and upper confidence bounds) contains the true value. In addition to sampling variability, the ACS estimates are subject to nonsampling error (for a discussion of nonsampling variability, see Accuracy of the Data). The effect of nonsampling error is not represented in these tables..Source: U.S. Census Bureau, 2010 American Community Survey

In 2019 the U.S. Geological Survey (USGS) quantitively assessed the potential for undiscovered, technically recoverable continuous (unconventional) oil and gas resources in the Niobrara interval of the Cody Shale in the Bighorn Basin Province (Finn and others, 2019). Leading up to the assessment, in 2017, the USGS collected samples from the Niobrara and underlying Sage Breaks intervals (Finn, 2019) to better characterize the source rock potential of the Niobrara interval. Eighty-two samples from 31 wells were collected from the well cuttings collection stored at the USGS Core Research Center in Lakewood, Colorado. The selected wells are located near the outcrop belt along the shallow margins of the basin to obtain samples that were not subjected to the effects of deep burial and subsequent organic carbon loss due to thermal maturation as described by Daly and Edman (1987) (fig. 1). Sixty samples are from the Niobrara interval, and 22 from the Sage Breaks interval (fig. 2).

Computed sample size, estimated assurance probability, and simulated assurance probability for 95% confidence interval of standardized contrast when the number of groups G = 3, standardized contrast effect ψ* = 0.5, assurance probability 1 –γ = 0.80, and covariate disparity θ = 0.

Supporting documentation on code lists, subject definitions, data accuracy, and statistical testing can be found on the American Community Survey website in the Data and Documentation section...Sample size and data quality measures (including coverage rates, allocation rates, and response rates) can be found on the American Community Survey website in the Methodology section..Tell us what you think. Provide feedback to help make American Community Survey data more useful for you..Although the American Community Survey (ACS) produces population, demographic and housing unit estimates, it is the Census Bureau''s Population Estimates Program that produces and disseminates the official estimates of the population for the nation, states, counties, cities and towns and estimates of housing units for states and counties..Explanation of Symbols:An ''**'' entry in the margin of error column indicates that either no sample observations or too few sample observations were available to compute a standard error and thus the margin of error. A statistical test is not appropriate..An ''-'' entry in the estimate column indicates that either no sample observations or too few sample observations were available to compute an estimate, or a ratio of medians cannot be calculated because one or both of the median estimates falls in the lowest interval or upper interval of an open-ended distribution..An ''-'' following a median estimate means the median falls in the lowest interval of an open-ended distribution..An ''+'' following a median estimate means the median falls in the upper interval of an open-ended distribution..An ''***'' entry in the margin of error column indicates that the median falls in the lowest interval or upper interval of an open-ended distribution. A statistical test is not appropriate..An ''*****'' entry in the margin of error column indicates that the estimate is controlled. A statistical test for sampling variability is not appropriate. .An ''N'' entry in the estimate and margin of error columns indicates that data for this geographic area cannot be displayed because the number of sample cases is too small..An ''(X)'' means that the estimate is not applicable or not available..Estimates of urban and rural population, housing units, and characteristics reflect boundaries of urban areas defined based on Census 2010 data. As a result, data for urban and rural areas from the ACS do not necessarily reflect the results of ongoing urbanization..While the 2016 American Community Survey (ACS) data generally reflect the February 2013 Office of Management and Budget (OMB) definitions of metropolitan and micropolitan statistical areas; in certain instances the names, codes, and boundaries of the principal cities shown in ACS tables may differ from the OMB definitions due to differences in the effective dates of the geographic entities..The Census Bureau introduced a new set of disability questions in the 2008 ACS questionnaire. Accordingly, comparisons of disability data from 2008 or later with data from prior years are not recommended. For more information on these questions and their evaluation in the 2006 ACS Content Test, see the Evaluation Report Covering Disability..Data are based on a sample and are subject to sampling variability. The degree of uncertainty for an estimate arising from sampling variability is represented through the use of a margin of error. The value shown here is the 90 percent margin of error. The margin of error can be interpreted roughly as providing a 90 percent probability that the interval defined by the estimate minus the margin of error and the estimate plus the margin of error (the lower and upper confidence bounds) contains the true value. In addition to sampling variability, the ACS estimates are subject to nonsampling error (for a discussion of nonsampling variability, see Accuracy of the Data). The effect of nonsampling error is not represented in these tables..Source: U.S. Census Bureau, 2016 American Community Survey 1-Year Estimates

With the rapid development of data acquisition and storage space, massive datasets exhibited with large sample size emerge increasingly and make more advanced statistical tools urgently need. To accommodate such big volume in the analysis, a variety of methods have been proposed in the circumstances of complete or right censored survival data. However, existing development of big data methodology has not attended to interval-censored outcomes, which are ubiquitous in cross-sectional or periodical follow-up studies. In this work, we propose an easily implemented divide-and-combine approach for analyzing massive interval-censored survival data under the additive hazards model. We establish the asymptotic properties of the proposed estimator, including the consistency and asymptotic normality. In addition, the divide-and-combine estimator is shown to be asymptotically equivalent to the full-data-based estimator obtained from analyzing all data together. Simulation studies suggest that, relative to the full-data-based approach, the proposed divide-and-combine approach has desirable advantage in terms of computation time, making it more applicable to large-scale data analysis. An application to a set of interval-censored data also demonstrates the practical utility of the proposed method.

