10.4 Power Type Errors Example - Mrs. McDonald
... 1. A research psychologist plans to administer a test designed to measure self-confidence to a random sample of fifty professional athletes. The psychologist theorizes that professional athletes tend to be more self-confident than others. Since the national norm of the test is known to be 72, the th ...
... 1. A research psychologist plans to administer a test designed to measure self-confidence to a random sample of fifty professional athletes. The psychologist theorizes that professional athletes tend to be more self-confident than others. Since the national norm of the test is known to be 72, the th ...
Chapter 5: Regression
... Comparative studies are more convincing than single-sample investigations. For that reason, one-sample inference is less common than comparative inference. Study designs that involve making two observations on the same individual, or one observation on each of two similar individuals, result in pair ...
... Comparative studies are more convincing than single-sample investigations. For that reason, one-sample inference is less common than comparative inference. Study designs that involve making two observations on the same individual, or one observation on each of two similar individuals, result in pair ...
Concepts in Hypothesis Testing
... a) identify the appropriate statistical test to be used b) identify type of data to be collected (variables) c) construct the sampling or experimental design so that it actually provides the data needed for the test Comment: These three cannot be separated as distinct activities Point: most of the t ...
... a) identify the appropriate statistical test to be used b) identify type of data to be collected (variables) c) construct the sampling or experimental design so that it actually provides the data needed for the test Comment: These three cannot be separated as distinct activities Point: most of the t ...
Notes: Discrete Random Variables
... We can define events using random variables. The notation {X = a} defines the event of all elements in our sample space for which the random variable X evaluates to a. In set notation {X = a} = {ω ∈ Ω : X(ω) = a} The probability of this event is denoted P (X = a). Example: Sum of dice What is {S = 5 ...
... We can define events using random variables. The notation {X = a} defines the event of all elements in our sample space for which the random variable X evaluates to a. In set notation {X = a} = {ω ∈ Ω : X(ω) = a} The probability of this event is denoted P (X = a). Example: Sum of dice What is {S = 5 ...
Presentation
... Statistics and Probability Students view statistical reasoning as a 4 step process ...
... Statistics and Probability Students view statistical reasoning as a 4 step process ...
Proposition 1.1 De Moargan’s Laws
... health hazard. The following is the results of a study in which six river locations were selected and the zinc concentrations in (mg/L) determined for both surface water and bottom water at each location. The six pairs of observations are displayed graphically below. ...
... health hazard. The following is the results of a study in which six river locations were selected and the zinc concentrations in (mg/L) determined for both surface water and bottom water at each location. The six pairs of observations are displayed graphically below. ...
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... mathematical problems involving mathematics of finance, fundamentals of statistics and probability, modeling functions, both linear and exponential. 4. Represent quantitative problems expressed in natural language in a suitable mathematical format such as algebraic, graphical or tabular form. 5. Eff ...
... mathematical problems involving mathematics of finance, fundamentals of statistics and probability, modeling functions, both linear and exponential. 4. Represent quantitative problems expressed in natural language in a suitable mathematical format such as algebraic, graphical or tabular form. 5. Eff ...
Notes 20 - Wharton Statistics
... number of successes in the n trials; X is a binomial ( n, p ) random variable. In Section 7.2, we used the following strategy to find E ( X ) . We noted that X is the number of the events A1 , , An that occur where Ai is the event that the ith trial is a success. We then defined indicator variables ...
... number of successes in the n trials; X is a binomial ( n, p ) random variable. In Section 7.2, we used the following strategy to find E ( X ) . We noted that X is the number of the events A1 , , An that occur where Ai is the event that the ith trial is a success. We then defined indicator variables ...
probability
... • 1-1: Toss a coin two times and note the sequence of heads and tails. • 1-2: Toss a coin three times and note the number of heads. ...
... • 1-1: Toss a coin two times and note the sequence of heads and tails. • 1-2: Toss a coin three times and note the number of heads. ...
John Lindhe - Northeastern University
... There will be two quizzes, two 1 hour tests, and two take-home quizzes. The final will be cumulative. This is an introduction course to the theory of probability and statistics. Its goal is to develop the mathematical tools and concepts necessary for modeling uncertainty and data analysis in real-wo ...
... There will be two quizzes, two 1 hour tests, and two take-home quizzes. The final will be cumulative. This is an introduction course to the theory of probability and statistics. Its goal is to develop the mathematical tools and concepts necessary for modeling uncertainty and data analysis in real-wo ...
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.