This document discusses statistical significance and its role in statistical hypothesis testing. It defines statistical significance as obtaining a p-value less than the predetermined significance level (often 0.05). The significance level is the probability of rejecting the null hypothesis when it is true. A statistically significant result means the observed effect is unlikely due to chance and reflects a true population characteristic. The concept originated with Fisher and was later developed by Neyman and Pearson to involve setting the significance level before data collection.
The document discusses significance tests and their role in hypothesis testing. It defines key terms like p-value, significance level, confidence level, rejection region, and classification of significance tests. The p-value represents the probability of observing the results by chance if the null hypothesis is true. The significance level is set before data collection and represents the probability of incorrectly rejecting the null hypothesis. A p-value less than the significance level leads to rejecting the null hypothesis.
Statistical tests of significance and Student`s T-TestVasundhraKakkar
Statistical tests of significance is explained along with steps involve in Statistical tests of significance and types of significance test are also mentioned. Student`s T-Test is explained
Parametric test _ t test and ANOVA _ Biostatistics and Research Methodology....AZCPh
Parametric test with t test and ANOVA on the bases of Biostatistics subject. The slide contains definition of particular test with their sums. Comparison of tests and some terminologies used in hypothesis testing. Useful for Pharmacy students.
Chapter 6 part2-Introduction to Inference-Tests of Significance, Stating Hyp...nszakir
Mathematics, Statistics, Introduction to Inference, Tests of Significance, The Reasoning of Tests of Significance, Stating Hypotheses, Test Statistics, P-values, Statistical Significance, Test for a Population Mean, Two-Sided Significance Tests and Confidence Intervals
Power Analysis and Sample Size DeterminationAjay Dhamija
This document discusses power analysis and sample size determination. It explains key concepts like power, effect size, significance level, and how changing these factors impacts the required sample size. Sample size is important to correctly power a study to detect clinically meaningful effects without excessive subjects. The document provides formulas and examples for calculating sample sizes for various study designs including randomized trials, pre-post, and equivalence studies. Researchers must consider these factors before collecting data to ensure their study is appropriately powered.
This document provides an overview of non-parametric statistics. It defines non-parametric tests as those that make fewer assumptions than parametric tests, such as not assuming a normal distribution. The document compares and contrasts parametric and non-parametric tests. It then explains several common non-parametric tests - the Mann-Whitney U test, Wilcoxon signed-rank test, sign test, and Kruskal-Wallis test - and provides examples of how to perform and interpret each test.
PPT on Sample Size, Importance of Sample Size,Naveen K L
This document discusses factors related to determining sample size for research studies. It defines key terms like sample size, population and importance of sample size. The selection of sample size involves planning the study, specifying parameters, choosing an effect size, and computing the sample size based on those factors. Sample size is influenced by expected effect size, study power, heterogeneity, error risk, and other variables. Dropouts from the sample during a study also impact sample size calculations. Proper determination of sample size is important for obtaining meaningful results and conducting ethical research.
This document discusses confidence intervals for population means and proportions. It explains how to construct confidence intervals using the normal distribution for large sample sizes (n ≥ 30) and the t-distribution for small sample sizes. Formulas are provided for calculating margin of error and determining necessary sample size. Guidelines are given for determining whether to use the normal or t-distribution based on sample size and characteristics. Confidence intervals can be constructed for variance and standard deviation using the chi-square distribution.
The document discusses significance tests and their role in hypothesis testing. It defines key terms like p-value, significance level, confidence level, rejection region, and classification of significance tests. The p-value represents the probability of observing the results by chance if the null hypothesis is true. The significance level is set before data collection and represents the probability of incorrectly rejecting the null hypothesis. A p-value less than the significance level leads to rejecting the null hypothesis.
Statistical tests of significance and Student`s T-TestVasundhraKakkar
Statistical tests of significance is explained along with steps involve in Statistical tests of significance and types of significance test are also mentioned. Student`s T-Test is explained
Parametric test _ t test and ANOVA _ Biostatistics and Research Methodology....AZCPh
Parametric test with t test and ANOVA on the bases of Biostatistics subject. The slide contains definition of particular test with their sums. Comparison of tests and some terminologies used in hypothesis testing. Useful for Pharmacy students.
Chapter 6 part2-Introduction to Inference-Tests of Significance, Stating Hyp...nszakir
Mathematics, Statistics, Introduction to Inference, Tests of Significance, The Reasoning of Tests of Significance, Stating Hypotheses, Test Statistics, P-values, Statistical Significance, Test for a Population Mean, Two-Sided Significance Tests and Confidence Intervals
Power Analysis and Sample Size DeterminationAjay Dhamija
This document discusses power analysis and sample size determination. It explains key concepts like power, effect size, significance level, and how changing these factors impacts the required sample size. Sample size is important to correctly power a study to detect clinically meaningful effects without excessive subjects. The document provides formulas and examples for calculating sample sizes for various study designs including randomized trials, pre-post, and equivalence studies. Researchers must consider these factors before collecting data to ensure their study is appropriately powered.
This document provides an overview of non-parametric statistics. It defines non-parametric tests as those that make fewer assumptions than parametric tests, such as not assuming a normal distribution. The document compares and contrasts parametric and non-parametric tests. It then explains several common non-parametric tests - the Mann-Whitney U test, Wilcoxon signed-rank test, sign test, and Kruskal-Wallis test - and provides examples of how to perform and interpret each test.
PPT on Sample Size, Importance of Sample Size,Naveen K L
This document discusses factors related to determining sample size for research studies. It defines key terms like sample size, population and importance of sample size. The selection of sample size involves planning the study, specifying parameters, choosing an effect size, and computing the sample size based on those factors. Sample size is influenced by expected effect size, study power, heterogeneity, error risk, and other variables. Dropouts from the sample during a study also impact sample size calculations. Proper determination of sample size is important for obtaining meaningful results and conducting ethical research.
This document discusses confidence intervals for population means and proportions. It explains how to construct confidence intervals using the normal distribution for large sample sizes (n ≥ 30) and the t-distribution for small sample sizes. Formulas are provided for calculating margin of error and determining necessary sample size. Guidelines are given for determining whether to use the normal or t-distribution based on sample size and characteristics. Confidence intervals can be constructed for variance and standard deviation using the chi-square distribution.
Biostatistics_Unit_II_Research Methodology & Biostatistics_M. Pharm (Pharmace...RAHUL PAL
This document provides an overview of biostatistics topics including parametric and non-parametric statistical tests, sample size calculation, and factors influencing sample size. It discusses commonly used parametric tests like the t-test, ANOVA, correlation coefficient, and regression analysis. Non-parametric tests like the Wilcoxon rank-sum test are also covered. The importance of considering sample size, factors that can impact it, and how dropouts are handled are summarized as well.
