Examples demonstrating how confidence intervals change depending on the level of confidence (90% versus 95% versus 99%) and on the size of the sample (CI for n=20 versus n=10 versus n=2). Developed for BIO211 (Statistics and Data Analysis: A Conceptual Approach) at Stony Brook University in Fall 2015.

Dataset

This dataset was created by Kleber Bernardo

Released under CC BY-NC-SA 4.0

Contents

Model performance evaluation: The Mean Winkler Interval score (MWIS)

We can assess the overall performance of a regression model that produces prediction intervals by using the mean Winkler Interval score [1,2,3] which, for an individual interval, is given by:

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where \(y\) is the true value, \(u\) it the upper prediction interval, \(l\) is the lower prediction interval, and \(\alpha\) is (1-coverage). For example, for 90% coverage, \(\alpha = 0.1\). Note that the Winkler Interval score constitutes a proper scoring rule [2,3].

• [1] Robert L. Winkler "*A Decision-Theoretic Approach to Interval Estimation*", Journal of the American Statistical Association, volume 67, pp. 187-191 (1972)
• [2] Tilmann Gneiting and Adrian E Raftery "*Strictly Proper Scoring Rules, Prediction, and Estimation*", Journal of the American Statistical Association, volume 102, pp. 359-378 (2007) (Section 6.2)
• [3] Jonas R. Brehmer, and Tilmann Gneiting "*Scoring interval forecasts: Equal-tailed, shortest, and modal interval*", Bernoulli volume 27 pp. 1993-2010 (2021)

Python code: Usage example

Attach this dataset to a notebook, then:

import sys
sys.path.append('/kaggle/input/winkler-interval-score-metric/')
import MWIS_metric
help(MWIS_metric.score)

MWIS,coverage = MWIS_metric.score(predictions["y_true"],predictions["lower"],predictions["upper"],alpha)
print(f"Local MWI score   ",round(MWIS,3))
print("Predictions coverage  ", round(coverage*100,1),"%")

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.

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.

Project Tycho datasets contain case counts for reported disease conditions for countries around the world. The Project Tycho data curation team extracts these case counts from various reputable sources, typically from national or international health authorities, such as the US Centers for Disease Control or the World Health Organization. These original data sources include both open- and restricted-access sources. For restricted-access sources, the Project Tycho team has obtained permission for redistribution from data contributors. All datasets contain case count data that are identical to counts published in the original source and no counts have been modified in any way by the Project Tycho team. The Project Tycho team has pre-processed datasets by adding new variables, such as standard disease and location identifiers, that improve data interpretability. We also formatted the data into a standard data format.

Each Project Tycho dataset contains case counts for a specific condition (e.g. measles) and for a specific country (e.g. The United States). Case counts are reported per time interval. In addition to case counts, datasets include information about these counts (attributes), such as the location, age group, subpopulation, diagnostic certainty, place of acquisition, and the source from which we extracted case counts. One dataset can include many series of case count time intervals, such as "US measles cases as reported by CDC", or "US measles cases reported by WHO", or "US measles cases that originated abroad", etc.

Depending on the intended use of a dataset, we recommend a few data processing steps before analysis: - Analyze missing data: Project Tycho datasets do not include time intervals for which no case count was reported (for many datasets, time series of case counts are incomplete, due to incompleteness of source documents) and users will need to add time intervals for which no count value is available. Project Tycho datasets do include time intervals for which a case count value of zero was reported. - Separate cumulative from non-cumulative time interval series. Case count time series in Project Tycho datasets can be "cumulative" or "fixed-intervals". Cumulative case count time series consist of overlapping case count intervals starting on the same date, but ending on different dates. For example, each interval in a cumulative count time series can start on January 1st, but end on January 7th, 14th, 21st, etc. It is common practice among public health agencies to report cases for cumulative time intervals. Case count series with fixed time intervals consist of mutually exclusive time intervals that all start and end on different dates and all have identical length (day, week, month, year). Given the different nature of these two types of case count data, we indicated this with an attribute for each count value, named "PartOfCumulativeCountSeries".

