Improving your statistical inferences

Start Date: 02/23/2020

Course Type: Common Course

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About Course

This course aims to help you to draw better statistical inferences from empirical research. First, we will discuss how to correctly interpret p-values, effect sizes, confidence intervals, Bayes Factors, and likelihood ratios, and how these statistics answer different questions you might be interested in. Then, you will learn how to design experiments where the false positive rate is controlled, and how to decide upon the sample size for your study, for example in order to achieve high statistical power. Subsequently, you will learn how to interpret evidence in the scientific literature given widespread publication bias, for example by learning about p-curve analysis. Finally, we will talk about how to do philosophy of science, theory construction, and cumulative science, including how to perform replication studies, why and how to pre-register your experiment, and how to share your results following Open Science principles. In practical, hands on assignments, you will learn how to simulate t-tests to learn which p-values you can expect, calculate likelihood ratio's and get an introduction the binomial Bayesian statistics, and learn about the positive predictive value which expresses the probability published research findings are true. We will experience the problems with optional stopping and learn how to prevent these problems by using sequential analyses. You will calculate effect sizes, see how confidence intervals work through simulations, and practice doing a-priori power analyses. Finally, you will learn how to examine whether the null hypothesis is true using equivalence testing and Bayesian statistics, and how to pre-register a study, and share your data on the Open Science Framework. All videos now have Chinese subtitles. More than 30.000 learners have enrolled so far! If you enjoyed this course, I can recommend following it up with me new course "Improving Your Statistical Questions"

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Course Introduction

Improving your statistical inferences In this course you will learn how to interpret data and practice interpreting data for accuracy and quality. You will learn the tools to interpret different types of data, such as public data, anonymized data, unstructured data, and custom data, and you will practice interpreting data for accuracy and quality. To begin, we recommend taking a few minutes to explore the course site. Review the material we have to offer you and get familiar with the course content. The first module in the course will introduce you to basic statistical inference and provide you with a set of tools to practice interpreting data. We will use a simple statistical inference technique, the Bonferroni correction, to make sure you are interpreting the data correctly. We will use different types of statistical tests and you will practice interpreting them. We will use different types of hypothesis tests and you will practice interpreting them. In week 2 we move to different types of hypothesis tests and you will practice interpreting them. In week 3 we move to different types of p-values and you will practice interpreting them. In week 4 we move to different types of significance tests and you will practice interpreting them. In week 5 we move to different types of significance tests and you will practice interpreting them. In week 6 we move to different types of statistical tests and you will practice interpreting them. In week 7 we move to different types of p-values and you will practice interpreting them. In week 8 we move to different types of significance tests and you

