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.

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.

Precision of the estimates expressed as 95% Confidence Interval (CI) for categorical and continuous endpoint accordingly to different sample size.

Means, confidence intervals, standard deviations and sample sizes for variables, split by sexual orientation groups.

Notes: Items use a 5-point Likert scale from Strongly Disagree to Strongly Agree.*ICCE = Informed, Committed, Collaborative, Engaged subscale.**TU = Tolerance of Uncertainty subscale.

Abstract

FAO has developed a monitoring system in 26 food crisis countries to better understand the impacts of various shocks on agricultural livelihoods, food security and local value chains. The Monitoring System consists of primary data collected from households on a periodic basis (more or less every four months, depending on seasonality).

Data was collected through telephone surveys in all regions of Niger (Agadez, Diffa, Dosso, Maradi, Tahoua, Tillabéry and Zinder), with the exception of the urban region of Niamey. Between 223 and 266 households were selected in each region, for a total sample of 1676 households interviewed. The survey was representative at admin level 1.

For more information, please go to https://data-in-emergencies.fao.org/pages/monitoring

Geographic coverage

National coverage

Analysis unit

Households

Kind of data

Sample survey data [ssd]

Sampling procedure

Between 223 and 266 households were selected in each region, for a total sample of 1 676 households interviewed. The survey was representative at admin level 1.

The results of this sixth-round survey have been compared to those of round 4 (lean season, August 2022) and round 5 (harvest season, December 2022).

Surveys are designed based on country-specific needs, objectives, and constraints. They aim to achieve a 10% margin of error, a 95% confidence level, administrative-level granularity, and sufficient sample sizes for key target populations, including agricultural households.

Mode of data collection

Computer Assisted Telephone Interview [cati]

Research instrument

A link to the questionnaire has been provided in the documentations tab. *

Cleaning operations

The datasets have been edited and processed for analysis by the Needs Assessment team at the Office of Emergencies and Resilience, FAO, with some dashboards and visualizations produced. For more information, see https://data-in-emergencies.fao.org/pages/countries.

STATISTICAL DISCLOSURE CONTROL (SDC)

The dataset was anonymized using Statistical Disclosure methods by the Data in Emergencies Hub team and reviewed by the Statistics Division of FAO. All direct identifiers have been removed prior to data submission.

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

Qualifications by Economic Activity Status by Borough Data has been reweighted in 2016 in line with the latest ONS estimates. 95% confidence interval of percent figure (+/-). ! Estimate and confidence interval not available since the group sample size is zero or disclosive (0-2). * Estimate and confidence interval unreliable since the group sample size is small (3-9). ~ Estimate is less than 500. See more on the NOMIS Website.