This document discusses sample size determination and different types of study designs used in research methodology, including cohort studies and clinical trials. Sample size determination is an essential step that requires determining the optimal number of subjects or units to be included based on the desired level of accuracy and validity of results. Cohort studies follow groups of individuals over time to compare outcomes based on exposures, while clinical trials randomly assign treatments to evaluate their effects and safety on health outcomes through statistical analysis of data from human subjects.
This document discusses parametric tests used for statistical analysis. It introduces t-tests, ANOVA, Pearson's correlation coefficient, and Z-tests. T-tests are used to compare means of small samples and include one-sample, unpaired two-sample, and paired two-sample t-tests. ANOVA compares multiple population means and includes one-way and two-way ANOVA. Pearson's correlation measures the strength of association between two continuous variables. Z-tests compare means or proportions of large samples. Key assumptions and calculations for each test are provided along with examples. The document emphasizes the importance of choosing the appropriate statistical test for research.
When you perform a hypothesis test in statistics, a p-value helps you determine the significance of your results. ... The p-value is a number between 0 and 1 and interpreted in the following way: A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.
This document provides information about the Kruskal-Wallis H test, a non-parametric method for testing whether samples originate from the same distribution. It describes how the Kruskal-Wallis test is a generalization of the Mann-Whitney U test that allows comparison of more than two independent groups. The test works by ranking all data from lowest to highest and then summing the ranks for each group to calculate the test statistic H, which is compared to a chi-squared distribution to determine whether to reject or fail to reject the null hypothesis that all population medians are equal.
The document describes the Wilcoxon Rank-Sum Test, a non-parametric statistical hypothesis test used to assess whether one of two independent samples of observations tends to have larger values than the other when normality cannot be assumed. It provides details on running the test, including ranking the combined observations and computing the test statistic to determine if it is less than or equal to the critical value, rejecting the null hypothesis. An example applies the test to compare the nicotine content of two cigarette brands, finding no significant difference between their medians.
- Confidence intervals provide an estimated range of values that is likely to include an unknown population parameter, such as a mean, with a specified degree of confidence.
- The margin of error depends on the sample size, standard deviation, and confidence level, with a larger sample size and smaller standard deviation yielding a smaller margin of error.
- When the sample size is small, a t-distribution rather than normal distribution is used to construct the confidence interval due to the unknown population standard deviation. The t-distribution is wider than the normal and accounts for additional uncertainty from an unknown standard deviation.
This document provides an overview of non-parametric tests presented by Ms. Prajakta Sawant. It discusses non-parametric tests as distribution-free statistical tests that do not require assumptions about the underlying population distribution. Common non-parametric tests described include the Wilcoxon rank-sum test, Kruskal-Wallis test, Spearman's rank correlation coefficient, and the chi-square test. Examples are provided for each test to illustrate their application and interpretation.
This document discusses hypothesis testing and p-values. It begins by defining a hypothesis as a proposition or prediction about the outcome of an experiment. Hypotheses are formulated and tested through science to evaluate their credibility. There are two main types of hypotheses: the null hypothesis, which corresponds to a default or general position, and the alternative hypothesis, which asserts a rival relationship. Hypothesis testing uses sample data to evaluate whether differences observed could be due to chance (the null hypothesis) or are real effects (the alternative hypothesis). Key concepts discussed include type 1 and type 2 errors, significance levels, one-sided and two-sided tests, and the relationship between p-values, confidence intervals, and the strength of evidence against
This document discusses a one-way analysis of variance (ANOVA) used to compare the effects of different oil types (A, B, C) on car mileage. It tests the null hypothesis that the mean mileages are equal against the alternative that at least two means differ. The ANOVA calculates sums of squares and F statistics to determine if there are significant differences between the treatment means, rejecting the null hypothesis if F exceeds the critical value. If differences exist, pairwise comparisons estimate the size of differences between each pair of means using confidence intervals.
Cross over design, Placebo and blinding techniques Dinesh Gangoda
A crossover design is a modified randomized block design in which each block receives more than one treatment at different dosing periods.
A block can be a patient or a group of patients.
Patients in each block receive different sequences of treatments.
A crossover design is called a complete crossover design if each sequence contains all treatments under investigation.
A placebo is a dummy medicine containing no active substance.
This substance has no therapeutic effect, used as a control in testing new drugs.
Latin- ‘ I shall please’
Basics of Hypothesis testing for PharmacyParag Shah
This presentation will clarify all basic concepts and terms of hypothesis testing. It will also help you to decide correct Parametric & Non-Parametric test for your data
Through this ppt you could learn what is Wilcoxon Signed Ranked Test. This will teach you the condition and criteria where it can be run and the way to use the test.
This document provides an outline for a presentation on determining sample size. It discusses key concepts like what sample size is, why determining an appropriate sample size is important, and factors that affect sample size calculations like available resources, required accuracy, and study design. The presentation aims to help audiences understand how to determine sample sizes and how to apply the concept in research and studies.
This document discusses blinding techniques in clinical trials. It defines blinding as keeping trial participants, investigators, or assessors unaware of treatment assignments to prevent bias. Single blinding means one group is unaware, while double blinding means participants, investigators, and assessors are all unaware of assignments. Placebos can be used to maintain blinding for subjective outcomes. Descriptions of blinding should state who was blinded and how similarity between treatments was maintained. Assessing success of blinding can involve directly asking groups to guess assignments or looking for disproportionate side effects between groups. Some surgical trials cannot be blinded.
Unit-III Non Parametric tests: Wilcoxon Rank Sum Test, Mann-Whitney U test, Kruskal-Wallis
test, Friedman Test. BP801T. BIOSTATISITCS AND RESEARCH METHODOLOGY (Theory)
A research hypothesis is a statement created by researchers to speculate on the outcome of an experiment. Hypotheses are generated through inductive reasoning from observations and must be testable, falsifiable, and realistic. There are two types of errors in hypothesis testing: type I errors which incorrectly reject a true null hypothesis, and type II errors which fail to reject a false null hypothesis. Examples of hypotheses and errors are given for building inspections and the effects of fluoride in toothpaste.
Parametric and non parametric test in biostatistics Mero Eye
This ppt will helpful for optometrist where and when to use biostatistic formula along with different examples
- it contains all test on parametric or non-parametric test
Researchers, as a whole, tend to underestimate the need for power. I'm just now starting to get it.
I recently gave a brief, easy-to-follow presentation on statistical power, it's importance, and how to go about getting it.