Course Tag

Likelihood Function Bayesian Statistics P-Value Statistical Inference

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Article Example
Statistical theory Apart from philosophical considerations about how to make statistical inferences and decisions, much of statistical theory consists of mathematical statistics, and is closely linked to probability theory, to utility theory, and to optimization.
Statistical inference Similarly, results from randomized experiments are recommended by leading statistical authorities as allowing inferences with greater reliability than do observational studies of the same phenomena.
Statistical genetics Statistical genetics is a scientific field concerned with the development and application of statistical methods for drawing inferences from genetic data. The term is most commonly used in the context of human genetics. Research in statistical genetics generally falls into one of three areas:
Statistical inference Statistical inference makes propositions about a population, using data drawn from the population with some form of sampling. Given a hypothesis about a population, for which we wish to draw inferences, statistical inference consists of (firstly) selecting a statistical model of the process that generates the data and (secondly) deducing propositions from the model.
Statistical inference Any statistical inference requires some assumptions. A statistical model is a set of assumptions concerning the generation of the observed data and similar data. Descriptions of statistical models usually emphasize the role of population quantities of interest, about which we wish to draw inference. Descriptive statistics are typically used as a preliminary step before more formal inferences are drawn.
Statistical theory Statistical theory provides a guide to comparing methods of data collection, where the problem is to generate informative data using optimization and randomization while measuring and controlling for observational error. Optimization of data collection reduces the cost of data while satisfying statistical goals, while randomization allows reliable inferences. Statistical theory provides a basis for good data collection and the structuring of investigations in the topics of:
Statistical inference Many statisticians prefer randomization-based analysis of data that was generated by well-defined randomization procedures. (However, it is true that in fields of science with developed theoretical knowledge and experimental control, randomized experiments may increase the costs of experimentation without improving the quality of inferences.)
Statistical theory Statistical models, once specified, can be tested to see whether they provide useful inferences for new data sets. Testing a hypothesis using the data that was used to specify the model is a fallacy, according to the natural science of Bacon and the scientific method of Peirce.
Statistical stability Pay attention, the possibility of adequate description of relative frequencies of actual events and sample averages of actual discrete samples by the expressions formula_6, formula_9 is only a hypothesis. It does not follow from any experiments and any logical inferences. It is easy to demonstrate that not all processes, even oscillatory type, have the property of perfect statistical stability.
Statistical proof Statistical proof is the rational demonstration of degree of certainty for a proposition, hypothesis or theory that is used to convince others subsequent to a statistical test of the supporting evidence and the types of inferences that can be drawn from the test scores. Statistical methods are used to increase the understanding of the facts and the proof demonstrates the validity and logic of inference with explicit reference to a hypothesis, the experimental data, the facts, the test, and the odds. Proof has two essential aims: the first is to convince and the second is to explain the proposition through peer and public review.
Statistical parameter Even if a family of distributions is not specified, quantities such as the mean and variance can still be regarded as parameters of the distribution of the population from which a sample is drawn. Statistical procedures can still attempt to make inferences about such population parameters. Parameters of this type are given names appropriate to their roles, including:
Statistical conclusion validity Most statistical tests (particularly inferential statistics) involve assumptions about the data that make the analysis suitable for testing a hypothesis. Violating the assumptions of statistical tests can lead to incorrect inferences about the cause-effect relationship. The robustness of a test indicates how sensitive it is to violations. Violations of assumptions may make tests more or less likely to make type I or II errors.
Statistical model All statistical hypothesis tests and all statistical estimators are derived from statistical models. More generally, statistical models are part of the foundation of statistical inference.
James F. Bandrowski Bandrowski, James, and Hayden Curry narrating, "Improving Your Tennis Game" (#20200), "Improving Your Golf Game" (#20201), and "Improving Your Golf Game" (#20202), "Psychology Today" Cassettes, New York, 1978.
Statistical inference The conclusion of a statistical inference is a statistical proposition. Some common forms of statistical proposition are the following:
Statistical theory When a statistical procedure has been specified in the study protocol, then statistical theory provides well-defined probability statements for the method when applied to all populations that could have arisen from the randomization used to generate the data. This provides an objective way of estimating parameters, estimating confidence intervals, testing hypotheses, and selecting the best. Even for observational data, statistical theory provides a way of calculating a value that can be used to interpret a sample of data from a population, it can provide a means of indicating how well that value is determined by the sample, and thus a means of saying corresponding values derived for different populations are as different as they might seem; however, the reliability of inferences from post-hoc observational data is often worse than for planned randomized generation of data.
Statistical power Statistical tests use data from samples to assess, or make inferences about, a statistical population. In the concrete setting of a two-sample comparison, the goal is to assess whether the mean values of some attribute obtained for individuals in two sub-populations differ. For example, to test the null hypothesis that the mean scores of men and women on a test do not differ, samples of men and women are drawn, the test is administered to them, and the mean score of one group is compared to that of the other group using a statistical test such as the two-sample "z"-test. The power of the test is the probability that the test will find a statistically significant difference between men and women, as a function of the size of the true difference between those two populations.
Statistical literacy The definition of statistical literacy and opinions about it have been somewhat historically variable. Before 1940 some statistical skills passed to the sciences. Some statistics was then taught in grade school, "So a degree of statistical literacy will be universal in the future...". More recently, expectations have been higher. "'Statistical Literacy' is the ability to understand and critically evaluate statistical results that permeate our lives...". Those statistical results often originate from inferential methods which reached college statistics textbooks in about 1940. Statistics continues to advance. A lack of statistical literacy has long been condemned under many labels. Psychologists do not believe statistical reasoning to be intuitive.
Statistical assembly In statistics, for example in statistical quality control, a statistical assembly is a collection of parts or components which makes up a statistical unit. Thus a statistical unit, which would be the prime item of concern, is made of discrete components like organs or machine parts. The reliability of the statistical unit is, in part, determined by the reliability of the components in the statistical assembly, and by their interactions.
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