Project Tycho datasets contain case counts for reported disease conditions for countries around the world. The Project Tycho data curation team extracts these case counts from various reputable sources, typically from national or international health authorities, such as the US Centers for Disease Control or the World Health Organization. These original data sources include both open- and restricted-access sources. For restricted-access sources, the Project Tycho team has obtained permission for redistribution from data contributors. All datasets contain case count data that are identical to counts published in the original source and no counts have been modified in any way by the Project Tycho team. The Project Tycho team has pre-processed datasets by adding new variables, such as standard disease and location identifiers, that improve data interpretability. We also formatted the data into a standard data format.

Each Project Tycho dataset contains case counts for a specific condition (e.g. measles) and for a specific country (e.g. The United States). Case counts are reported per time interval. In addition to case counts, datasets include information about these counts (attributes), such as the location, age group, subpopulation, diagnostic certainty, place of acquisition, and the source from which we extracted case counts. One dataset can include many series of case count time intervals, such as "US measles cases as reported by CDC", or "US measles cases reported by WHO", or "US measles cases that originated abroad", etc.

Depending on the intended use of a dataset, we recommend a few data processing steps before analysis: - Analyze missing data: Project Tycho datasets do not include time intervals for which no case count was reported (for many datasets, time series of case counts are incomplete, due to incompleteness of source documents) and users will need to add time intervals for which no count value is available. Project Tycho datasets do include time intervals for which a case count value of zero was reported. - Separate cumulative from non-cumulative time interval series. Case count time series in Project Tycho datasets can be "cumulative" or "fixed-intervals". Cumulative case count time series consist of overlapping case count intervals starting on the same date, but ending on different dates. For example, each interval in a cumulative count time series can start on January 1st, but end on January 7th, 14th, 21st, etc. It is common practice among public health agencies to report cases for cumulative time intervals. Case count series with fixed time intervals consist of mutually exclusive time intervals that all start and end on different dates and all have identical length (day, week, month, year). Given the different nature of these two types of case count data, we indicated this with an attribute for each count value, named "PartOfCumulativeCountSeries".

Wetland sediment data was collected from coastal Louisiana as part of a pilot study to develop a diatom-based proxy for past wetland water chemistry and the identification of sediment deposits for tropical storms. The complete dataset includes forty-six surface sediment samples and nine sediment cores. The surface sediment samples were collected in fresh to brackish marsh throughout the southwest Louisiana Chenier Plain and are located coincident with Coastwide Reference Monitoring System (CRMS). Sediment cores were collected at Rockefeller Wildlife Refuge. The data described here include sedimentary properties, radioisotopes, x-radiographs, and diatom species counts for depth-interval samples of sediment cores.

Abstract–In the pharmaceutical industry, all analytical methods must be shown to deliver unbiased and precise results. In an assay qualification or validation study, the trueness, accuracy, and intermediate precision are usually assessed by comparing the measured concentrations to their nominal levels. Trueness is assessed by using Confidence Intervals (CIs) of mean measured concentration, accuracy by Prediction Intervals (PIs) for a future measured concentration, and the intermediate precision by the total variance. ICH and USP guidelines alike request that all relevant sources of variability must be studied, for example, the effect of different technicians, the day-to-day variability or the use of multiple reagent lots. Those different random effects must be modeled as crossed, nested, or a combination of both; while concatenating them to simplify the model is often taken place. This article compares this simplified approach to a mixed model with the actual design. Our simulation study shows an under-estimation of the intermediate precision and, therefore, a substantial reduction of the CI and PI. The power for accuracy or trueness is consequently over-estimated when designing a new study. Two real datasets from assay validation study during vaccine development are used to illustrate the impact of such concatenation of random variables.

Project Tycho datasets contain case counts for reported disease conditions for countries around the world. The Project Tycho data curation team extracts these case counts from various reputable sources, typically from national or international health authorities, such as the US Centers for Disease Control or the World Health Organization. These original data sources include both open- and restricted-access sources. For restricted-access sources, the Project Tycho team has obtained permission for redistribution from data contributors. All datasets contain case count data that are identical to counts published in the original source and no counts have been modified in any way by the Project Tycho team. The Project Tycho team has pre-processed datasets by adding new variables, such as standard disease and location identifiers, that improve data interpretabilty. We also formatted the data into a standard data format.