Hope you find it useful.
The document provides an overview of a data analysis course covering topics such as descriptive statistics, probability distributions, correlation and regression analysis, hypothesis testing, clustering, and time series analysis. The course notes were written by Venkat Reddy as an informal summary of the key concepts covered, with the intention of serving as a high-level overview rather than a comprehensive treatment of each topic. Hypothesis testing is discussed as a process involving five steps: making assumptions, stating the null hypothesis, selecting a sampling distribution and critical region, computing a test statistic, and determining whether to reject or fail to reject the null hypothesis based on the p-value.
This document discusses meta-analysis, which involves systematically combining results from multiple studies to derive conclusions about a body of research. It describes the key steps in conducting a meta-analysis, including writing a research question and protocol, performing a comprehensive literature search, selecting studies, assessing study quality, extracting data, and analyzing data. Statistical methods for pooling results across studies using fixed and random effects models are also outlined. The document highlights strengths and limitations of meta-analysis for providing more precise estimates of treatment effects and identifying areas needing further research.
Common statistical pitfalls in basic science researchRamachandra Barik
This document discusses common statistical pitfalls in basic science research. It notes that while clinical studies undergo rigorous statistical review, basic science studies are often handled less uniformly. Some key issues it identifies include: treating repeated measurements of the same unit as independent observations, underestimating required sample sizes, lack of consideration for control groups and randomization in study design, and improper presentation of data through unclear reporting of sample sizes, use of standard deviations instead of standard errors, and inappropriate graphical displays. The document provides guidance on how to properly determine sample sizes, design studies, analyze data, and present results to address these common pitfalls.
Biostatistics_Unit_II_Research Methodology & Biostatistics_M. Pharm (Pharmace...RAHUL PAL
This document provides an overview of biostatistics topics including parametric and non-parametric statistical tests, sample size calculation, and factors influencing sample size. It discusses commonly used parametric tests like the t-test, ANOVA, correlation coefficient, and regression analysis. Non-parametric tests like the Wilcoxon rank-sum test are also covered. The importance of considering sample size, factors that can impact it, and how dropouts are handled are summarized as well.
This document discusses sample size determination and different types of study designs used in research methodology, including cohort studies and clinical trials. Sample size determination is an essential step that requires determining the optimal number of subjects or units to be included based on the desired level of accuracy and validity of results. Cohort studies follow groups of individuals over time to compare outcomes based on exposures, while clinical trials randomly assign treatments to evaluate their effects and safety on health outcomes through statistical analysis of data from human subjects.
This document discusses parametric tests used for statistical analysis. It introduces t-tests, ANOVA, Pearson's correlation coefficient, and Z-tests. T-tests are used to compare means of small samples and include one-sample, unpaired two-sample, and paired two-sample t-tests. ANOVA compares multiple population means and includes one-way and two-way ANOVA. Pearson's correlation measures the strength of association between two continuous variables. Z-tests compare means or proportions of large samples. Key assumptions and calculations for each test are provided along with examples. The document emphasizes the importance of choosing the appropriate statistical test for research.
When you perform a hypothesis test in statistics, a p-value helps you determine the significance of your results. ... The p-value is a number between 0 and 1 and interpreted in the following way: A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.
This document provides information about the Kruskal-Wallis H test, a non-parametric method for testing whether samples originate from the same distribution. It describes how the Kruskal-Wallis test is a generalization of the Mann-Whitney U test that allows comparison of more than two independent groups. The test works by ranking all data from lowest to highest and then summing the ranks for each group to calculate the test statistic H, which is compared to a chi-squared distribution to determine whether to reject or fail to reject the null hypothesis that all population medians are equal.
The document describes the Wilcoxon Rank-Sum Test, a non-parametric statistical hypothesis test used to assess whether one of two independent samples of observations tends to have larger values than the other when normality cannot be assumed. It provides details on running the test, including ranking the combined observations and computing the test statistic to determine if it is less than or equal to the critical value, rejecting the null hypothesis. An example applies the test to compare the nicotine content of two cigarette brands, finding no significant difference between their medians.
- Confidence intervals provide an estimated range of values that is likely to include an unknown population parameter, such as a mean, with a specified degree of confidence.
- The margin of error depends on the sample size, standard deviation, and confidence level, with a larger sample size and smaller standard deviation yielding a smaller margin of error.
- When the sample size is small, a t-distribution rather than normal distribution is used to construct the confidence interval due to the unknown population standard deviation. The t-distribution is wider than the normal and accounts for additional uncertainty from an unknown standard deviation.
This document provides an overview of non-parametric tests presented by Ms. Prajakta Sawant. It discusses non-parametric tests as distribution-free statistical tests that do not require assumptions about the underlying population distribution. Common non-parametric tests described include the Wilcoxon rank-sum test, Kruskal-Wallis test, Spearman's rank correlation coefficient, and the chi-square test. Examples are provided for each test to illustrate their application and interpretation.
This document discusses hypothesis testing and p-values. It begins by defining a hypothesis as a proposition or prediction about the outcome of an experiment. Hypotheses are formulated and tested through science to evaluate their credibility. There are two main types of hypotheses: the null hypothesis, which corresponds to a default or general position, and the alternative hypothesis, which asserts a rival relationship. Hypothesis testing uses sample data to evaluate whether differences observed could be due to chance (the null hypothesis) or are real effects (the alternative hypothesis). Key concepts discussed include type 1 and type 2 errors, significance levels, one-sided and two-sided tests, and the relationship between p-values, confidence intervals, and the strength of evidence against
This document discusses a one-way analysis of variance (ANOVA) used to compare the effects of different oil types (A, B, C) on car mileage. It tests the null hypothesis that the mean mileages are equal against the alternative that at least two means differ. The ANOVA calculates sums of squares and F statistics to determine if there are significant differences between the treatment means, rejecting the null hypothesis if F exceeds the critical value. If differences exist, pairwise comparisons estimate the size of differences between each pair of means using confidence intervals.
Cross over design, Placebo and blinding techniques Dinesh Gangoda
A crossover design is a modified randomized block design in which each block receives more than one treatment at different dosing periods.
A block can be a patient or a group of patients.
Patients in each block receive different sequences of treatments.
A crossover design is called a complete crossover design if each sequence contains all treatments under investigation.
A placebo is a dummy medicine containing no active substance.
This substance has no therapeutic effect, used as a control in testing new drugs.
Latin- ‘ I shall please’
Basics of Hypothesis testing for PharmacyParag Shah
This presentation will clarify all basic concepts and terms of hypothesis testing. It will also help you to decide correct Parametric & Non-Parametric test for your data
Through this ppt you could learn what is Wilcoxon Signed Ranked Test. This will teach you the condition and criteria where it can be run and the way to use the test.
