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Descriptive statistics
Descriptive statistics

... What we have done so far is useful, but not useful enough! If we think about it, we will see that the estimate of the population mean (i.e. all the measurements that we ever could make of the same type - the diameter of this type of cell, etc.) has been fixed by the sample of four individuals. If we ...
standard deviation
standard deviation

Populations and Samples Chapter 8
Populations and Samples Chapter 8

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Multi-Means Comparisons: Analysis of Variance (ANOVA)

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ppt file

WHY DOES THE SAMPLE VARIANCE HAVE N
WHY DOES THE SAMPLE VARIANCE HAVE N

Binus Repository
Binus Repository

... – Autocorrelation (errors are not independent) • Usually happens in time-series data • Consequences of Any Violation of the Assumptions – Predictions and estimations obtained from the sample regression line will not be accurate – Hypothesis testing results will not be reliable • It is Important to V ...
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... amount of abuse (weather, pressure, friction etc.). How can a manufacturer guarantee that each bolt they manufacture will consistently function properly under such conditions? ...
AP Statistics: ANOVA Section 2
AP Statistics: ANOVA Section 2

... several groups. However, that test only tells us when differences exist, not which specific groups differ. The goal of this section is to adapt the inference procedures of section 13.1 to use the results of the ANOVA analysis. This will allow us to find a confidence interval for the mean of any grou ...
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File

Mr. Pryor's First Test (page 86)
Mr. Pryor's First Test (page 86)

Everything You Wanted to know about Statistics but were afraid to ask
Everything You Wanted to know about Statistics but were afraid to ask

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7. Point Estimation and Confidence Intervals for Means

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Mathematical Notation

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Chapter17

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The t Tests

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1. A New York Times poll on women`s issues interviewed

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Hypothesis Testing

... statistics in science. It is often the "Expected Value" i.e. the value we expect to get. • The mean is found by totalling the values for all observations (∑x) and dividing by the total number of observations (n). The formula for finding the mean is: ...
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CHAPTER TWELVE Between-Groups ANOVA NOTE TO

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... • So we just use the mean of the sample as the estimate of the mean of the population. X is called a point estimator of µ Hard part: • What can we say about the quality of X as an estimator of µ? • e.g. what’s the probability that X is within 3 of µ? ...
Year 12 Normal Distribution Test
Year 12 Normal Distribution Test

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Degrees of freedom (statistics)

In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.The number of independent ways by which a dynamic system can move, without violating any constraint imposed on it, is called number of degrees of freedom. In other words, the number of degrees of freedom can be defined as the minimum number of independent coordinates that can specify the position of the system completely.Estimates of statistical parameters can be based upon different amounts of information or data. The number of independent pieces of information that go into the estimate of a parameter are called the degrees of freedom. In general, the degrees of freedom of an estimate of a parameter are equal to the number of independent scores that go into the estimate minus the number of parameters used as intermediate steps in the estimation of the parameter itself (i.e. the sample variance has N-1 degrees of freedom, since it is computed from N random scores minus the only 1 parameter estimated as intermediate step, which is the sample mean).Mathematically, degrees of freedom is the number of dimensions of the domain of a random vector, or essentially the number of ""free"" components (how many components need to be known before the vector is fully determined).The term is most often used in the context of linear models (linear regression, analysis of variance), where certain random vectors are constrained to lie in linear subspaces, and the number of degrees of freedom is the dimension of the subspace. The degrees of freedom are also commonly associated with the squared lengths (or ""sum of squares"" of the coordinates) of such vectors, and the parameters of chi-squared and other distributions that arise in associated statistical testing problems.While introductory textbooks may introduce degrees of freedom as distribution parameters or through hypothesis testing, it is the underlying geometry that defines degrees of freedom, and is critical to a proper understanding of the concept. Walker (1940) has stated this succinctly as ""the number of observations minus the number of necessary relations among these observations.""
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