The document summarizes key statistical concepts for journalists. It discusses percentages, rates, probabilities, averages, standard deviation, sampling, inference, and correlation. Some key points are:
- The EU produces 4.7% more wheat than China but consumes 21% less.
- A probability of 0.2 means a 20% chance. More occurrences do not necessarily mean a higher probability.
- Standard deviation measures the spread of data, with larger values indicating more variation.
The document explains how to use a single sample t-test to determine if a sample is statistically similar to or different from a population. It discusses the properties of a normal distribution and how percentages of scores fall within standard deviations of the mean. For example, there is a 68% chance a randomly selected score will be within 1 standard deviation of the population mean. It then uses an example of IQ scores to demonstrate how to calculate the standard deviations and determine the probability a sample mean came from the same population distribution.
A confidence interval provides a range of values that is likely to include an unknown population parameter, with a specified confidence level. A 95% confidence interval states that if you were to repeat the sampling process numerous times, 95% of the calculated confidence intervals would contain the true population parameter. It does not mean there is a 95% chance that the population parameter falls within the given interval. Larger sample sizes are needed to achieve smaller margins of error or higher confidence levels when estimating population parameters from sample data.
The summary discusses criteria for evaluating qualitative research, including credibility/trustworthiness and consistency/dependability. It explains how these criteria relate to philosophical assumptions about knowledge (epistemology) and the nature of reality (ontology). It also identifies potential ethical issues that could influence research design, such as protecting participants' privacy, and discusses how some topics are well-suited to qualitative study by allowing exploration of meanings and experiences.
Summary statistics for binary data lecture DrZahid Khan
This document summarizes key concepts related to analyzing binary and categorical data. It discusses binary variables, prevalence, rates, case-control studies, cohort studies, relative risk, number needed to treat, and crossover trials. For case-control studies, it provides an example comparing smoking status between lung cancer patients and normal individuals, calculating an odds ratio of 6. For cohort studies, it gives data comparing lung cancer incidence between smokers and non-smokers, calculating a relative risk of 4. It also discusses how to calculate absolute risk difference and number needed to treat from cohort study data.
The document explains how to use a single sample t-test to determine if a sample is statistically similar to or different from a population. It discusses the properties of a normal distribution and how percentages of scores fall within standard deviations of the mean. For example, there is a 68% chance a randomly selected score will be within 1 standard deviation of the population mean. It then uses an example of IQ scores to demonstrate how to calculate the standard deviations and determine the probability a sample mean came from the same population distribution.
A confidence interval provides a range of values that is likely to include an unknown population parameter, with a specified confidence level. A 95% confidence interval states that if you were to repeat the sampling process numerous times, 95% of the calculated confidence intervals would contain the true population parameter. It does not mean there is a 95% chance that the population parameter falls within the given interval. Larger sample sizes are needed to achieve smaller margins of error or higher confidence levels when estimating population parameters from sample data.
The summary discusses criteria for evaluating qualitative research, including credibility/trustworthiness and consistency/dependability. It explains how these criteria relate to philosophical assumptions about knowledge (epistemology) and the nature of reality (ontology). It also identifies potential ethical issues that could influence research design, such as protecting participants' privacy, and discusses how some topics are well-suited to qualitative study by allowing exploration of meanings and experiences.
Summary statistics for binary data lecture DrZahid Khan
This document summarizes key concepts related to analyzing binary and categorical data. It discusses binary variables, prevalence, rates, case-control studies, cohort studies, relative risk, number needed to treat, and crossover trials. For case-control studies, it provides an example comparing smoking status between lung cancer patients and normal individuals, calculating an odds ratio of 6. For cohort studies, it gives data comparing lung cancer incidence between smokers and non-smokers, calculating a relative risk of 4. It also discusses how to calculate absolute risk difference and number needed to treat from cohort study data.
This document discusses sampling distributions and their properties. It defines key terms like population parameter, sample statistic, and sampling distribution. The central limit theorem states that as sample size increases, the sampling distribution of the mean will approach a normal distribution, regardless of the shape of the original population. This allows us to use properties of the normal distribution, like calculating confidence intervals, when making inferences about a population based on a sample. Several examples show how to apply the central limit theorem to find probabilities and determine necessary sample sizes. Practice questions at the end test understanding of these concepts.
Sample size calculation for cohort studies Subhashini N
This document discusses sample size calculations for different types of cohort studies. It provides examples of calculating sample sizes for studies measuring one variable, differences between two means, rates, or proportions. The key factors considered are the confidence interval, power, estimated outcomes in exposed and unexposed groups, and standard deviation or error terms. Sample size formulas are provided for prospective and retrospective cohort studies comparing outcomes within or between groups.
The document discusses z-scores, z-tests, and standard error. It defines z-scores as deviations from the mean in standard deviation units. It explains that z-tests are used to test sampling variability when samples are larger than 30. The standard error measures chance variation in sample statistics from population parameters and decreases with larger sample sizes. The document provides examples of calculating standard error of the mean and the difference between two means or proportions to determine if observed differences are statistically significant.
The document discusses statistical analysis and concepts such as standard deviation, normal distribution, and t-tests. It provides examples of how to calculate and interpret standard deviation to understand the variation in data compared to the mean. It also explains how a t-test can be used to determine if there is a statistically significant difference between the means of two samples by taking into account the means, standard deviations, and population sizes.
1. The document provides an overview of key statistical concepts including populations and samples, the mean, standard deviation, and statistical models. It explains that the mean and standard deviation are used to measure how well a model fits the data and describes the variability.
2. It discusses the differences between samples and populations and how statistics like the mean and standard deviation from a sample can be used to make estimates about the overall population. Confidence intervals are presented as a way to indicate the reliability of sample estimates.
3. The document covers important statistical topics like effect sizes, which provide a standardized measure of the magnitude of an observed effect, and the differences between statistical and practical significance.
Standard Error & Confidence Intervals.pptxhanyiasimple
Certainly! Let's delve into the concept of **standard error**.