This document provides an outline for a presentation on determining sample size. It discusses key concepts like what sample size is, why determining an appropriate sample size is important, and factors that affect sample size calculations like available resources, required accuracy, and study design. The presentation aims to help audiences understand how to determine sample sizes and how to apply the concept in research and studies.
This document discusses blinding techniques in clinical trials. It defines blinding as keeping trial participants, investigators, or assessors unaware of treatment assignments to prevent bias. Single blinding means one group is unaware, while double blinding means participants, investigators, and assessors are all unaware of assignments. Placebos can be used to maintain blinding for subjective outcomes. Descriptions of blinding should state who was blinded and how similarity between treatments was maintained. Assessing success of blinding can involve directly asking groups to guess assignments or looking for disproportionate side effects between groups. Some surgical trials cannot be blinded.
Unit-III Non Parametric tests: Wilcoxon Rank Sum Test, Mann-Whitney U test, Kruskal-Wallis
test, Friedman Test. BP801T. BIOSTATISITCS AND RESEARCH METHODOLOGY (Theory)
A research hypothesis is a statement created by researchers to speculate on the outcome of an experiment. Hypotheses are generated through inductive reasoning from observations and must be testable, falsifiable, and realistic. There are two types of errors in hypothesis testing: type I errors which incorrectly reject a true null hypothesis, and type II errors which fail to reject a false null hypothesis. Examples of hypotheses and errors are given for building inspections and the effects of fluoride in toothpaste.
Parametric and non parametric test in biostatistics Mero Eye
This ppt will helpful for optometrist where and when to use biostatistic formula along with different examples
- it contains all test on parametric or non-parametric test
Researchers, as a whole, tend to underestimate the need for power. I'm just now starting to get it.
I recently gave a brief, easy-to-follow presentation on statistical power, it's importance, and how to go about getting it.
Hope you find it useful.
The document provides an overview of a data analysis course covering topics such as descriptive statistics, probability distributions, correlation and regression analysis, hypothesis testing, clustering, and time series analysis. The course notes were written by Venkat Reddy as an informal summary of the key concepts covered, with the intention of serving as a high-level overview rather than a comprehensive treatment of each topic. Hypothesis testing is discussed as a process involving five steps: making assumptions, stating the null hypothesis, selecting a sampling distribution and critical region, computing a test statistic, and determining whether to reject or fail to reject the null hypothesis based on the p-value.
This document discusses meta-analysis, which involves systematically combining results from multiple studies to derive conclusions about a body of research. It describes the key steps in conducting a meta-analysis, including writing a research question and protocol, performing a comprehensive literature search, selecting studies, assessing study quality, extracting data, and analyzing data. Statistical methods for pooling results across studies using fixed and random effects models are also outlined. The document highlights strengths and limitations of meta-analysis for providing more precise estimates of treatment effects and identifying areas needing further research.
Common statistical pitfalls in basic science researchRamachandra Barik
This document discusses common statistical pitfalls in basic science research. It notes that while clinical studies undergo rigorous statistical review, basic science studies are often handled less uniformly. Some key issues it identifies include: treating repeated measurements of the same unit as independent observations, underestimating required sample sizes, lack of consideration for control groups and randomization in study design, and improper presentation of data through unclear reporting of sample sizes, use of standard deviations instead of standard errors, and inappropriate graphical displays. The document provides guidance on how to properly determine sample sizes, design studies, analyze data, and present results to address these common pitfalls.
This document discusses determining sample size for research studies. It defines key terms like sample size, population, and discusses factors that affect sample size like desired accuracy and available resources. It describes common methods for calculating sample size like formulas, tables, and software. Formulas use specifications like confidence level, margin of error, and population proportion to determine the needed sample size. The document emphasizes that determining an appropriate sample size is essential for research validity and making inferences to the target population.
The document discusses key statistical concepts including variance, standard deviation, the normal distribution, frequency distributions, data matrices, properties of good graphs, populations and parameters, hypothesis testing, and point and interval estimation. It provides definitions and examples of these terms and how they relate to drawing statistical inferences from data.
The document provides an overview of key statistical concepts including variance, standard deviation, the normal distribution, frequency distributions, data matrices, properties of good graphs, populations and samples, parameters and statistics, hypothesis testing, and point and interval estimation. It defines these terms and explains concepts like the null hypothesis, alternative hypothesis, critical regions, test statistics, and making decisions based on probability thresholds.
Statistics and experimental design are important for drawing valid conclusions from research. Well-designed experiments produce unbiased comparisons, precise estimates, and account for variability. Hypothesis tests answer yes/no questions about population values and aim to reject false null hypotheses. P-values indicate the likelihood of obtaining extreme data if the null is true. Multiple testing increases chances of false positives, requiring adjustments. Sample size impacts power to detect effects and precision of estimates. Both statistical and practical significance must be considered.
This document provides an overview of sampling and statistical inference concepts. It defines key terms like population, sample, parameter, and statistic. It discusses reasons for sampling and types of sampling and non-sampling errors. It also explains important sampling distributions like the sampling distribution of the mean, t-distribution, sampling distribution of a proportion, F distribution, and chi-square distribution. It defines concepts like degrees of freedom, standard error, and the central limit theorem.
Statistical data analysis helps achieve scientific goals of description, prediction, explanation, and control. There are descriptive statistics like measures of central tendency (mean, median, mode) and variability (range, variance, standard deviation) to describe data. Inferential statistics allow inferences about populations from samples using hypothesis testing, estimation, and considerations of sampling error, assumptions, and spatial autocorrelation. Key challenges include accounting for spatial dependencies in geographic data and issues like the modifiable areal unit problem.
The use of data and its modelling in science provides meaningful interpretation of real world problems. This presentation provides an easy to understand overview of data visualization and analytics , and snippets of data science applications using R - programming.
This document provides an overview of quantitative data analysis methods for medical education research. It discusses summary measures, hypothesis testing, statistical methodologies, sample size determination, and additional resources for statistical support. Key points covered include choosing appropriate statistical tests based on study design, translating research questions into testable hypotheses, interpreting p-values and making conclusions, and factors that influence required sample size such as effect size and variability.
1. The document discusses key concepts in inferential statistics including point estimation, interval estimation, hypothesis testing, types of errors, p-values, power, and one-tailed and two-tailed tests.
2. It explains that inferential statistics allows generalization from a sample to a population and includes estimation of parameters and hypothesis testing.
