TRANSCRIPT: This is Dr. Chumney. The focus of this lecture is
... Data collected from samples are eventually used to evaluate the credibility of null hypotheses. The data will either support the null hypothesis or refute it. If there is a big discrepancy between the data and the hypothesis, we conclude that the hypothesis is wrong. To formalize the decision proc ...
... Data collected from samples are eventually used to evaluate the credibility of null hypotheses. The data will either support the null hypothesis or refute it. If there is a big discrepancy between the data and the hypothesis, we conclude that the hypothesis is wrong. To formalize the decision proc ...
8 Looking for relationships: batches and scatter graphs
... To discuss the nature of sampling, a simple artificial example will be used. Suppose you have a bag containing a very large number of 1p coins. The composition of 1p coins was changed in 1992, so from that year they were magnetic while before then they were not. Without using a magnet, how could you ...
... To discuss the nature of sampling, a simple artificial example will be used. Suppose you have a bag containing a very large number of 1p coins. The composition of 1p coins was changed in 1992, so from that year they were magnetic while before then they were not. Without using a magnet, how could you ...
Microarrays and gene expression
... distinct sets of genes with similar expressions, suggesting that they may be biologically related. In supervised problems a response measurement is also available for each sample and the goal of the experiment is to find sets of genes that, for example, relate to different kind of diseases, so that ...
... distinct sets of genes with similar expressions, suggesting that they may be biologically related. In supervised problems a response measurement is also available for each sample and the goal of the experiment is to find sets of genes that, for example, relate to different kind of diseases, so that ...
Expected Value of a Random Variable
... This distribution seems to be centered at 2.5. Can we say that the “average” or “mean” number of tails is 2.5? ...
... This distribution seems to be centered at 2.5. Can we say that the “average” or “mean” number of tails is 2.5? ...
Research Questions, Hypotheses, and Variables
... Hypotheses are predictions about the relationship among two or more variables or groups based on a theory or previous research (Pittenger, 2003) Hypotheses are Assumptions or theories that a researcher makes and tests. Why are hypotheses important? ...
... Hypotheses are predictions about the relationship among two or more variables or groups based on a theory or previous research (Pittenger, 2003) Hypotheses are Assumptions or theories that a researcher makes and tests. Why are hypotheses important? ...
Conditional Probability Name: Alg2 CC Conditional Probability A
... performs a diagnostic test on 137 patients – 67 with known renal disease and 70 who are known to be healthy. The diagnostic test comes back either positive (the patient has renal disease) or negative (the patient does not have renal disease). Here are the results of her experiment. ...
... performs a diagnostic test on 137 patients – 67 with known renal disease and 70 who are known to be healthy. The diagnostic test comes back either positive (the patient has renal disease) or negative (the patient does not have renal disease). Here are the results of her experiment. ...
Lecture 3 : Hypothesis testing and model
... Why was this poor statistics? The p-value quoted by the LHC experiments is not the probability the Higgs particle doesn’t exist. It is the probability of obtaining the measurement assuming the Higgs doesn’t exist. ...
... Why was this poor statistics? The p-value quoted by the LHC experiments is not the probability the Higgs particle doesn’t exist. It is the probability of obtaining the measurement assuming the Higgs doesn’t exist. ...
Binomial Distribution
... Eggs are packed in boxes of 12. The probability that each egg is broken is 0.35 Find the probability in a random box of eggs: There are less than 3 broken eggs ...
... Eggs are packed in boxes of 12. The probability that each egg is broken is 0.35 Find the probability in a random box of eggs: There are less than 3 broken eggs ...
communicate and reason mathematically
... •determine what can be measured and how, using appropriate methods and formulas; •use units to give meaning to measurements; ...
... •determine what can be measured and how, using appropriate methods and formulas; •use units to give meaning to measurements; ...
Chapter 4 Continuous Random Variables and their Probability
... Continuous Random Variables Experiments and tests can result in values that are spread over a continuum. Even if our measurement device has discrete values, it is often impractical to use a discrete distribution because the number of allowed values is so large. We gain modeling flexibility by expan ...
... Continuous Random Variables Experiments and tests can result in values that are spread over a continuum. Even if our measurement device has discrete values, it is often impractical to use a discrete distribution because the number of allowed values is so large. We gain modeling flexibility by expan ...
Statistics
Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In applying statistics to, e.g., a scientific, industrial, or societal problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as ""all persons living in a country"" or ""every atom composing a crystal"". Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments.When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can safely extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation.Two main statistical methodologies are used in data analysis: descriptive statistics, which summarizes data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draws conclusions from data that are subject to random variation (e.g., observational errors, sampling variation). Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): central tendency (or location) seeks to characterize the distribution's central or typical value, while dispersion (or variability) characterizes the extent to which members of the distribution depart from its center and each other. Inferences on mathematical statistics are made under the framework of probability theory, which deals with the analysis of random phenomena.A standard statistical procedure involves the test of the relationship between two statistical data sets, or a data set and a synthetic data drawn from idealized model. An hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets. Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test. Working from a null hypothesis, two basic forms of error are recognized: Type I errors (null hypothesis is falsely rejected giving a ""false positive"") and Type II errors (null hypothesis fails to be rejected and an actual difference between populations is missed giving a ""false negative""). Multiple problems have come to be associated with this framework: ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis.Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random (noise) or systematic (bias), but other important types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also be important. The presence of missing data and/or censoring may result in biased estimates and specific techniques have been developed to address these problems.Statistics can be said to have begun in ancient civilization, going back at least to the 5th century BC, but it was not until the 18th century that it started to draw more heavily from calculus and probability theory. Statistics continues to be an area of active research, for example on the problem of how to analyze Big data.