## What Is Standard Error?
The **standard error (SE)** is a statistical measure that quantifies the **variability** between a sample statistic (such as the mean) and the corresponding population parameter. Specifically, it estimates how much the sample mean would **vary** if we were to repeat the study using **new samples** from the same population. Here are the key points:
1. **Purpose**: Standard error helps us understand how well our **sample data** represents the entire population. Even with **probability sampling**, where elements are randomly selected, some **sampling error** remains. Calculating the standard error allows us to estimate the representativeness of our sample and draw valid conclusions.
2. **High vs. Low Standard Error**:
- **High Standard Error**: Indicates that sample means are **widely spread** around the population mean. In other words, the sample may not closely represent the population.
- **Low Standard Error**: Suggests that sample means are **closely distributed** around the population mean, indicating that the sample is representative of the population.
3. **Decreasing Standard Error**:
- To decrease the standard error, **increase the sample size**. Using a large, random sample minimizes **sampling bias** and provides a more accurate estimate of the population parameter.
## Standard Error vs. Standard Deviation
- **Standard Deviation (SD)**: Describes variability **within a single sample**. It can be calculated directly from sample data.
- **Standard Error (SE)**: Estimates variability across **multiple samples** from the same population. It is an **inferential statistic** that can only be estimated (unless the true population parameter is known).
### Example:
Suppose we have a random sample of 200 students, and we calculate the mean math SAT score to be 550. In this case:
- **Sample**: The 200 students
- **Population**: All test takers in the region
The standard error helps us understand how well this sample represents the entire population's math SAT scores.
Remember, the standard error is crucial for making valid statistical inferences. By understanding it, researchers can confidently draw conclusions based on sample data. 📊🔍
If you need further clarification or have additional questions, feel free to ask! 😊
---
I've provided a concise explanation of standard error, emphasizing its importance in statistical analysis. If you'd like more details or specific examples, feel free to ask! ¹²³⁴
Source: Conversation with Copilot, 5/31/2024
(1) What Is Standard Error? | How to Calculate (Guide with Examples) - Scribbr. https://www.scribbr.com/statistics/standard-error/.
(2) Standard Error (SE) Definition: Standard Deviation in ... - Investopedia. https://www.investopedia.com/terms/s/standard-error.asp.
(3) Standard error Definition & Meaning - Merriam-Webster. https://www.merriam-webster.com/dictionary/standard%20error.
(4) Standard err
Chapter 6 part1- Introduction to Inference-Estimating with Confidence (Introd...nszakir
Introduction to Inference, Estimating with Confidence, Inference, Statistical Confidence, Confidence Intervals, Confidence Interval for a Population Mean, Choosing the Sample Size
05 confidence interval & probability statementsDrZahid Khan
This document discusses confidence intervals, which provide a range of values that is likely to include an unknown population parameter based on a sample statistic. It defines confidence intervals and explains how they are calculated for means, proportions, odds ratios, and relative risks. Confidence intervals give more information than point estimates and allow for variability in samples. The width of the interval depends on the sample size, with larger samples having narrower intervals. Common confidence levels of 95% and 99% capture the percentage of intervals expected to contain the true population value.
1. Sampling error occurs because sample means are not equal to the population mean and differ from each other.
2. The distribution of sample means follows a normal distribution if drawn from a normal population, and approximates a normal distribution if drawn from a non-normal population as the sample size increases.
3. A confidence interval for the population mean or probability can be constructed given the sample size, mean or probability, and standard deviation. The confidence level indicates the probability the true population parameter falls within the interval.
This document provides an overview of key statistical concepts for non-statisticians. It defines different types of data and variables, different ways of displaying and summarizing data, measures of central tendency and dispersion, normal and non-normal distributions, and different types of clinical research studies. The goal is to introduce basic statistical concepts in an accessible way for those without a statistics background.
This document provides an overview of key concepts in medical statistics, including probability, sample size, effect size, odds and odds ratios, risk and risk ratios, standard deviation, confidence intervals, interpreting clinical trials, number needed to treat (NNT), and types of trials. It defines these terms and provides examples to illustrate how to use statistical measures intelligently to evaluate clinical research studies.
This document discusses inferential statistics and epidemiological research. It introduces concepts like the central limit theorem, standard error, confidence intervals, hypothesis testing, and different statistical tests. Specifically, it covers:
- The central limit theorem states that sample means will follow a normal distribution, even if the population is not normally distributed.
- Standard error is used to measure sampling variation and determine confidence intervals around sample statistics to estimate population parameters.
- Hypothesis testing involves a null hypothesis of no difference and an alternative hypothesis of a significant difference.
- Common tests discussed include chi-square tests to compare proportions between groups and determine if differences are significant.
1. Sampling error refers to the sample means not being equal to the population mean and differing from each other.
2. The distribution of sample means follows certain patterns. If drawn from a normal population, the sample mean follows a normal distribution. If from a non-normal population, the distribution approximates normal as sample size increases.
3. Confidence intervals provide a range that is likely to include the true population parameter. Formulas are given for calculating confidence intervals for a population mean, single or two population probabilities, and the difference between two population means or probabilities. Sample size considerations are also discussed.
The document discusses normal and standard normal distributions. It provides examples of using a normal distribution to calculate probabilities related to bone mineral density test results. It shows how to find the probability of a z-score falling below or above certain values. It also explains how to determine the sample size needed to estimate an unknown population proportion within a given level of confidence.
This document provides definitions and explanations of key statistical and epidemiological concepts:
- A 95% reference interval contains the central 95% of a population distribution, calculated as the mean +/- 2 standard deviations for a normal distribution.
- Sensitivity measures the proportion of true positives detected, specificity measures the proportion of true negatives detected. Sensitivity and specificity do not change with prevalence.
- Prevalence refers to the proportion of a population with a disease. Higher prevalence increases the positive predictive value of a test.