3. Common statistical techniques covered are confidence intervals, which provide a range of values that likely contain the true population parameter, and hypothesis testing, which evaluates theories about populations.
This document provides an overview of basic concepts in inferential statistics. It defines descriptive statistics as describing and summarizing data through measures like mean, median, variance and standard deviation. Inferential statistics is defined as using sample data and statistics to draw conclusions about populations through hypothesis testing and estimates. Key concepts explained include parameters, statistics, sampling distributions, null and alternative hypotheses, and the hypothesis testing process. Examples of descriptive and inferential analyses are also provided.
This document provides an overview of different types of statistical tests used for data analysis and interpretation. It discusses scales of measurement, parametric vs nonparametric tests, formulating hypotheses, types of statistical errors, establishing decision rules, and choosing the appropriate statistical test based on the number and types of variables. Key statistical tests covered include t-tests, ANOVA, chi-square tests, and correlations. Examples are provided to illustrate how to interpret and report the results of these common statistical analyses.
Hypothesis Testing and its process which includes the following steps:
1.Formulation of a null hypothesis (H0) and an alternative hypothesis (Ha).
2. Determination the level of significance (α)
3. Choosing a test statistic and calculate its value.
4. Comparison between the test statistic and the critical value.
5. Making a decision and interpret the results.
This is a summary of the whole process along with easy definitions of the associated terms.
This document discusses statistical principles for writing scientific manuscripts, including how to describe sampling uncertainty, present results using measures of central tendency and variability, and report findings using confidence intervals and p-values. It emphasizes quantifying and conveying measurement uncertainty and effect sizes rather than relying solely on hypothesis testing. Guidelines are proposed for systematically reporting the design, methods, results and interpretation of laboratory experiments to improve transparency and enable verification.
This document provides information about the chi-square test, including:
- The chi-square test determines if there is a significant difference between expected and observed frequencies. It tests if differences are due to chance or are real differences.
- Examples of chi-square tests given include Pearson's chi-square test, Yates's correction, and tests for variance, independence, and homogeneity using contingency tables.
- Requirements for the chi-square test include quantitative data, categories, independent observations, adequate sample size, simple random sampling, and frequency data. All observations must be used.
Statistical skepticism: How to use significance tests effectively jemille6
Prof. D. Mayo, presentation Oct. 12, 2017 at the ASA Symposium on Statistical Inference : “A World Beyond p < .05” in the session: “What are the best uses for P-values?“
The document provides an overview of the chi-square distribution and its applications in statistical hypothesis testing. It discusses how the chi-square distribution describes the sum of squares of independent normal variables, making it useful for analyzing categorical data. It then summarizes several common chi-square tests, including goodness of fit tests, tests of independence, and tests of variance. It also reviews key assumptions, calculations, interpretations and applications of chi-square tests, as well as some limitations.
MELJUN CORTES research lectures_evaluating_data_statistical_treatmentMELJUN CORTES
This document discusses the importance of statistics in research and the proper treatment of data. It notes that statistics are the backbone of research and help organize data in tables and graphs to guide meaningful interpretations. The document outlines the data analysis process and different levels of measurement for variables. It provides a matrix for statistical treatment of different types of data and describes common statistical operations like measures of central tendency, variance, correlation, and statistical tests. Dangers of misusing statistics are also discussed.
The book discusses Warren Buffett's approach to analyzing companies using financial statements. Buffett looks for companies with durable competitive advantages, such as unique products or low costs, that allow high returns on revenue of over 20%. He favors those with consistent earnings, low expenses for research, depreciation and interest, and strong liquidity with little debt. By identifying firms with these characteristics in their financial statements, Buffett has been able to achieve remarkable investment returns over decades.
The human brain is far more complex than previously understood. Recent discoveries show we have two brains - the left side deals with logic, language, and analysis while the right deals with imagery, creativity, and pattern recognition. Developing both sides synergistically improves overall mental performance. Historical examples show many great thinkers used both sides of their brains. The potential of the human brain is greater than typically realized, and with the right nurturing, dormant abilities can flourish. Developing both logical and intuitive thought using techniques in the book can help unlock our full potential.
Here are key words for the first 5 paragraphs:
1. Cage: Small, cricket-sized, difficult to see
2. Cricket: Mosquito-sized, fine antennae, "Grass-Lark"
3. Value: 12 cents, more than weight in gold, eats eggplant
4. Awakens at sunset: Delicate, ghostly, electric bells, penetrating, weird
5. Song: Love, organic memory, generations ago, fields, amorous
This document discusses theoretical ecology, which uses theoretical methods such as mathematical models, computational simulations, and data analysis to study ecological systems. It provides examples of different types of mathematical models used to model population dynamics and species interactions, including exponential growth models, logistic growth models, structured population models using matrices, predator-prey models, host-pathogen models, and competition/mutualism models. It also discusses how theoretical ecology aims to explain a variety of ecological phenomena and how computational modeling has benefited from increased computing power.
The document summarizes a study that finds the historically large difference between average returns on equity and short-term debt cannot be accounted for by standard economic models without frictions. Over 1889-1978, average annual equity returns were around 7% compared to less than 1% for short-term debt. The authors analyze economies where consumption growth follows observed US patterns but find such models cannot simultaneously generate the high equity returns and low risk-free returns observed in the data. They conclude a model allowing some market friction is needed to explain the "equity premium puzzle".
Strategic thinking involves generating business insights and opportunities to create a competitive advantage. It can be done individually or collaboratively, and involves considering different perspectives on critical issues. Strategic thinking is defined as a cognitive process that produces thought for achieving success, whereas strategic planning is a separate but related process that realizes strategies through integration back into the business. Key attributes of strategic thinkers include having a systems perspective, being intent-focused, thinking in time about past, present and future, being hypothesis-driven, and demonstrating intelligent opportunism.
A technology stack comprises the layers of components or services that are used to provide a software solution or application. Technology stacks are often articulated as a list of technologies or as a diagram. Examples include the OSI seven-layer model, the TCP/IP model, and the W3C technology stack.
1. The standard deviation is a measure of how spread out numbers are from the average value.
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This document discusses Lenovo's strategies for achieving dominance in the corporate notebook computer market. It analyzes Lenovo's current 19% market share inherited from its acquisition of IBM's notebook division. While Lenovo faces competition from HP and Dell who control larger market shares, the document suggests strategies for Lenovo to maintain and improve its position, such as focusing on high-end products and marketing mid-range laptops to become a "one-stop shop" for corporate customers. It also considers spinning off the Thinkpad brand under a new name to avoid associations with lower quality Chinese brands as Lenovo loses rights to the IBM name.