Disclaimer: This dataset is distributed by Daniel Gayo-Avello, an associate professor at the Department of Computer Science in the University of Oviedo, for the sole purpose of non-commercial research and it just includes tweet ids. The dataset contains tweet IDs for all the published tweets (in any language) bettween March 21, 2006 and July 31, 2009 thus comprising the first whole three years of Twitter from its creation, that is, about 1.5 billion tweets (see file Twitter-historical-20060321-20090731.zip). It covers several defining issues in Twitter, such as the invention of hashtags, retweets and trending topics, and it includes tweets related to the 2008 US Presidential Elections, the first Obama’s inauguration speech or the 2009 Iran Election protests (one of the so-called Twitter Revolutions). Finally, it does contain tweets in many major languages (mainly English, Portuguese, Japanese, Spanish, German and French) so it should be possible–at least in theory–to analyze international events from different cultural perspectives. The dataset was completed in November 2016 and, therefore, the tweet IDs it contains were publicly available at that moment. This means that there could be tweets public during that period that do not appear in the dataset and also that a substantial part of tweets in the dataset has been deleted (or locked) since 2016. To make easier to understand the decay of tweet IDs in the dataset a number of representative samples (99% confidence level and 0.5 confidence interval) are provided. In general terms, 85.5% ±0.5 of the historical tweets are available as of May 19, 2020 (see file Twitter-historical-20060321-20090731-sample.txt). However, since the amount of tweets vary greatly throughout the period of three years covered in the dataset, additional representative samples are provided for 90-day intervals (see the file 90-day-samples.zip). In that regard, the ratio of publicly available tweets (as of May 19, 2020) is as follows: March 21, 2006 to June 18, 2006: 88.4% ±0.5 (from 5,512 tweets). June 18, 2006 to September 16, 2006: 82.7% ±0.5 (from 14,820 tweets). September 16, 2006 to December 15, 2006: 85.7% ±0.5 (from 107,975 tweets). December 15, 2006 to March 15, 2007: 88.2% ±0.5 (from 852,463 tweets). March 15, 2007 to June 13, 2007: 89.6% ±0.5 (from 6,341,665 tweets). June 13, 2007 to September 11, 2007: 88.6% ±0.5 (from 11,171,090 tweets). September 11, 2007 to December 10, 2007: 87.9% ±0.5 (from 15,545,532 tweets). December 10, 2007 to March 9, 2008: 89.0% ±0.5 (from 23,164,663 tweets). March 9, 2008 to June 7, 2008: 66.5% ±0.5 (from 56,416,772 tweets; see below for more details on this). June 7, 2008 to September 5, 2008: 78.3% ±0.5 (from 62,868,189 tweets; see below for more details on this). September 5, 2008 to December 4, 2008: 87.3% ±0.5 (from 89,947,498 tweets). December 4, 2008 to March 4, 2009: 86.9% ±0.5 (from 169,762,425 tweets). March 4, 2009 to June 2, 2009: 86.4% ±0.5 (from 474,581,170 tweets). June 2, 2009 to July 31, 2009: 85.7% ±0.5 (from 589,116,341 tweets). The apparent drop in available tweets from March 9, 2008 to September 5, 2008 has an easy, although embarrassing, explanation. At the moment of cleaning all the data to publish this dataset there seemed to be a gap between April 1, 2008 to July 7, 2008 (actually, the data was not missing but in a different backup). Since tweet IDs are easy to regenerate for that Twitter era (source code is provided in generate-ids.m) I simply produced all those that were created between those two dates. All those tweets actually existed but a number of them were obviously private and not crawlable. For those regenerated IDs the actual ratio of public tweets (as of May 19, 2020) is 62.3% ±0.5. In other words, what you see in that period (April to July, 2008) is not actually a huge number of tweets having been deleted but the combination of deleted and non-public tweets (whose IDs should not be in the dataset for performance purposes when rehydrating the dataset). Additionally, given that not everybody will need the whole period of time the earliest tweet ID for each date is provided in the file date-tweet-id.tsv. For additional details regarding this dataset please see: Gayo-Avello, Daniel. "How I Stopped Worrying about the Twitter Archive at the Library of Congress and Learned to Build a Little One for Myself." arXiv preprint arXiv:1611.08144 (2016). If you use this dataset in any way please cite that preprint (in addition to the dataset itself). If you need to contact me you can find me as @PFCdgayo in Twitter.

This dataset is about: Confidence intervals (0.95) for absolute counts of pollen taxa comprising >5% of the total pollen sum of TS III samples, Tso Moriri. Please consult parent dataset @ https://doi.org/10.1594/PANGAEA.885267 for more information.

This dataset is about: Confidence intervals (0.95) for absolute counts of pollen taxa comprising >5% of the total pollen sum of TS I samples, Okunevoe peat bog. Please consult parent dataset @ https://doi.org/10.1594/PANGAEA.885267 for more information.

Total sample partial correlations with confidence intervals.

Error Rate Simulation CodeR script used to evaluate the statistical error rates of the z-score methodevolution.2016.adams.collyer.error.rates.rSimulation ResultsRaw Data from simulation used to evaluate method's statistical error ratesrun.results.RdataR-PLS behaviorR script used to examine the behavior of R-PLS and other statistical measures as a function of sample size and number of variablesevolution.2016.adams.collyer.r.pls.trends.r

Percentage of responses in range 0-6 out of 10 (corresponding to 'low wellbeing') for 'Worthwhile' in the First ONS Annual Experimental Subjective Wellbeing survey.

The Office for National Statistics has included the four subjective well-being questions below on the Annual Population Survey (APS), the largest of their household surveys.

• Overall, how satisfied are you with your life nowadays?
• Overall, to what extent do you feel the things you do in your life are worthwhile?
• Overall, how happy did you feel yesterday?
• Overall, how anxious did you feel yesterday?

This dataset presents results from the second of these questions, "Overall, to what extent do you feel the things you do in your life are worthwhile?" Respondents answer these questions on an 11 point scale from 0 to 10 where 0 is ‘not at all’ and 10 is ‘completely’. The well-being questions were asked of adults aged 16 and older.

Well-being estimates for each unitary authority or county are derived using data from those respondents who live in that place. Responses are weighted to the estimated population of adults (aged 16 and older) as at end of September 2011.

The data cabinet also makes available the proportion of people in each county and unitary authority that answer with ‘low wellbeing’ values. For the ‘worthwhile’ question answers in the range 0-6 are taken to be low wellbeing.

This dataset contains the percentage of responses in the range 0-6. It also contains the standard error, the sample size and lower and upper confidence limits at the 95% level.