Confidence Intervals in the Life Sciences PresentationNamesS.docxmaxinesmith73660
Confidence Intervals in the Life Sciences Presentation
Names
Statistics for the Life Sciences STAT/167
Date
Fahad M. Gohar M.S.A.S
1
Conservation Biology of Bears
Normal Distribution
Standard normal distribution
Confidence Interval
Population Mean
Population Variance
Confidence Level
Point Estimate
Critical Value
Margin of Error
Welcome to the presentation on Confidence Intervals of Conservation Biology on Bears.
The team will define normal distribution and use an example of variables why this is important. A standard and normal distribution is discussed as well as the difference between standard and other normal distributions. Confidence interval will be defined and how it is used in Conservation Biology and Bears. We will learn how a confidence interval helps researchers estimate of population mean and population variance. The presenters defined a point estimate and try to explain how a point estimate found from a confidence interval. Confidence level is defined and a short explanation of confidence level is related to the confidence interval. Lastly, a critical value and margin of error are explained with examples from the Statdisk.
2
Normal Distribution
A normal distribution is one which has the mean, median, and mode are the same and the standard deviations are apart from the mean in the probabilities that go with the empirical rule. Not all data has the measures of central tendency, since some data sets may not have one unique value which occurs more than once. But every data set has a mean and median. The mean is only good with interval and ratio data, while the median can be used with interval, ratio and ordinal data. Mean is used when they're a lot of outliers, and median is used when there are few.
The normal distribution is continuous, and has only two parameters - mean and variance. The mean can be any positive number and variance can be any positive number (can't be negative - the mean and variance), so there are an infinite number of normal distributions. You want your data to represent the population distribution because when you make claims from the distribution of the sample you took, you want it to represent the whole entire population.
Some examples in the business world: Some industries which use normal distributions are pharmaceutical companies. They model the average blood pressure through normal distributions, and can make medicine which will help majority of the people with high blood pressure. A company can also model its average time to create something using the normal distribution. Several statistics can be calculated with the normal distribution, and hypothesis tests can be done with the normal distribution which models the average time.
Our chosen life science is BEARS. The age of the bears can be modeled by normal distributions and it is important to monitor since that tells us the average age of the bear, and can tell us a lot about the population. If the mean is high and the standard deviatio.
The document discusses key concepts in statistics related to populations, samples, and sampling distributions. Some main points:
- We collect sample data to make inferences about unknown population parameters. Samples should be representative of the overall population.
- The sampling distribution of sample means approximates a normal distribution as long as sample sizes are large. This allows us to calculate confidence intervals and test hypotheses about population means and proportions.
- Common statistical tests include z-tests and t-tests for single means and proportions using the standard error to determine confidence intervals and assess significance. These can determine if sample results align with hypothesized population values.
Inferential statistics are used to draw conclusions about populations based on samples. The two primary inferential methods are estimation and hypothesis testing. Estimation involves using sample statistics to estimate unknown population parameters, such as means or proportions. Interval estimation provides a range of plausible values for the population parameter based on the sample data and a level of confidence, such as a 95% confidence interval. The width of the confidence interval depends on factors like the sample size, standard deviation, and desired confidence level.
Confidence interval & probability statements DrZahid Khan
This document discusses confidence intervals and probability. It defines confidence intervals as a range of values that provide more information than a point estimate by taking into account variability between samples. The document provides examples of how to calculate 95% confidence intervals for a proportion, mean, odds ratio, and relative risk using sample data and the appropriate formulas. It explains that confidence intervals convey the level of uncertainty associated with point estimates and allow estimation of how close a sample statistic is to the unknown population parameter.
This document outlines key concepts related to estimation and confidence intervals. It defines point estimates as single values used to estimate population parameters and interval estimates as ranges of values within which the population parameter is expected to occur. Confidence intervals provide an interval range based on sample observations within which the population parameter is expected to fall at a specified confidence level, such as 95% or 99%. The document discusses how to construct confidence intervals for the population mean when the population standard deviation is known or unknown.
Acolyte Episodes review (TV series) The Acolyte. Learn about the influence of the program on the Star Wars world, as well as new characters and story twists.
This document discusses sampling distributions and their properties. It defines key terms like population parameter, sample statistic, and sampling distribution. The central limit theorem states that as sample size increases, the sampling distribution of the mean will approach a normal distribution, regardless of the shape of the original population. This allows us to use properties of the normal distribution, like calculating confidence intervals, when making inferences about a population based on a sample. Several examples show how to apply the central limit theorem to find probabilities and determine necessary sample sizes. Practice questions at the end test understanding of these concepts.
Sample size calculation for cohort studies Subhashini N
This document discusses sample size calculations for different types of cohort studies. It provides examples of calculating sample sizes for studies measuring one variable, differences between two means, rates, or proportions. The key factors considered are the confidence interval, power, estimated outcomes in exposed and unexposed groups, and standard deviation or error terms. Sample size formulas are provided for prospective and retrospective cohort studies comparing outcomes within or between groups.
The document discusses z-scores, z-tests, and standard error. It defines z-scores as deviations from the mean in standard deviation units. It explains that z-tests are used to test sampling variability when samples are larger than 30. The standard error measures chance variation in sample statistics from population parameters and decreases with larger sample sizes. The document provides examples of calculating standard error of the mean and the difference between two means or proportions to determine if observed differences are statistically significant.
The document discusses statistical analysis and concepts such as standard deviation, normal distribution, and t-tests. It provides examples of how to calculate and interpret standard deviation to understand the variation in data compared to the mean. It also explains how a t-test can be used to determine if there is a statistically significant difference between the means of two samples by taking into account the means, standard deviations, and population sizes.
1. The document provides an overview of key statistical concepts including populations and samples, the mean, standard deviation, and statistical models. It explains that the mean and standard deviation are used to measure how well a model fits the data and describes the variability.
2. It discusses the differences between samples and populations and how statistics like the mean and standard deviation from a sample can be used to make estimates about the overall population. Confidence intervals are presented as a way to indicate the reliability of sample estimates.