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Statistical significance
1. Statistical significance
In statistics, statistical significance (or a statistically
significant result) is attained when a p-value is less than
the significance level.[1][2][3][4][5][6][7]
The p-value is the
probability of observing an effect given that the null hy-
pothesis is true whereas the significance or alpha (α) level
is the probability of rejecting the null hypothesis given
that it is true.[8]
As a matter of good scientific practice, a
significance level is chosen before data collection and is
usually set to 0.05 (5%).[9]
Other significance levels (e.g.,
0.01) may be used, depending on the field of study.[10]
Statistical significance is fundamental to statistical hy-
pothesis testing.[11][12]
In any experiment or observation
that involves drawing a sample from a population, there is
always the possibility that an observed effect would have
occurred due to sampling error alone.[13][14]
But if the p-
value is less than the significance level (e.g., p < 0.05),
then an investigator may conclude that the observed ef-
fect actually reflects the characteristics of the population
rather than just sampling error.[11]
An investigator may
then report that the result attains statistical significance,
thereby rejecting the null hypothesis.[15]
The present-day concept of statistical significance origi-
nated with Ronald Fisher when he developed statistical
hypothesis testing based on p-values in the early 20th
century.[2][16][17]
It was Jerzy Neyman and Egon Pearson
who later recommended that the significance level be set
ahead of time, prior to any data collection.[18][19]
The term significance does not imply importance and the
term statistical significance is not the same as research,
theoretical, or practical significance.[11][12][20]
For exam-
ple, the term clinical significance refers to the practical
importance of a treatment effect.
1 History
Main article: History of statistics
The concept of statistical significance was originated by
Ronald Fisher when he developed statistical hypothesis
testing, which he described as “tests of significance”,
in his 1925 publication, Statistical Methods for Research
Workers.[2][16][17]
Fisher suggested a probability of one in
twenty (0.05) as a convenient cutoff level to reject the null
hypothesis.[18]
In their 1933 paper, Jerzy Neyman and
Egon Pearson recommended that the significance level
(e.g. 0.05), which they called α, be set ahead of time,
prior to any data collection.[18][19]
Despite his initial suggestion of 0.05 as a significance
level, Fisher did not intend this cutoff value to be fixed,
and in his 1956 publication Statistical methods and scien-
tific inference he recommended that significant levels be
set according to specific circumstances.[18]
2 Role in statistical hypothesis test-
ing
Main articles: Statistical hypothesis testing, Null hypoth-
esis, p-value and Type I and type II errors
Statistical significance plays a pivotal role in statistical
In a two-tailed test, the rejection region for a significance level of
α=0.05 is partitioned to both ends of the sampling distribution
and makes up 5% of the area under the curve (white areas).
hypothesis testing, where it is used to determine whether
a null hypothesis should be rejected or retained. A null
hypothesis is the general or default statement that noth-
ing happened or changed.[21]
For a null hypothesis to be
rejected as false, the result has to be identified as being
statistically significant, i.e. unlikely to have occurred due
to sampling error alone.
To determine whether a result is statistically significant,
a researcher would have to calculate a p-value, which is
the probability of observing an effect given that the null
hypothesis is true.[7]
The null hypothesis is rejected if the
p-value is less than the significance or α level. The α level
is the probability of rejecting the null hypothesis given
that it is true (type I error) and is most often set at 0.05
(5%). If the α level is 0.05, then the conditional probabil-
ity of a type I error, given that the null hypothesis is true,
is 5%.[22]
Then a statistically significant result is one in
which the observed p-value is less than 5%, which is for-
mally written as p < 0.05.[22]
1
2. 2 6 REFERENCES
If an observed p-value is not lower than the significance
level, then rather than simply accepting the null hypoth-
esis, where feasible it would often appear to be appro-
priate to increase the sample size of the study, and see
whether the significance level is then reached.[23]
Never-
theless, the practice of increasing the number of subjects
may result in the smallest effect having statistical signifi-
cance. [24]
In these cases, reporting effect sizes becomes
particularly important.
If the α level is set at 0.05, it means that the rejection re-
gion comprises 5% of the sampling distribution.[25]
These
5% can be allocated to one side of the sampling distribu-
tion, as in a one-tailed test, or partitioned to both sides
of the distribution as in a two-tailed test, with each tail
(or rejection region) containing 2.5% of the distribution.
One-tailed tests are more powerful than two-tailed tests,
as a null hypothesis can be rejected with a less extreme
result.
3 Stringent significance thresholds
in specific fields
Main articles: Standard deviation and Normal distribu-
tion
In specific fields such as particle physics and
manufacturing, statistical significance is often ex-
pressed in multiples of the standard deviation or sigma
(σ) of a normal distribution, with significance thresholds
set at a much stricter level (e.g. 5σ).[26][27]
For instance,
the certainty of the Higgs boson particle’s existence was
based on the 5σ criterion, which corresponds to a p-value
of about 1 in 3.5 million.[27][28]
In other fields of scientific research such as genome-wide
association studies significance levels as low as 5×10−8
are
not uncommon.[29][30]
4 Effect size
Main article: Effect size
Researchers focusing solely on whether their results are
statistically significant might report findings that are not
substantive[31]
and not replicable.[32]
To gauge the re-
search significance of their result, researchers are there-
fore encouraged to always report the effect size along with
p-values (in cases where the effect being tested for is de-
fined in terms of an effect size): the effect size quantifies
the strength of an effect, such as the distance between
two means (cf. Cohen’s d), the correlation between two
variables or its square, and other measures.[33]
5 See also
• A/B testing
• ABX test
• Confidence level, the complement of the signifi-
cance level
• Effect size
• Fisher’s method for combining independent tests of
significance
• Look-elsewhere effect
• Multiple comparisons problem
• Texas sharpshooter fallacy (gives examples of tests
where the significance level was set too high)
• Reasonable doubt
• Statistical hypothesis testing
6 References
[1] Redmond, Carol; Colton, Theodore (2001). “Clinical sig-
nificance versus statistical significance”. Biostatistics in
Clinical Trials. Wiley Reference Series in Biostatistics
(3rd ed.). West Sussex, United Kingdom: John Wiley &
Sons Ltd. pp. 35–36. ISBN 0-471-82211-6.
[2] Cumming, Geoff (2012). Understanding The New Statis-
tics: Effect Sizes, Confidence Intervals, and Meta-Analysis.
New York, USA: Routledge. pp. 27–28.
[3] Krzywinski, Martin; Altman, Naomi (30 October 2013).