Each Project Tycho dataset contains case counts for a specific condition (e.g. measles) and for a specific country (e.g. The United States). Case counts are reported per time interval. In addition to case counts, datsets include information about these counts (attributes), such as the location, age group, subpopulation, diagnostic certainty, place of aquisition, and the source from which we extracted case counts. One dataset can include many series of case count time intervals, such as "US measles cases as reported by CDC", or "US measles cases reported by WHO", or "US measles cases that originated abroad", etc.

Depending on the intended use of a dataset, we recommend a few data processing steps before analysis:

• Analyze missing data: Project Tycho datasets do not inlcude time intervals for which no case count was reported (for many datasets, time series of case counts are incomplete, due to incompleteness of source documents) and users will need to add time intervals for which no count value is available. Project Tycho datasets do include time intervals for which a case count value of zero was reported.
• Separate cumulative from non-cumulative time interval series. Case count time series in Project Tycho datasets can be "cumulative" or "fixed-intervals". Cumulative case count time series consist of overlapping case count intervals starting on the same date, but ending on different dates. For example, each interval in a cumulative count time series can start on January 1st, but end on January 7th, 14th, 21st, etc. It is common practice among public health agencies to report cases for cumulative time intervals. Case count series with fixed time intervals consist of mutually exxclusive time intervals that all start and end on different dates and all have identical length (day, week, month, year). Given the different nature of these two types of case count data, we indicated this with an attribute for each count value, named "PartOfCumulativeCountSeries".

Example drills from the low-volume high-intensity interval training sessions.

Project Tycho datasets contain case counts for reported disease conditions for countries around the world. The Project Tycho data curation team extracts these case counts from various reputable sources, typically from national or international health authorities, such as the US Centers for Disease Control or the World Health Organization. These original data sources include both open- and restricted-access sources. For restricted-access sources, the Project Tycho team has obtained permission for redistribution from data contributors. All datasets contain case count data that are identical to counts published in the original source and no counts have been modified in any way by the Project Tycho team. The Project Tycho team has pre-processed datasets by adding new variables, such as standard disease and location identifiers, that improve data interpretability. We also formatted the data into a standard data format.

Each Project Tycho dataset contains case counts for a specific condition (e.g. measles) and for a specific country (e.g. The United States). Case counts are reported per time interval. In addition to case counts, datasets include information about these counts (attributes), such as the location, age group, subpopulation, diagnostic certainty, place of acquisition, and the source from which we extracted case counts. One dataset can include many series of case count time intervals, such as "US measles cases as reported by CDC", or "US measles cases reported by WHO", or "US measles cases that originated abroad", etc.

Depending on the intended use of a dataset, we recommend a few data processing steps before analysis: - Analyze missing data: Project Tycho datasets do not include time intervals for which no case count was reported (for many datasets, time series of case counts are incomplete, due to incompleteness of source documents) and users will need to add time intervals for which no count value is available. Project Tycho datasets do include time intervals for which a case count value of zero was reported. - Separate cumulative from non-cumulative time interval series. Case count time series in Project Tycho datasets can be "cumulative" or "fixed-intervals". Cumulative case count time series consist of overlapping case count intervals starting on the same date, but ending on different dates. For example, each interval in a cumulative count time series can start on January 1st, but end on January 7th, 14th, 21st, etc. It is common practice among public health agencies to report cases for cumulative time intervals. Case count series with fixed time intervals consist of mutually exclusive time intervals that all start and end on different dates and all have identical length (day, week, month, year). Given the different nature of these two types of case count data, we indicated this with an attribute for each count value, named "PartOfCumulativeCountSeries".