3. The document covers important statistical topics like effect sizes, which provide a standardized measure of the magnitude of an observed effect, and the differences between statistical and practical significance.
Standard Error & Confidence Intervals.pptxhanyiasimple
Certainly! Let's delve into the concept of **standard error**.
## What Is Standard Error?
The **standard error (SE)** is a statistical measure that quantifies the **variability** between a sample statistic (such as the mean) and the corresponding population parameter. Specifically, it estimates how much the sample mean would **vary** if we were to repeat the study using **new samples** from the same population. Here are the key points:
1. **Purpose**: Standard error helps us understand how well our **sample data** represents the entire population. Even with **probability sampling**, where elements are randomly selected, some **sampling error** remains. Calculating the standard error allows us to estimate the representativeness of our sample and draw valid conclusions.
2. **High vs. Low Standard Error**:
- **High Standard Error**: Indicates that sample means are **widely spread** around the population mean. In other words, the sample may not closely represent the population.
- **Low Standard Error**: Suggests that sample means are **closely distributed** around the population mean, indicating that the sample is representative of the population.
3. **Decreasing Standard Error**:
- To decrease the standard error, **increase the sample size**. Using a large, random sample minimizes **sampling bias** and provides a more accurate estimate of the population parameter.
## Standard Error vs. Standard Deviation
- **Standard Deviation (SD)**: Describes variability **within a single sample**. It can be calculated directly from sample data.
- **Standard Error (SE)**: Estimates variability across **multiple samples** from the same population. It is an **inferential statistic** that can only be estimated (unless the true population parameter is known).
### Example:
Suppose we have a random sample of 200 students, and we calculate the mean math SAT score to be 550. In this case:
- **Sample**: The 200 students
- **Population**: All test takers in the region
The standard error helps us understand how well this sample represents the entire population's math SAT scores.
Remember, the standard error is crucial for making valid statistical inferences. By understanding it, researchers can confidently draw conclusions based on sample data. 📊🔍
If you need further clarification or have additional questions, feel free to ask! 😊
---
I've provided a concise explanation of standard error, emphasizing its importance in statistical analysis. If you'd like more details or specific examples, feel free to ask! ¹²³⁴
Source: Conversation with Copilot, 5/31/2024
(1) What Is Standard Error? | How to Calculate (Guide with Examples) - Scribbr. https://www.scribbr.com/statistics/standard-error/.
(2) Standard Error (SE) Definition: Standard Deviation in ... - Investopedia. https://www.investopedia.com/terms/s/standard-error.asp.
(3) Standard error Definition & Meaning - Merriam-Webster. https://www.merriam-webster.com/dictionary/standard%20error.
(4) Standard err
Chapter 6 part1- Introduction to Inference-Estimating with Confidence (Introd...nszakir
Introduction to Inference, Estimating with Confidence, Inference, Statistical Confidence, Confidence Intervals, Confidence Interval for a Population Mean, Choosing the Sample Size
05 confidence interval & probability statementsDrZahid Khan
This document discusses confidence intervals, which provide a range of values that is likely to include an unknown population parameter based on a sample statistic. It defines confidence intervals and explains how they are calculated for means, proportions, odds ratios, and relative risks. Confidence intervals give more information than point estimates and allow for variability in samples. The width of the interval depends on the sample size, with larger samples having narrower intervals. Common confidence levels of 95% and 99% capture the percentage of intervals expected to contain the true population value.
1. Sampling error occurs because sample means are not equal to the population mean and differ from each other.
2. The distribution of sample means follows a normal distribution if drawn from a normal population, and approximates a normal distribution if drawn from a non-normal population as the sample size increases.
3. A confidence interval for the population mean or probability can be constructed given the sample size, mean or probability, and standard deviation. The confidence level indicates the probability the true population parameter falls within the interval.
This document provides an overview of key statistical concepts for non-statisticians. It defines different types of data and variables, different ways of displaying and summarizing data, measures of central tendency and dispersion, normal and non-normal distributions, and different types of clinical research studies. The goal is to introduce basic statistical concepts in an accessible way for those without a statistics background.
This document provides an overview of key concepts in medical statistics, including probability, sample size, effect size, odds and odds ratios, risk and risk ratios, standard deviation, confidence intervals, interpreting clinical trials, number needed to treat (NNT), and types of trials. It defines these terms and provides examples to illustrate how to use statistical measures intelligently to evaluate clinical research studies.
This document discusses inferential statistics and epidemiological research. It introduces concepts like the central limit theorem, standard error, confidence intervals, hypothesis testing, and different statistical tests. Specifically, it covers:
- The central limit theorem states that sample means will follow a normal distribution, even if the population is not normally distributed.
- Standard error is used to measure sampling variation and determine confidence intervals around sample statistics to estimate population parameters.
- Hypothesis testing involves a null hypothesis of no difference and an alternative hypothesis of a significant difference.
- Common tests discussed include chi-square tests to compare proportions between groups and determine if differences are significant.
1. Sampling error refers to the sample means not being equal to the population mean and differing from each other.
2. The distribution of sample means follows certain patterns. If drawn from a normal population, the sample mean follows a normal distribution. If from a non-normal population, the distribution approximates normal as sample size increases.
3. Confidence intervals provide a range that is likely to include the true population parameter. Formulas are given for calculating confidence intervals for a population mean, single or two population probabilities, and the difference between two population means or probabilities. Sample size considerations are also discussed.
The document discusses normal and standard normal distributions. It provides examples of using a normal distribution to calculate probabilities related to bone mineral density test results. It shows how to find the probability of a z-score falling below or above certain values. It also explains how to determine the sample size needed to estimate an unknown population proportion within a given level of confidence.
This document provides definitions and explanations of key statistical and epidemiological concepts:
- A 95% reference interval contains the central 95% of a population distribution, calculated as the mean +/- 2 standard deviations for a normal distribution.
- Sensitivity measures the proportion of true positives detected, specificity measures the proportion of true negatives detected. Sensitivity and specificity do not change with prevalence.