“Points of significance: Significance, P values and t-
tests”. Nature Methods (Nature Publishing Group) 10
(11): 1041–1042. doi:10.1038/nmeth.2698. Retrieved
3 July 2014.
[4] Sham, Pak C.; Purcell, Shaun M (17 April 2014).
“Statistical power and significance testing in large-scale
genetic studies”. Nature Reviews Genetics (Nature Pub-
lishing Group) 15 (5): 335–346. doi:10.1038/nrg3706.
Retrieved 3 July 2014.
[5] Johnson, Valen E. (October 9, 2013). “Revised stan-
dards for statistical evidence”. Proceedings of the National
Academy of Sciences (National Academies of Science).
doi:10.1073/pnas.1313476110. Retrieved 3 July 2014.
[6] Altman, Douglas G. (1999). Practical Statistics for Med-
ical Research. New York, USA: Chapman & Hall/CRC.
p. 167. ISBN 978-0412276309.
[7] Devore, Jay L. (2011). Probability and Statistics for Engi-
neering and the Sciences (8th ed.). Boston, MA: Cengage
Learning. pp. 300–344. ISBN 0-538-73352-7.
[8] Schlotzhauer, Sandra (2007). Elementary Statistics Using
JMP (SAS Press) (PAP/CDR ed.). Cary, NC: SAS Insti-
tute. pp. 166–169. ISBN 1-599-94375-1.
3. 3
[9] Craparo, Robert M. (2007). “Significance level”. In
Salkind, Neil J. Encyclopedia of Measurement and Statis-
tics 3. Thousand Oaks, CA: SAGE Publications. pp.
889–891. ISBN 1-412-91611-9.
[10] Sproull, Natalie L. (2002). “Hypothesis testing”. Hand-
book of Research Methods: A Guide for Practitioners and
Students in the Social Science (2nd ed.). Lanham, MD:
Scarecrow Press, Inc. pp. 49–64. ISBN 0-810-84486-9.
[11] Sirkin, R. Mark (2005). “Two-sample t tests”. Statistics
for the Social Sciences (3rd ed.). Thousand Oaks, CA:
SAGE Publications, Inc. pp. 271–316. ISBN 1-412-
90546-X.
[12] Borror, Connie M. (2009). “Statistical decision making”.
The Certified Quality Engineer Handbook (3rd ed.). Mil-
waukee, WI: ASQ Quality Press. pp. 418–472. ISBN
0-873-89745-5.
[13] Babbie, Earl R. (2013). “The logic of sampling”. The
Practice of Social Research (13th ed.). Belmont, CA: Cen-
gage Learning. pp. 185–226. ISBN 1-133-04979-6.
[14] Faherty, Vincent (2008). “Probability and statistical sig-
nificance”. Compassionate Statistics: Applied Quantitative
Analysis for Social Services (With exercises and instruc-
tions in SPSS) (1st ed.). Thousand Oaks, CA: SAGE Pub-
lications, Inc. pp. 127–138. ISBN 1-412-93982-8.
[15] McKillup, Steve (2006). “Probability helps you make a
decision about your results”. Statistics Explained: An In-
troductory Guide for Life Scientists (1st ed.). Cambridge,
United Kingdom: Cambridge University Press. pp. 44–
56. ISBN 0-521-54316-9.
[16] Poletiek, Fenna H. (2001). “Formal theories of testing”.
Hypothesis-testing Behaviour. Essays in Cognitive Psy-
chology (1st ed.). East Sussex, United Kingdom: Psy-
chology Press. pp. 29–48. ISBN 1-841-69159-3.
[17] Fisher, Ronald A. (1925). Statistical Methods for Research
Workers. Edinburgh, UK: Oliver and Boyd. p. 43. ISBN
0-050-02170-2.
[18] Quinn, Geoffrey R.; Keough, Michael J. (2002). Experi-
mental Design and Data Analysis for Biologists (1st ed.).
Cambridge, UK: Cambridge University Press. pp. 46–69.
ISBN 0-521-00976-6.
[19] Neyman, J.; Pearson, E.S. (1933). “The testing of statisti-
cal hypotheses in relation to probabilities a priori”. Math-
ematical Proceedings of the Cambridge Philosophical So-
ciety 29: 492–510. doi:10.1017/S030500410001152X.
[20] Myers, Jerome L.; Well, Arnold D.; Lorch Jr, Robert F.
(2010). “The t distribution and its applications”. Research
Design and Statistical Analysis: Third Edition (3rd ed.).
New York, NY: Routledge. pp. 124–153. ISBN 0-805-
86431-8.
[21] Meier, Kenneth J.; Brudney, Jeffrey L.; Bohte, John
(2011). Applied Statistics for Public and Nonprofit Admin-
istration (3rd ed.). Boston, MA: Cengage Learning. pp.
189–209. ISBN 1-111-34280-6.
[22] Healy, Joseph F. (2009). The Essentials of Statistics: A
Tool for Social Research (2nd ed.). Belmont, CA: Cen-
gage Learning. pp. 177–205. ISBN 0-495-60143-8.
[23] Cohen, Barry H. (2008). Explaining Psychological Statis-
tics (3rd ed.). Hoboken, NJ: John Wiley and Sons. pp.
46–83. ISBN 0-470-00718-4.
[24] Friston, Karl (2012). article “Ten ironic rules for non-
statistical reviewers”. NeuroImage 61 (4): 1300–1310.
[25] Health, David (1995). An Introduction To Experimental
Design And Statistics For Biology (1st ed.). Boston, MA:
CRC press. pp. 123–154. ISBN 1-857-28132-2.
[26] Vaughan, Simon (2013). Scientific Inference: Learning
from Data (1st ed.). Cambridge, UK: Cambridge Uni-
versity Press. pp. 146–152. ISBN 1-107-02482-X.
[27] Bracken, Michael B. (2013). Risk, Chance, and Causa-
tion: Investigating the Origins and Treatment of Disease
(1st ed.). New Haven, CT: Yale University Press. pp.
260–276. ISBN 0-300-18884-6.
[28] Franklin, Allan (2013). “Prologue: The rise of the sig-
mas”. Shifting Standards: Experiments in Particle Physics
in the Twentieth Century (1st ed.). Pittsburgh, PA: Univer-
sity of Pittsburgh Press. pp. Ii–Iii. ISBN 0-822-94430-8.
[29] Clarke, GM; Anderson, CA; Pettersson, FH; Cardon, LR;
Morris, AP; Zondervan, KT (February 6, 2011). “Basic
statistical analysis in genetic case-control studies”. Nature
Protocols 6 (2): 121–33. doi:10.1038/nprot.2010.182.
PMID 21293453.