Many biomedical and clinical studies with time-to-event outcomes involve competing risks data. These data are frequently subject to interval censoring. This means that the failure time is not precisely observed, but is only known to lie between two observation times such as clinical visits in a cohort study. Not taking into account the interval censoring may result in biased estimation of the cause-specific cumulative incidence function, an important quantity in the competing risk framework, used for evaluating interventions in populations, for studying the prognosis of various diseases and for prediction and implementation science purposes. In this work we consider the class of semiparametric generalized odds-rate transformation models in the context of sieve maximum likelihood estimation based on B-splines. This large class of models includes both the proportional odds and the proportional subdistribution hazard models (i.e., the Fine-Gray model) as special cases. The estimator for the regression parameter is shown to be semiparametrically efficient and asymptotically normal. Simulation studies suggest that the method performs well even with small sample sizes. As an illustration we use the proposed method to analyze data from HIV-infected individuals obtained from a large cohort study in sub-Saharan Africa. We also provide the R function ciregic that implements the proposed method, and present an illustrate example.

This 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. The height and color of columns at wind generation areas are scaled and shaded to represent capacity factors (CFs) of the areas in a specific time interval. Capacity factor is the ratio of the energy produced to the amount of energy that could ideally have been produced in the same period using the rated nameplate capacity. Due to natural variations in wind speeds, higher factors tend to be seen over short time periods, with lower factors over longer periods. The capacity used is the reported nameplate capacity from the Quarterly Fuel and Energy Report, CEC-1304A. CFs are based on wind plants in service in the wind generation areas.Renewable energy resources like wind facilities vary in size and geographic distribution within each state. Resource planning, land use constraints, climate zones, and weather patterns limit availability of these resources and where they can be developed. National, state, and local policies also set limits on energy generation and use. An example of resource planning in California is the Desert Renewable Energy Conservation Plan. By exploring the visualization, a viewer can gain a three-dimensional understanding of temporal variation in generation CFs, along with how the wind generation areas compare to one another. The viewer can observe that areas peak in generation in different periods. The large range in CFs is also visible.

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

Project Tycho datasets contain case counts for reported disease conditions for countries around the world. The Project Tycho data curation team extracts these case counts from various reputable sources, typically from national or international health authorities, such as the US Centers for Disease Control or the World Health Organization. These original data sources include both open- and restricted-access sources. For restricted-access sources, the Project Tycho team has obtained permission for redistribution from data contributors. All datasets contain case count data that are identical to counts published in the original source and no counts have been modified in any way by the Project Tycho team. The Project Tycho team has pre-processed datasets by adding new variables, such as standard disease and location identifiers, that improve data interpretabilty. We also formatted the data into a standard data format.

Each Project Tycho dataset contains case counts for a specific condition (e.g. measles) and for a specific country (e.g. The United States). Case counts are reported per time interval. In addition to case counts, datsets include information about these counts (attributes), such as the location, age group, subpopulation, diagnostic certainty, place of aquisition, and the source from which we extracted case counts. One dataset can include many series of case count time intervals, such as "US measles cases as reported by CDC", or "US measles cases reported by WHO", or "US measles cases that originated abroad", etc.

Depending on the intended use of a dataset, we recommend a few data processing steps before analysis:

• Analyze missing data: Project Tycho datasets do not inlcude time intervals for which no case count was reported (for many datasets, time series of case counts are incomplete, due to incompleteness of source documents) and users will need to add time intervals for which no count value is available. Project Tycho datasets do include time intervals for which a case count value of zero was reported.
• Separate cumulative from non-cumulative time interval series. Case count time series in Project Tycho datasets can be "cumulative" or "fixed-intervals". Cumulative case count time series consist of overlapping case count intervals starting on the same date, but ending on different dates. For example, each interval in a cumulative count time series can start on January 1st, but end on January 7th, 14th, 21st, etc. It is common practice among public health agencies to report cases for cumulative time intervals. Case count series with fixed time intervals consist of mutually exxclusive time intervals that all start and end on different dates and all have identical length (day, week, month, year). Given the different nature of these two types of case count data, we indicated this with an attribute for each count value, named "PartOfCumulativeCountSeries".