- Prevalence refers to the proportion of a population with a disease. Higher prevalence increases the positive predictive value of a test.
Confidence Intervals in the Life Sciences PresentationNamesS.docxmaxinesmith73660
Confidence Intervals in the Life Sciences Presentation
Names
Statistics for the Life Sciences STAT/167
Date
Fahad M. Gohar M.S.A.S
1
Conservation Biology of Bears
Normal Distribution
Standard normal distribution
Confidence Interval
Population Mean
Population Variance
Confidence Level
Point Estimate
Critical Value
Margin of Error
Welcome to the presentation on Confidence Intervals of Conservation Biology on Bears.
The team will define normal distribution and use an example of variables why this is important. A standard and normal distribution is discussed as well as the difference between standard and other normal distributions. Confidence interval will be defined and how it is used in Conservation Biology and Bears. We will learn how a confidence interval helps researchers estimate of population mean and population variance. The presenters defined a point estimate and try to explain how a point estimate found from a confidence interval. Confidence level is defined and a short explanation of confidence level is related to the confidence interval. Lastly, a critical value and margin of error are explained with examples from the Statdisk.
2
Normal Distribution
A normal distribution is one which has the mean, median, and mode are the same and the standard deviations are apart from the mean in the probabilities that go with the empirical rule. Not all data has the measures of central tendency, since some data sets may not have one unique value which occurs more than once. But every data set has a mean and median. The mean is only good with interval and ratio data, while the median can be used with interval, ratio and ordinal data. Mean is used when they're a lot of outliers, and median is used when there are few.
The normal distribution is continuous, and has only two parameters - mean and variance. The mean can be any positive number and variance can be any positive number (can't be negative - the mean and variance), so there are an infinite number of normal distributions. You want your data to represent the population distribution because when you make claims from the distribution of the sample you took, you want it to represent the whole entire population.
Some examples in the business world: Some industries which use normal distributions are pharmaceutical companies. They model the average blood pressure through normal distributions, and can make medicine which will help majority of the people with high blood pressure. A company can also model its average time to create something using the normal distribution. Several statistics can be calculated with the normal distribution, and hypothesis tests can be done with the normal distribution which models the average time.
Our chosen life science is BEARS. The age of the bears can be modeled by normal distributions and it is important to monitor since that tells us the average age of the bear, and can tell us a lot about the population. If the mean is high and the standard deviatio.
The document discusses key concepts in statistics related to populations, samples, and sampling distributions. Some main points:
- We collect sample data to make inferences about unknown population parameters. Samples should be representative of the overall population.
- The sampling distribution of sample means approximates a normal distribution as long as sample sizes are large. This allows us to calculate confidence intervals and test hypotheses about population means and proportions.
- Common statistical tests include z-tests and t-tests for single means and proportions using the standard error to determine confidence intervals and assess significance. These can determine if sample results align with hypothesized population values.
Inferential statistics are used to draw conclusions about populations based on samples. The two primary inferential methods are estimation and hypothesis testing. Estimation involves using sample statistics to estimate unknown population parameters, such as means or proportions. Interval estimation provides a range of plausible values for the population parameter based on the sample data and a level of confidence, such as a 95% confidence interval. The width of the confidence interval depends on factors like the sample size, standard deviation, and desired confidence level.
Confidence interval & probability statements DrZahid Khan
This document discusses confidence intervals and probability. It defines confidence intervals as a range of values that provide more information than a point estimate by taking into account variability between samples. The document provides examples of how to calculate 95% confidence intervals for a proportion, mean, odds ratio, and relative risk using sample data and the appropriate formulas. It explains that confidence intervals convey the level of uncertainty associated with point estimates and allow estimation of how close a sample statistic is to the unknown population parameter.
This document outlines key concepts related to estimation and confidence intervals. It defines point estimates as single values used to estimate population parameters and interval estimates as ranges of values within which the population parameter is expected to occur. Confidence intervals provide an interval range based on sample observations within which the population parameter is expected to fall at a specified confidence level, such as 95% or 99%. The document discusses how to construct confidence intervals for the population mean when the population standard deviation is known or unknown.
Acolyte Episodes review (TV series) The Acolyte. Learn about the influence of the program on the Star Wars world, as well as new characters and story twists.
An astonishing, first-of-its-kind, report by the NYT assessing damage in Ukraine. Even if the war ends tomorrow, in many places there will be nothing to go back to.
El Puerto de Algeciras continúa un año más como el más eficiente del continente europeo y vuelve a situarse en el “top ten” mundial, según el informe The Container Port Performance Index 2023 (CPPI), elaborado por el Banco Mundial y la consultora S&P Global.
El informe CPPI utiliza dos enfoques metodológicos diferentes para calcular la clasificación del índice: uno administrativo o técnico y otro estadístico, basado en análisis factorial (FA). Según los autores, esta dualidad pretende asegurar una clasificación que refleje con precisión el rendimiento real del puerto, a la vez que sea estadísticamente sólida. En esta edición del informe CPPI 2023, se han empleado los mismos enfoques metodológicos y se ha aplicado un método de agregación de clasificaciones para combinar los resultados de ambos enfoques y obtener una clasificación agregada.
Here is Gabe Whitley's response to my defamation lawsuit for him calling me a rapist and perjurer in court documents.
You have to read it to believe it, but after you read it, you won't believe it. And I included eight examples of defamatory statements/
Essential Tools for Modern PR Business .pptxPragencyuk
Discover the essential tools and strategies for modern PR business success. Learn how to craft compelling news releases, leverage press release sites and news wires, stay updated with PR news, and integrate effective PR practices to enhance your brand's visibility and credibility. Elevate your PR efforts with our comprehensive guide.
04062024_First India Newspaper Jaipur.pdfFIRST INDIA
Find Latest India News and Breaking News these days from India on Politics, Business, Entertainment, Technology, Sports, Lifestyle and Coronavirus News in India and the world over that you can't miss. For real time update Visit our social media handle. Read First India NewsPaper in your morning replace. Visit First India.