[30] Barsh, GS; Copenhaver, GP; Gibson, G; Williams, SM
(July 5, 2012). “Guidelines for Genome-Wide As-
sociation Studies”. PLoS Genetics 8 (7): e1002812.
doi:10.1371/journal.pgen.1002812. PMID 22792080.
[31] Carver, Ronald P. (1978). “The Case Against Statistical
Significance Testing”. Harvard Educational Review 48:
378–399.
[32] Ioannidis, John P. A. (2005). “Why most published re-
search findings are false”. PLoS Medicine 2: e124.
[33] Pedhazur, Elazar J.; Schmelkin, Liora P. (1991). Mea-
surement, Design, and Analysis: An Integrated Approach
(Student ed.). New York, NY: Psychology Press. pp.
180–210. ISBN 0-805-81063-3.
7 Further reading
• Ziliak, Stephen and Deirdre McCloskey (2008), The
Cult of Statistical Significance: How the Standard Er-
ror Costs Us Jobs, Justice, and Lives. Ann Arbor,
University of Michigan Press, 2009. ISBN 978-0-
472-07007-7. Reviews and reception: (compiled by
Ziliak)
• Thompson, Bruce (2004). “The “signifi-
cance” crisis in psychology and education”.
Journal of Socio-Economics 33: 607–613.
doi:10.1016/j.socec.2004.09.034.
4. 4 8 EXTERNAL LINKS
• Chow, Siu L., (1996). Statistical Significance: Ra-
tionale, Validity and Utility, Volume 1 of series In-
troducing Statistical Methods, Sage Publications Ltd,
ISBN 978-0-7619-5205-3 – argues that statistical
significance is useful in certain circumstances.
• Kline, Rex, (2004). Beyond Significance Testing:
Reforming Data Analysis Methods in Behavioral Re-
search Washington, DC: American Psychological
Association.
8 External links
• The article "Earliest Known Uses of Some of the
Words of Mathematics (S)" contains an entry on Sig-
nificance that provides some historical information.
• "The Concept of Statistical Significance Testing"
(February 1994): article by Bruce Thompon hosted
by the ERIC Clearinghouse on Assessment and
Evaluation, Washington, D.C.
• "What does it mean for a result to be “statistically
significant"?" (no date): an article from the Statis-
tical Assessment Service at George Mason Univer-
sity, Washington, D.C.
5. 5
9 Text and image sources, contributors, and licenses
9.1 Text
• Statistical significance Source: http://en.wikipedia.org/wiki/Statistical_significance?oldid=649544777 Contributors: Bryan Derksen, The
Anome, William Avery, Michael Hardy, Kku, Gabbe, Dcljr, Ellywa, Nichtich~enwiki, Den fjättrade ankan~enwiki, Nerd~enwiki, Cherkash,
Topbanana, Paranoid, Gak, Henrygb, Giftlite, BrendanH, Pgan002, Antandrus, L353a1, DanielCD, Rich Farmbrough, Yknott, Kndiaye,
Slb, Cretog8, Arcadian, Andrewpmk, John Quiggin, Seans Potato Business, Alkarex, Woohookitty, Btyner, Rjwilmsi, Smoe, Thomas Are-
latensis, Thisismikesother, ElKevbo, Cjpuffin, EvanSeeds, Lborelli~enwiki, Mathbot, Riki, Preslethe, Vonkje, Chobot, YurikBot, Wave-
length, Gaius Cornelius, ENeville, Nephron, DRosenbach, Jon Olav Vik, Doc pune, Lt-wiki-bot, Davril2020, Badgettrg, Darrel francis,
SmackBot, McGeddon, Jtneill, Robfuller, Ohnoitsjamie, Josefec, Nbarth, Danielkueh, Richard001, G716, Arodb, Euchiasmus, Tim bates,
Nijdam, Tommyzee, Mmiller0712, Mdgross50, Grapplequip, DwightKingsbury, Joseph Solis in Australia, Abeg92, Tawkerbot4, LarryQ,
Thijs!bot, Tallred, Wildthing61476, Tillman, Erxnmedia, Fetchcomms, Magioladitis, Torchiest, Inhumandecency, MartinBot, ChemN-
erd, Lilac Soul, Coppertwig, Yym1997, Kenneth M Burke, Spellcast, Philip Trueman, Don Quixote de la Mancha, MuanN, Seraphim,
Sprasad.ee, SQL, Wangerin, Lavers, Jasondet, Strasburger, The-G-Unit-Boss, Melcombe, Wjmummert, Martarius, ClueBot, Binkster-
net, Srudes2, Winsteps, Pwestfall, Lot49a, Qwfp, Staticshakedown, Dthomsen8, SilvonenBot, Mifter, Aam aadmi, ZooFari, Jmkim dot
com, Tayste, Addbot, Eric Drexler, DOI bot, Fgnievinski, Bulletproofman19, MrOllie, Palmerabollo, Numbo3-bot, Ehrenkater, Zorrobot,
Luckas-bot, AnomieBOT, ChristopheS, Materialscientist, SvartMan, Xqbot, Bbarkley, Sylwia Ufnalska, M12107, Constructive editor,
FrescoBot, Sławomir Biały, Pinethicket, Edderso, Georg Hurtig, RedBot, Gjsis, Cerebis, Animalparty, Indicedigini, Raylyons, Billare, Sir
Arthur Williams, Rgmooney C109, GoingBatty, Schwa dk, HiW-Bot, Kostya 888, Muditjai, Mysticyx, L Kensington, Mikhail Ryazanov,
ClueBot NG, Mathstat, Michael D. Stephens, Helpful Pixie Bot, BG19bot, Wikstar7, Lilingxi, Matthieu Vergne, Manoguru, Minsbot,
MathewTownsend, BattyBot, HankW512, ChrisGualtieri, Eggingerik, BetseyTrotwood, NicenFriendlyPerson, Sa publishers, Soranoch,
Thewikiguru1, Rgiordan, EmilKarlsson, 1980na, Isambard Kingdom, ChrisLloyd58 and Anonymous: 154
9.2 Images
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nal); Pbroks13 (talk) (redraw)
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tors:
self-made
Original artist:
Qwfp (talk)
• File:People_icon.svg Source: http://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg License: CC0 Contributors: Open-
Clipart Original artist: OpenClipart
• File:Portal-puzzle.svg Source: http://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg License: Public domain Contributors: ?
Original artist: ?
• File:Wikiversity-logo.svg Source: http://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg License: CC BY-SA 3.0
Contributors: Snorky (optimized and cleaned up by verdy_p) Original artist: Snorky (optimized and cleaned up by verdy_p)
9.3 Content license
• Creative Commons Attribution-Share Alike 3.0