Project Tycho datasets contain case counts for reported disease conditions for countries around the world. The Project Tycho data curation team extracts these case counts from various reputable sources, typically from national or international health authorities, such as the US Centers for Disease Control or the World Health Organization. These original data sources include both open- and restricted-access sources. For restricted-access sources, the Project Tycho team has obtained permission for redistribution from data contributors. All datasets contain case count data that are identical to counts published in the original source and no counts have been modified in any way by the Project Tycho team. The Project Tycho team has pre-processed datasets by adding new variables, such as standard disease and location identifiers, that improve data interpretability. We also formatted the data into a standard data format.

Each Project Tycho dataset contains case counts for a specific condition (e.g. measles) and for a specific country (e.g. The United States). Case counts are reported per time interval. In addition to case counts, datasets include information about these counts (attributes), such as the location, age group, subpopulation, diagnostic certainty, place of acquisition, and the source from which we extracted case counts. One dataset can include many series of case count time intervals, such as "US measles cases as reported by CDC", or "US measles cases reported by WHO", or "US measles cases that originated abroad", etc.

Depending on the intended use of a dataset, we recommend a few data processing steps before analysis: - Analyze missing data: Project Tycho datasets do not include time intervals for which no case count was reported (for many datasets, time series of case counts are incomplete, due to incompleteness of source documents) and users will need to add time intervals for which no count value is available. Project Tycho datasets do include time intervals for which a case count value of zero was reported. - Separate cumulative from non-cumulative time interval series. Case count time series in Project Tycho datasets can be "cumulative" or "fixed-intervals". Cumulative case count time series consist of overlapping case count intervals starting on the same date, but ending on different dates. For example, each interval in a cumulative count time series can start on January 1st, but end on January 7th, 14th, 21st, etc. It is common practice among public health agencies to report cases for cumulative time intervals. Case count series with fixed time intervals consist of mutually exclusive time intervals that all start and end on different dates and all have identical length (day, week, month, year). Given the different nature of these two types of case count data, we indicated this with an attribute for each count value, named "PartOfCumulativeCountSeries".

Project Tycho datasets contain case counts for reported disease conditions for countries around the world. The Project Tycho data curation team extracts these case counts from various reputable sources, typically from national or international health authorities, such as the US Centers for Disease Control or the World Health Organization. These original data sources include both open- and restricted-access sources. For restricted-access sources, the Project Tycho team has obtained permission for redistribution from data contributors. All datasets contain case count data that are identical to counts published in the original source and no counts have been modified in any way by the Project Tycho team. The Project Tycho team has pre-processed datasets by adding new variables, such as standard disease and location identifiers, that improve data interpretabilty. We also formatted the data into a standard data format.

Each Project Tycho dataset contains case counts for a specific condition (e.g. measles) and for a specific country (e.g. The United States). Case counts are reported per time interval. In addition to case counts, datsets include information about these counts (attributes), such as the location, age group, subpopulation, diagnostic certainty, place of aquisition, and the source from which we extracted case counts. One dataset can include many series of case count time intervals, such as "US measles cases as reported by CDC", or "US measles cases reported by WHO", or "US measles cases that originated abroad", etc.

Depending on the intended use of a dataset, we recommend a few data processing steps before analysis:

• Analyze missing data: Project Tycho datasets do not inlcude time intervals for which no case count was reported (for many datasets, time series of case counts are incomplete, due to incompleteness of source documents) and users will need to add time intervals for which no count value is available. Project Tycho datasets do include time intervals for which a case count value of zero was reported.
• Separate cumulative from non-cumulative time interval series. Case count time series in Project Tycho datasets can be "cumulative" or "fixed-intervals". Cumulative case count time series consist of overlapping case count intervals starting on the same date, but ending on different dates. For example, each interval in a cumulative count time series can start on January 1st, but end on January 7th, 14th, 21st, etc. It is common practice among public health agencies to report cases for cumulative time intervals. Case count series with fixed time intervals consist of mutually exxclusive time intervals that all start and end on different dates and all have identical length (day, week, month, year). Given the different nature of these two types of case count data, we indicated this with an attribute for each count value, named "PartOfCumulativeCountSeries".