CLICK:- https://firstindia.co.in/
#First_India_NewsPaper
2. Percentage starting points
Wheat in millions of tonnes
Produce Consume
China 99.7 115.4
EU 104.4 91.2
Change
%= x 100
Starting value
3. Percentage starting points
Wheat in millions of tonnes
Produce Consume
China 99.7 115.4
EU 104.4 91.2
EU produces 4.7% more wheat than China
China produces 4.5% less wheat than the EU
China consumes 26.5% more than the EU
The EU consumes 21% less than China
The EU produces 14.5% more than it consumes
The EU consumes 12.6% less than it produces
4. Rates and decimals
In scientific notation:
10n means 1 followed by n 0s
2.1 e 10n means 2.1 followed by n 0s
2.1 e 10-n means 2.1 with the point moved
n places to the right
2.1 e 102 = 210
2.1 e 10-2 = 0.021
2.1 e 10-5 = 0.000021 or 2.1 out of 105
(105 = 100,000)
5. Rounding
Too much detail confuses so rounding help
the reader understand.
3,123,918 is better written as 3.1m
If the part you are throwing away begins
with 4 or less, just through it away. If it
begins with a 5 or more, increase the final
digit of your rounded number by one.
3,138,487 is 3.1m
3,176,918 is 3.2m
Beware rounding errors (percentages may
add up to 99% or 101%)
6. Probability
If 2 out of 10 cars has a defect, the probability
that any given car has a defect is
2/10
or 0.2
or 20%
Don’t confuse probability with quantity
More does not necessarily mean more likely
7. http://www.guardian.co.uk/society/2003/mar/27/medicineandhealth.lifeandhealth
Skin cancer kills thousands of Britons
Guardian Thursday 27 March 2003
Thousands more Britons than Australians die from skin cancer even though more cases of the
disease are diagnosed in Australia, new figures showed today.
Cancer Research UK, Britain's biggest charity, and the government today launched a
nationwide campaign to encourage more Britons to protect themselves and their children
from the sun's harmful rays.
Figures released as part of the Sun Smart campaign show that in the last five years there
have been 8,100 British deaths from malignant melanoma compared to 4,900 in Australia.
The figures showed that nearly 8,000 cases of malignant melanomas are diagnosed in
Australia each year, and nearly 6,000 in the UK. Yet 600 more people die from the disease
each year in Britain than in Australia.
Dermatologists, from CRUK said that a lack of public awareness about skin cancer is leading
to needless deaths.
Many patients failed to use proper protection in the sun and others did not spot early
symptoms of malignant melanomas, they added.
People should seek medical advice if they notice that a mole changes shape, gets bigger,
alters in colour (particularly getting darker or multi-shaded) bleeds or becomes itchy or
painful.
The campaign stresses that pre-cancerous moles are easy to treat and are usually removed
under local anaesthetic. An early melanoma can be cured in this way, but if left, the disease
can spread.
The main risk factor for malignant melanoma is ultraviolet light from the sun or sun beds.
People are considered more at risk if they have lots of moles, are fair skinned with blue eyes,
tend to sunburn easily or have freckles.
Dr Charlotte Proby, consultant dermatologist for CRUK said: "Malignant melanoma
is a preventable cancer. We need the public to be aware of what they can do to
help prevent the disease."
She added: "The success of sun awareness campaigns in Australia is self evident."
8. Are you more likely to die in the UK?
Population Number of Chance of
deaths* dying
UK 63 million 8,100 1: 7,700
Australia 20 million 4,900 1: 4000
* Deaths over five years due to malignant melanoma. Source: Cancer Research UK.
Impression given: twice as likely to die
from skin cancer in the UK.
Truth: half as likely to die from skin cancer
in the UK.
9. Averages
Mean or average = sum of values/number of values
Median = Rank values and find middle
Mode = Value that occurs most frequently
Mean useful for comparing groups of figures which
have a normal distribution
Median useful for comparing groups of figures which
do not have a normal distribution
Warnings:
Do NOT average averages
Average does not necessarily mean typical
11. Standard deviation
Measures the spread of data.
s, sn, sn-1, sn and sn-1 are all different ways of
calculating the spread but give more or less the same
answer provided the number of values in the data
sample is more than 20
Large SD
Small SD
12. Standard deviation
For a normal distribution:
1s 67% of the data is within one standard deviation of the mean
2s 95% is within two standard deviations of the mean
3s 99% is within three standard deviations of the mean
1 SD 1 SD
2 SDs 2 SDs
3 SDs 3 SDs
Mean
13. Standard deviation example
If a survey shows that average height of athletes on a
team is 175cm with a standard deviation of 10cm
then it is reasonable to estimate that:
67% of athletes are between 165 and 185cm
95% of athletes are between 155 and 195cm
14. Graphing
Pie charts good for showing how a whole
is made up of parts. NB Groups should be
distinct and separate.
Bar charts for comparing. NB the impact
of bar charts can be distorted if the origin
is not zero or if 3-D columns are used.
Line graphs are good as showing how
things change over time. Y origin should
be 0. Dates should be evenly spaced
15. Estimating from a sample
Using a sample of a population to predict something
about the whole population
Estimates can never be 100% accurate so they should
come with a margin of error
Margin of error at 90% confidence is 0.82/ n
Margin of error at 95% confidence is 0.98/ n
Margin of error at 99% confidence is 1.29/ n
** Provided the whole population is a large number,
the margin of error is NOT dependent on population
size **
16. Estimating from a sample
Sample Margin of error
size (95% confidence)
50 ±13.9%*
100 ±9.8%*
200 ±6.9%*
300 ±5.7%*
400 ±4.9%*
500 ±4.4%*
750 ±3.6%*
1000 ±3.1%*
2000 ±2.2%*
* % is actually percentage points
17. Estimating a mean
The margin of error of the mean can be calculated
thus:
Margin of error at 2(sample’s standard deviation)
=
95% confidence
number in sample
Margin of error at 1.7(sample’s standard deviation)
=
90% confidence
number in sample
Use this formula only for sample sizes greater than 30
18. How scientists work
Observational (epidemiological)
research
Experimental studies
Peer review
Systematic review (meta analysis)
Risk factor based on converging
data
50:1
19. Inference
To draw conclusions from data, you need to have
confidence in that data.