The ONS survey covers the whole of the UK, but this dataset only includes results for counties and unitary authorities in England, for consistency with other statistics available at this website.

At this stage the estimates are considered ‘experimental statistics’, published at an early stage to involve users in their development and to allow feedback. Feedback can be provided to the ONS via this email address.

The APS is a continuous household survey administered by the Office for National Statistics. It covers the UK, with the chief aim of providing between-census estimates of key social and labour market variables at a local area level. Apart from employment and unemployment, the topics covered in the survey include housing, ethnicity, religion, health and education. When a household is surveyed all adults (aged 16+) are asked the four subjective well-being questions.

The 12 month Subjective Well-being APS dataset is a sub-set of the general APS as the well-being questions are only asked of persons aged 16 and above, who gave a personal interview and proxy answers are not accepted. This reduces the size of the achieved sample to approximately 120,000 adult respondents in England.

The original data is available from the ONS website.

Detailed information on the APS and the Subjective Wellbeing dataset is available here.

As well as collecting data on well-being, the Office for National Statistics has published widely on the topic of wellbeing. Papers and further information can be found here.

Transect-based monitoring has long been a valuable tool in ecosystem monitoring. These transects are often used to measure multiple ecosystem attributes. The line-point intercept (LPI), vegetation height, and canopy gap intercept methods comprise a set of core methods, which provide indicators of ecosystem condition. However, users struggle to design a sampling strategy that optimizes the ability to detect ecological change using transect-based methods. We assessed the sensitivity of these core methods on a one-hectare plot to transect length, number, and sampling interval to determine: 1) minimum sampling required to describe ecosystem characteristics and detect change for each method and 2) optimal transect length and number for all three methods to make recommendations for future analyses and monitoring efforts. We used data from 13 National Wind Erosion Research Network locations spanning the western US, which included 151 measurements over time across five biomes. We found that longer and increased numbers of transects were more important for reducing sampling error than increased sample intensity along transects. For all methods and indicators across plots, three 100-m transects reduced sampling error so that indicator estimates fall within an 95% confidence interval of +/- 5% for canopy gap intercept and LPI-total foliar cover, +/- 5 cm for height and +/- two species for LPI-species counts. For the same criteria at 80% confidence intervals, two 100-m transects are needed. Site-scale inference was strongly affected by sample design, consequently our understanding of ecological dynamics may be influenced by sampling decisions.

This dataset contains customer satisfaction scores collected from a survey, alongside key demographic and behavioral data. It includes variables such as customer age, gender, location, purchase history, support contact status, loyalty level, and satisfaction factors. The dataset is designed to help analyze customer satisfaction, identify trends, and develop insights that can drive business decisions.

File Information: File Name: customer_satisfaction_data.csv (or your specific file name)

File Type: CSV (or the actual file format you are using)

Number of Rows: 120

Number of Columns: 10

Column Names:

Customer_ID – Unique identifier for each customer (e.g., 81-237-4704)

Group – The group to which the customer belongs (A or B)

Satisfaction_Score – Customer's satisfaction score on a scale of 1-10

Age – Age of the customer

Gender – Gender of the customer (Male, Female)

Location – Customer's location (e.g., Phoenix.AZ, Los Angeles.CA)

Purchase_History – Whether the customer has made a purchase (Yes or No)

Support_Contacted – Whether the customer has contacted support (Yes or No)

Loyalty_Level – Customer's loyalty level (Low, Medium, High)

Satisfaction_Factor – Primary factor contributing to customer satisfaction (e.g., Price, Product Quality)

Statistical Analyses:

Descriptive Statistics:

Calculate mean, median, mode, standard deviation, and range for key numerical variables (e.g., Satisfaction Score, Age).

Summarize categorical variables (e.g., Gender, Loyalty Level, Purchase History) with frequency distributions and percentages.

Two-Sample t-Test (Independent t-test):

Compare the mean satisfaction scores between two independent groups (e.g., Group A vs. Group B) to determine if there is a significant difference in their average satisfaction scores.

Paired t-Test:

If there are two related measurements (e.g., satisfaction scores before and after a certain event), you can compare the means using a paired t-test.

One-Way ANOVA (Analysis of Variance):

Test if there are significant differences in mean satisfaction scores across more than two groups (e.g., comparing the mean satisfaction score across different Loyalty Levels).

Chi-Square Test for Independence:

Examine the relationship between two categorical variables (e.g., Gender vs. Purchase History or Loyalty Level vs. Support Contacted) to determine if there’s a significant association.