Project Tycho datasets contain case counts for reported disease conditions for countries around the world. The Project Tycho data curation team extracts these case counts from various reputable sources, typically from national or international health authorities, such as the US Centers for Disease Control or the World Health Organization. These original data sources include both open- and restricted-access sources. For restricted-access sources, the Project Tycho team has obtained permission for redistribution from data contributors. All datasets contain case count data that are identical to counts published in the original source and no counts have been modified in any way by the Project Tycho team. The Project Tycho team has pre-processed datasets by adding new variables, such as standard disease and location identifiers, that improve data interpretability. We also formatted the data into a standard data format.

Each Project Tycho dataset contains case counts for a specific condition (e.g. measles) and for a specific country (e.g. The United States). Case counts are reported per time interval. In addition to case counts, datasets include information about these counts (attributes), such as the location, age group, subpopulation, diagnostic certainty, place of acquisition, and the source from which we extracted case counts. One dataset can include many series of case count time intervals, such as "US measles cases as reported by CDC", or "US measles cases reported by WHO", or "US measles cases that originated abroad", etc.

Depending on the intended use of a dataset, we recommend a few data processing steps before analysis: - Analyze missing data: Project Tycho datasets do not include time intervals for which no case count was reported (for many datasets, time series of case counts are incomplete, due to incompleteness of source documents) and users will need to add time intervals for which no count value is available. Project Tycho datasets do include time intervals for which a case count value of zero was reported. - Separate cumulative from non-cumulative time interval series. Case count time series in Project Tycho datasets can be "cumulative" or "fixed-intervals". Cumulative case count time series consist of overlapping case count intervals starting on the same date, but ending on different dates. For example, each interval in a cumulative count time series can start on January 1st, but end on January 7th, 14th, 21st, etc. It is common practice among public health agencies to report cases for cumulative time intervals. Case count series with fixed time intervals consist of mutually exclusive time intervals that all start and end on different dates and all have identical length (day, week, month, year). Given the different nature of these two types of case count data, we indicated this with an attribute for each count value, named "PartOfCumulativeCountSeries".

Project Tycho datasets contain case counts for reported disease conditions for countries around the world. The Project Tycho data curation team extracts these case counts from various reputable sources, typically from national or international health authorities, such as the US Centers for Disease Control or the World Health Organization. These original data sources include both open- and restricted-access sources. For restricted-access sources, the Project Tycho team has obtained permission for redistribution from data contributors. All datasets contain case count data that are identical to counts published in the original source and no counts have been modified in any way by the Project Tycho team. The Project Tycho team has pre-processed datasets by adding new variables, such as standard disease and location identifiers, that improve data interpretability. We also formatted the data into a standard data format.

Each Project Tycho dataset contains case counts for a specific condition (e.g. measles) and for a specific country (e.g. The United States). Case counts are reported per time interval. In addition to case counts, datasets include information about these counts (attributes), such as the location, age group, subpopulation, diagnostic certainty, place of acquisition, and the source from which we extracted case counts. One dataset can include many series of case count time intervals, such as "US measles cases as reported by CDC", or "US measles cases reported by WHO", or "US measles cases that originated abroad", etc.

Depending on the intended use of a dataset, we recommend a few data processing steps before analysis: - Analyze missing data: Project Tycho datasets do not include time intervals for which no case count was reported (for many datasets, time series of case counts are incomplete, due to incompleteness of source documents) and users will need to add time intervals for which no count value is available. Project Tycho datasets do include time intervals for which a case count value of zero was reported. - Separate cumulative from non-cumulative time interval series. Case count time series in Project Tycho datasets can be "cumulative" or "fixed-intervals". Cumulative case count time series consist of overlapping case count intervals starting on the same date, but ending on different dates. For example, each interval in a cumulative count time series can start on January 1st, but end on January 7th, 14th, 21st, etc. It is common practice among public health agencies to report cases for cumulative time intervals. Case count series with fixed time intervals consist of mutually exclusive time intervals that all start and end on different dates and all have identical length (day, week, month, year). Given the different nature of these two types of case count data, we indicated this with an attribute for each count value, named "PartOfCumulativeCountSeries".