The statistical measure of confidence is p. The smaller
the number the better.
p is a probability between 0 and 1
In social science the p value should be at most 0.05
In medicine the p value should be at most 0.005
Often, all you have to do is check that the p-value is
appropriately small.
20. Correlation r
The correlation of two factors is calculated with the
correlation coefficient (r) ranging from 0 to 1. Near 0
means little correlation. Near 1 means closely correlated.
r=-1.0 means an inverse correlation.
EG: The weight of people in a sample is likely to be
correlated with height (tall people are heavier) and
inversely correlated with life expectancy (heavier people
die younger)
21. Correlation based on a sample
Correlation based on a sample with p= 0.05
For a sample of 10 if r is greater than 0.63 then there
is a (non-trivial) correlation
For a sample of 30 if r is greater than 0.36 then there
is a (non-trivial) correlation
For a sample of 100 if r is greater than 0.2 then there
is a (non-trivial) correlation
22. Coefficient of determination
The value of r2 for two characteristics gives the %
variation in one quantity that is explained by another
EG:
If the correlation coefficient between weight and
2
height is r = 0.07 then r = 0.49 which means that
about 49% of the variation in weight is explained by
height. 51% will be explained by other factors
NB: Correlation does NOT imply causation
If correlation between X and Y is high then we can
say X is a good predictor of Y
If r is v small and confidence is high (p is also small)
then may be statistically significant but not significant
isn the real world
23. Correlation does NOT imply causation
Facebook fuelling divorce, research claims
n
io
Telegraph 21 December 2009
at
The social networking site, which connects old friends and allows users to make
us
new ones online, is being blamed for an increasing number of marital
breakdowns.
ca
Divorce lawyers claim the explosion in the popularity of websites such as
Facebook and Bebo is tempting to people to cheat on their partners.
http://www.telegraph.co.uk/technology/facebook/6857918/
y
pl
Suspicious spouses have also used the websites to find evidence of flirting and
even affairs which have led to divorce.
im
One law firm, which specialises in divorce, claimed almost one in five petitions
they processed cited Facebook.
Facebook-fuelling-divorce-research-claims.html
T
Mark Keenan, Managing Director of Divorce-Online said: "I had heard from my
NO
staff that there were a lot of people saying they had found out things about
their partners on Facebook and I decided to see how prevalent it was I was
really surprised to see 20 per cent of all the petitions containing references to
Facebook. es
do
"The most common reason seemed to be people having inappropriate sexual
chats with people they were not supposed to."
n
Flirty emails and messages found on Facebook pages are increasingly being
io
cited as evidence of unreasonable behaviour.
at
...
The UK’s divorce rate has fallen in recent years, but two in five marriages are
el
still failing according the latest statistics.
rr
Mr Keenan believes that the general divorce rate will rocket in 2010 with the
Co
recession taking the blame.
24. Surveys
Sample should be random
High response rate
Don’t depend on volunteered responses
Careful in constructing questions: not good if you are
interpreting the answers; if the answers are
ambiguous; if the phrasing of questions pushes
people towards a particular answer
Always state who conducted survey and give margin
of error
25. Experiment
Treatment = the thing you are testing
Control group = group not treated for comparison
Random assignment = people are assigned to control
group or treatment group randomly
Placebo = fake treatment given to control group so
they do not realise they are the control group
Double blind = neither those being experimented
upon nor those giving the treatment know who is
getting the the treatment and who the placebo.
26. 'Seafarers' disease' scurvy on rise among
children due to lack of vitamin C in diet
Daily Mail 7 November 2009
Scurvy is making a comeback among England's children.
Caused by a lack of vitamin C, the potentially fatal disease was a scourge of
Seafarers-disease-Scurvy-rise-children-lack-vitamin-C-diet.html
pirates and sailors in the heyday of the British Empire, but was thought to be
largely a thing of the past.
However, newly released statistics show that the number of children admitted
http://www.dailymail.co.uk/health/article-1225905/
to hospital with scurvy soared by over 50 per cent in the past three years.
Released following a parliamentary question, the figures show that in 2004/05
there were 61 children admitted with scurvy in England.
But by 2007/08, the latest year for which figures are available, there were no
fewer than 94 cases: up 54 per cent in three years.
Because the figures cover only those admitted to hospital with scurvy as a
primary or secondary diagnosis, the actual numbers with the disease will be far
higher as many will not get further than their GP.
Others may be listed under the wider term of 'malnutrition'.
Scurvy occurs if people do not eat enough foods containing vitamin C such as
fruits, tomatoes, potatoes, liver and oysters.
Scurvy leads to spots on the skin, particularly the legs, as capillaries break
down. There is cracking and bleeding of the lips, nostrils and ears. Gums go
spongy and teeth fall out.
... continues
27. 'Seafarers' disease' scurvy on rise among
children due to lack of vitamin C in diet
. . . continued
Wounds cannot heal properly, and old scars reappear. There is internal
haemorrhaging and left untreated, victims will die.
Seafarers-disease-Scurvy-rise-children-lack-vitamin-C-diet.html
Conservative health spokesman Stephen O'Brien, who uncovered the figures,
said: 'It is shocking that this disease of 17th-century pirates is on the rise again
in 21st-century England.'
http://www.dailymail.co.uk/health/article-1225905/
Ursula Arens, of the British Dietetic Association, said it was not possible to say
how the children were getting scurvy: whether it was from a poor diet, or as a
by-product of other diseases such as cancer.
'There may be examples of children just living on bread and jam and nothing
else because of poverty,' she said.