Supporting documentation on code lists, subject definitions, data accuracy, and statistical testing can be found on the American Community Survey website in the Data and Documentation section...Sample size and data quality measures (including coverage rates, allocation rates, and response rates) can be found on the American Community Survey website in the Methodology section..Although the American Community Survey (ACS) produces population, demographic and housing unit estimates, it is the Census Bureau''s Population Estimates Program that produces and disseminates the official estimates of the population for the nation, states, counties, cities and towns and estimates of housing units for states and counties..Explanation of Symbols:An ''**'' entry in the margin of error column indicates that either no sample observations or too few sample observations were available to compute a standard error and thus the margin of error. A statistical test is not appropriate..An ''-'' entry in the estimate column indicates that either no sample observations or too few sample observations were available to compute an estimate, or a ratio of medians cannot be calculated because one or both of the median estimates falls in the lowest interval or upper interval of an open-ended distribution..An ''-'' following a median estimate means the median falls in the lowest interval of an open-ended distribution..An ''+'' following a median estimate means the median falls in the upper interval of an open-ended distribution..An ''***'' entry in the margin of error column indicates that the median falls in the lowest interval or upper interval of an open-ended distribution. A statistical test is not appropriate..An ''*****'' entry in the margin of error column indicates that the estimate is controlled. A statistical test for sampling variability is not appropriate. .An ''N'' entry in the estimate and margin of error columns indicates that data for this geographic area cannot be displayed because the number of sample cases is too small..An ''(X)'' means that the estimate is not applicable or not available..Estimates of urban and rural population, housing units, and characteristics reflect boundaries of urban areas defined based on Census 2010 data. As a result, data for urban and rural areas from the ACS do not necessarily reflect the results of ongoing urbanization..While the 2009-2013 American Community Survey (ACS) data generally reflect the February 2013 Office of Management and Budget (OMB) definitions of metropolitan and micropolitan statistical areas; in certain instances the names, codes, and boundaries of the principal cities shown in ACS tables may differ from the OMB definitions due to differences in the effective dates of the geographic entities..Methodological changes to data collection in 2013 may have affected language data for 2013. Users should be aware of these changes when using multi-year data containing data from 2013..Data are based on a sample and are subject to sampling variability. The degree of uncertainty for an estimate arising from sampling variability is represented through the use of a margin of error. The value shown here is the 90 percent margin of error. The margin of error can be interpreted roughly as providing a 90 percent probability that the interval defined by the estimate minus the margin of error and the estimate plus the margin of error (the lower and upper confidence bounds) contains the true value. In addition to sampling variability, the ACS estimates are subject to nonsampling error (for a discussion of nonsampling variability, see Accuracy of the Data). The effect of nonsampling error is not represented in these tables..Source: U.S. Census Bureau, 2009-2013 5-Year American Community Survey

Supporting documentation on code lists, subject definitions, data accuracy, and statistical testing can be found on the American Community Survey website in the Data and Documentation section...Sample size and data quality measures (including coverage rates, allocation rates, and response rates) can be found on the American Community Survey website in the Methodology section..Although the American Community Survey (ACS) produces population, demographic and housing unit estimates, it is the Census Bureau''s Population Estimates Program that produces and disseminates the official estimates of the population for the nation, states, counties, cities and towns and estimates of housing units for states and counties..Explanation of Symbols:An ''**'' entry in the margin of error column indicates that either no sample observations or too few sample observations were available to compute a standard error and thus the margin of error. A statistical test is not appropriate..An ''-'' entry in the estimate column indicates that either no sample observations or too few sample observations were available to compute an estimate, or a ratio of medians cannot be calculated because one or both of the median estimates falls in the lowest interval or upper interval of an open-ended distribution..An ''-'' following a median estimate means the median falls in the lowest interval of an open-ended distribution..An ''+'' following a median estimate means the median falls in the upper interval of an open-ended distribution..An ''***'' entry in the margin of error column indicates that the median falls in the lowest interval or upper interval of an open-ended distribution. A statistical test is not appropriate..An ''*****'' entry in the margin of error column indicates that the estimate is controlled. A statistical test for sampling variability is not appropriate. .An ''N'' entry in the estimate and margin of error columns indicates that data for this geographic area cannot be displayed because the number of sample cases is too small..An ''(X)'' means that the estimate is not applicable or not available..Estimates of urban and rural population, housing units, and characteristics reflect boundaries of urban areas defined based on Census 2010 data. As a result, data for urban and rural areas from the ACS do not necessarily reflect the results of ongoing urbanization..While the 2013 American Community Survey (ACS) data generally reflect the February 2013 Office of Management and Budget (OMB) definitions of metropolitan and micropolitan statistical areas; in certain instances the names, codes, and boundaries of the principal cities shown in ACS tables may differ from the OMB definitions due to differences in the effective dates of the geographic entities..Tables for ACS data year 2010 and later are not completely comparable to the table based on 2009 ACS data due to slight changes in the field of degree coding and classifications. More information can be found at http://www.census.gov/hhes/socdemo/education/data/acs/index.html..Respondents could report more than one major for their bachelor's degree. This table only counts the first major that was reported and does not necessarily reflect the first degree earned..In data year 2013, there were a series of changes to data collection operations that could have affected some estimates. These changes include the addition of Internet as a mode of data collection, the end of the content portion of Failed Edit Follow-Up interviewing, and the loss of one monthly panel due to the Federal Government shut down in October 2013. For more information, see: User Notes.Data are based on a sample and are subject to sampling variability. The degree of uncertainty for an estimate arising from sampling variability is represented through the use of a margin of error. The value shown here is the 90 percent margin of error. The margin of error can be interpreted roughly as providing a 90 percent probability that the interval defined by the estimate minus the margin of error and the estimate plus the margin of error (the lower and upper confidence bounds) contains the true value. In addition to sampling variability, the ACS estimates are subject to nonsampling error (for a discussion of nonsampling variability, see Accuracy of the Data). The effect of nonsampling error is not represented in these tables..Source: U.S. Census Bureau, 2013 American Community Survey