Mann-Whitney U Test:

For non-normally distributed data, use this test to compare satisfaction scores between two independent groups (e.g., Group A vs. Group B) to see if their distributions differ significantly.

Kruskal-Wallis Test:

Similar to ANOVA, but used for non-normally distributed data. This test can compare the median satisfaction scores across multiple groups (e.g., comparing satisfaction scores across Loyalty Levels or Satisfaction Factors).

Spearman’s Rank Correlation:

Test for a monotonic relationship between two ordinal or continuous variables (e.g., Age vs. Satisfaction Score or Satisfaction Score vs. Loyalty Level).

Regression Analysis:

Linear Regression: Model the relationship between a continuous dependent variable (e.g., Satisfaction Score) and independent variables (e.g., Age, Gender, Loyalty Level).

Logistic Regression: If analyzing binary outcomes (e.g., Purchase History or Support Contacted), you could model the probability of an outcome based on predictors.

Factor Analysis:

To identify underlying patterns or groups in customer behavior or satisfaction factors, you can apply Factor Analysis to reduce the dimensionality of the dataset and group similar variables.

Cluster Analysis:

Use K-Means Clustering or Hierarchical Clustering to group customers based on similarity in their satisfaction scores and other features (e.g., Loyalty Level, Purchase History).

Confidence Intervals:

Calculate confidence intervals for the mean of satisfaction scores or any other metric to estimate the range in which the true population mean might lie.

This dataset is about: Confidence intervals (0.95) for absolute counts of pollen taxa comprising >5% of the total pollen sum of TS V samples, Lake Kushu. Please consult parent dataset @ https://doi.org/10.1594/PANGAEA.885267 for more information.

Compton Gamma-Ray Observatory (CGRO) BATSE Earth-occultation data have been used by Malizia et al. (1999, ApJ, 519, 637) to search for emission in the 20-100 keV band from all sources in the Piccinotti sample (Piccinotti et al. 1982, ApJ, 253, 485: the HEASARC A2PIC database), which represents the only complete 20-10 keV survey to date of the extragalactic sky down to a limiting flux of 3.1 x 10^-11 ergs cm^-2 s^-1. Nearly 4 years of observations have been analyzed to reach a 5-sigma confidence level of about 7.8 x 10^-11 ergs cm^-2 s^-1 in the band considered. Of the 36 sources in the sample, 14 have been detected above the 5-sigma confidence level, while marginal detection (3 <= sigma <= 5) can be claimed for 13 sources; for nine objects, 2 sigma upper limits are reported. A comparison of BATSE results with data at higher energies is used to estimate the robustness of the data analysis. While the detection level of each source is reliable, the flux measurement may be overestimated in some sources by as much as 35%, probably because of incomplete data cleaning. Comparison of BATSE fluxes with X-ray fluxes obtained in the 2-10 keV range and averaged over years indicates that a canonical power law of photon index 1.7 gives a good description of the broadband spectra of bright active galactic nuclei (AGNs) and that spectral breaks preferentially occur above 100 keV. This HEASARC database was created in October 1999 based primarily on Table 1 of Malizia et al. (1999), together with the positions and HEAO-1 designations taken from the original Piccinotti Catalog (Piccinotti et al. 1982, ApJ, 253, 485: the HEASARC A2PIC database). This is a service provided by NASA HEASARC .

This dataset is about: Confidence intervals (0.95) for absolute counts of pollen taxa comprising >5% of the total pollen sum of TS II samples, Lake Kotokel. Please consult parent dataset @ https://doi.org/10.1594/PANGAEA.885267 for more information.

Background Acceptability curves have been proposed for quantifying the probability that a treatment under investigation in a clinical trial is cost-effective. Various definitions and estimation methods have been proposed. Loosely speaking, all the definitions, Bayesian or otherwise, relate to the probability that the treatment under consideration is cost-effective as a function of the value placed on a unit of effectiveness. These definitions are, in fact, expressions of the certainty with which the current evidence would lead us to believe that the treatment under consideration is cost-effective, and are dependent on the amount of evidence (i.e. sample size).

   Methods
   An alternative for quantifying the probability that the treatment under consideration is cost-effective, which is independent of sample size, is proposed.


   Results
   Non-parametric methods are given for point and interval estimation. In addition, these methods provide a non-parametric estimator and confidence interval for the incremental cost-effectiveness ratio. An example is provided.


   Conclusions
   The proposed parameter for quantifying the probability that a new therapy is cost-effective is superior to the acceptability curve because it is not sample size dependent and because it can be interpreted as the proportion of patients who would benefit if given the new therapy. Non-parametric methods are used to estimate the parameter and its variance, providing the appropriate confidence intervals and test of hypothesis.