'It is such an unusual thing now that perhaps it is something that many GPs
would not be able to diagnose.'
A spokesman for the Department of Health said: 'Families in lower income
groups tend to consume less vitamin C in their diet.
'The Department of Health promotes consumption through its "five a day"
campaign and Healthy Start, which provides free vitamin supplements for
beneficiaries.'
28. 'Seafarers' disease' scurvy on rise among
children due to lack of vitamin C in diet
Scurvy cases
Data on which Mail story was based 2007-08 94
showed primary and secondary 2006-07 101
hospital diagnosis of absorbic acid 2005-06 68
deficiency (scurvy). 2004-05 61
2003-04 72
Problems:
1) Showed all patients not just children
2) Based on small numbers with large
year-year variations (noise)
3) Picked two years with biggest
difference (longer time period and
window average would have been
more convincing)
4) Data contains no info about CAUSES
of scurvy. Actually more likely to be
caused by increased cancer survival.
29. Media studies graduates
The Press Gazette reports that Media Studies graduates
are among the most successful at finding jobs.
It is true that 73.6% are in employment compared with
66.9% figure for all graduates.
The implication is that you are less likely to be
unemployed. But PG has excluded the figures for people
who stay in education.
Actually the figure for those who are unemployed is
more revealling: 10.1% for media studies compared
with 6.9% for all subjects.
Perhaps a more significant story is that only
11.5% found jobs in the media. Those ending up
as secretaries, shop assistants and bar staff
adds up to a far higher figure.
30. Where graduates are after six months
All subjects
Employed (73.6%)
Study (9.1%)
Employed (66.9%)
Study (18.7%)
Unemployed
(10.1%)
Unemployed
Media studies (6.9%)
31. 4%
8%
12%
16%
Marketing, sales, PR advertising
Commercial, public sector managers
Scientific research, analysis
Engineering
Health
Teaching
All subjects
Business & Finance
Media studies
Information technology
Nursing & health associate
Business & finance associate
Media, literary, design, sport
Other porfessional & technical
Types of work
Numerical clerks & cashiers
Other clerical & secretarial
Retail assts, waiting & bar staff
Health & childcare
Armed forces & public protection
Other
Unknown
32. Apples & oranges
August 2000 US Justice Policy Institute’s claimed that
“more African American men are incarcerated than
enrolled in college.”
You can go to prison at any age, for any length of time,
but most people go to college for only a few years during
their late teens and twenties.
33. The new phenomena phenomenon
Actual figures
Perception
Cases of AIDS
55 60 65 70 75 80 85 90 95 00 05 10 15
Year
34. Care with comparisons
A new study claims that Autism has risen ten-fold in
the US in the past decade.
Most media sources reported this as proof that a
worrying increase in the condition has gone unnoticed,
while others raised the possibility of a link to the
substance thimerosal, an ingredient in childhood
vaccinations.
In fact, the increase was probably due to a massive
increase in the definition of autistic disorders over the
past 10 years.
35. Dangerous conclusions
Burglary
Robbery
International Crime
Assault
Victimisation Survey
2000
UK 6.0% 1.2% 2.8%
South Africa 5.8% 4.6% 6.3%
Conclusion: UK nearly as dangerous as South Africa?
Murder rate (1997 figures):
UK 1.4 per 100,000
SA 58.4 per 100,000
36. Sampling
26 February 2002 former US Secretary of Health,
Education and Welfare Joseph Califano’s claimed that
under-age drinkers consume a quarter of all alcohol
drunk in the United States.
The survey over-sampled teenagers. As The New York
Times conceded in a subsequent correction, the actual
figure is only 11%.
37. Time periods
11 June 2002 The New York Times claimed the
average temperature in Alaska “has risen about seven
degrees over the last 30 years.”
This surprised experts at the Alaska Climate Research
Center, whose figures show an increase of only 2.5
degrees in the same period.
The Times corrected its mistake on 11 July, but still
claimed an increase of 5.4 degrees, which it justified
by using the period from 1966 to 1995, rather than the
“last 30 years” from 1973 to 2002.
39. Massaged figures
A US government task force on college drinking
claimed that 1,400 students are killed and 600,000
are assaulted each year because of alcohol.
That figure would represent two thirds of all the
assaults in the US, according to the FBI.
But the “assaults” included everyone who said they
were “pushed or hit” by anyone as a result of someone
drinking. And the deaths included fatal auto and other
accidents in which anyone (not only drivers) tested
positive for any amount of alcohol.
40. Fear from simplifying
Lancet: "fear of breast cancer is so pervasive among US
women that it is causing them to ignore far more serious
health threats."
The commonly reported figure that 1 in 8 figure women
will develop breast cancer only applies to those already
in their 80s
Office of National Statistics shows that the risk for
women under age 35 is 1:625, rising to 1:56 by age 50.
Before the age of 50 only one woman out of 136 dies of
breast cancer. By the age of 60 this is one out of 65.
And by the age of 80 only one woman in 26 dies of
breast cancer, which represents the lifetime risk for
most women - that means the other 25 will die of
something else.
42. Questions
WHO? Reputable statistician or hopeful charity?
Political spin doctor or civil service department.
Ask yourself how reliable you think the
organisation compiling the statistics is and rate
the results accordingly.
WHY? Do they have a vested interest in producing a
particular result? If so is the way they compiled
the data reasonable? Did they ask the right
questions? Have they focused on the most
helpful result to them and distorted the truth in
the process?
HOW? Was the sample representative? Was it big
enough? Was there bias built into the way they
conducted the survey?
43. Checklist
Where possible, go back to original numbers and check
assumptions and spin
Ask yourself whether the numbers you are reporting tell
the whole story
Like any other aspect of journalism, check sources
Watch time periods
Take care with percentages and other rates
With surveys, find out what questions were asked
Question the conclusions that you and others derive from
figures
Watch out for spin - figures selected or presented for one
party’s advantage
Check that comparisons are valid