Supporting documentation on code lists, subject definitions, data accuracy, and statistical testing can be found on the American Community Survey website in the Data and Documentation section...Sample size and data quality measures (including coverage rates, allocation rates, and response rates) can be found on the American Community Survey website in the Methodology section..Although the American Community Survey (ACS) produces population, demographic and housing unit estimates, it is the Census Bureau''s Population Estimates Program that produces and disseminates the official estimates of the population for the nation, states, counties, cities and towns and estimates of housing units for states and counties..Explanation of Symbols:An ''**'' entry in the margin of error column indicates that either no sample observations or too few sample observations were available to compute a standard error and thus the margin of error. A statistical test is not appropriate..An ''-'' entry in the estimate column indicates that either no sample observations or too few sample observations were available to compute an estimate, or a ratio of medians cannot be calculated because one or both of the median estimates falls in the lowest interval or upper interval of an open-ended distribution..An ''-'' following a median estimate means the median falls in the lowest interval of an open-ended distribution..An ''+'' following a median estimate means the median falls in the upper interval of an open-ended distribution..An ''***'' entry in the margin of error column indicates that the median falls in the lowest interval or upper interval of an open-ended distribution. A statistical test is not appropriate..An ''*****'' entry in the margin of error column indicates that the estimate is controlled. A statistical test for sampling variability is not appropriate. .An ''N'' entry in the estimate and margin of error columns indicates that data for this geographic area cannot be displayed because the number of sample cases is too small..An ''(X)'' means that the estimate is not applicable or not available..Estimates of urban and rural population, housing units, and characteristics reflect boundaries of urban areas defined based on Census 2000 data. Boundaries for urban areas have not been updated since Census 2000. As a result, data for urban and rural areas from the ACS do not necessarily reflect the results of ongoing urbanization..While the 2011 American Community Survey (ACS) data generally reflect the December 2009 Office of Management and Budget (OMB) definitions of metropolitan and micropolitan statistical areas; in certain instances the names, codes, and boundaries of the principal cities shown in ACS tables may differ from the OMB definitions due to differences in the effective dates of the geographic entities..The health insurance coverage category names were modified in 2010. See ACS Health Insurance Definitions for a list of the insurance type definitions..Data are based on a sample and are subject to sampling variability. The degree of uncertainty for an estimate arising from sampling variability is represented through the use of a margin of error. The value shown here is the 90 percent margin of error. The margin of error can be interpreted roughly as providing a 90 percent probability that the interval defined by the estimate minus the margin of error and the estimate plus the margin of error (the lower and upper confidence bounds) contains the true value. In addition to sampling variability, the ACS estimates are subject to nonsampling error (for a discussion of nonsampling variability, see Accuracy of the Data). The effect of nonsampling error is not represented in these tables..Source: U.S. Census Bureau, 2011 American Community Survey

In genomic study, log transformation is a common prepossessing step to adjust for skewness in data. This standard approach often assumes that log-transformed data is normally distributed, and two sample t-test (or its modifications) is used for detecting differences between two experimental conditions. However, recently it was shown that two sample t-test can lead to exaggerated false positives, and the Wilcoxon-Mann-Whitney (WMW) test was proposed as an alternative for studies with larger sample sizes. In addition, studies have demonstrated that the specific distribution used in modeling genomic data has profound impact on the interpretation and validity of results. The aim of this paper is three-fold: 1) to present the Exp-gamma distribution (exponential-gamma distribution stands for log-transformed gamma distribution) as a proper biological and statistical model for the analysis of log-transformed protein abundance data from single-cell experiments; 2) to demonstrate the inappropriateness of two sample t-test and the WMW test in analyzing log-transformed protein abundance data; 3) to propose and evaluate statistical inference methods for hypothesis testing and confidence interval estimation when comparing two independent samples under the Exp-gamma distributions. The proposed methods are applied to analyze protein abundance data from a single-cell dataset.