Chapter 12
Estimation and Hypothesis Testing
By Boundless
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Estimating population parameters from sample parameters is one of the major applications of inferential statistics.
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Here, we present how to calculate the minimum sample size needed to estimate a population mean (
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Point estimation involves the use of sample data to calculate a single value which serves as the "best estimate" of an unknown population parameter.
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Interval estimation is the use of sample data to calculate an interval of possible (or probable) values of an unknown population parameter.
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In order to estimate a population proportion of some attribute, it is helpful to rely on the proportions observed within a sample of the population.
The problem of comparing more than two means results from the increase in Type I error that occurs when statistical tests are used repeatedly.
Completely randomized designs study the effects of one primary factor without the need to take other nuisance variables into account.
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ANOVA is useful in the multiple comparisons of means due to its reduction in the Type I error rate.
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Block design is the arranging of experimental units into groups (blocks) that are similar to one another, to control for certain factors.
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A full factorial experiment is an experiment whose design consists of two or more factors with discrete possible levels.
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A confidence interval is a type of interval estimate of a population parameter and is used to indicate the reliability of an estimate.
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For users of frequentist methods, various interpretations of a confidence interval can be given.
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Readers of polls, such as the Gallup Poll, should exercise Caveat Emptor by taking into account the poll's margin of error.
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The proportion of confidence intervals that contain the true value of a parameter will match the confidence level.
A major factor determining the length of a confidence interval is the size of the sample used in the estimation procedure.
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The procedure to find the confidence interval and the confidence level for a proportion is similar to that for the population mean.
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In this section, we outline an example of finding the confidence interval for a population mean when we know the standard deviation.
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In this section, we outline an example of finding the confidence interval for a population mean when we do not know the standard deviation.
The chi-square distribution is used to construct confidence intervals for a population variance.
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Tests of significance are a statistical technology used for ascertaining the likelihood of empirical data, and (from there) for inferring a real effect.
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A statistical hypothesis test is a method of making decisions using data from a scientific study.
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The alternative hypothesis and the null hypothesis are the two rival hypotheses that are compared by a statistical hypothesis test.
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If the result of a hypothesis test does not correspond with reality, then an error has occurred.
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If a test of significance gives a
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A one-tailed hypothesis is one in which the value of a parameter is either above or equal to a certain value or below or equal to a certain value.
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Creating a hypothesis test generally follows a five-step procedure.
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Here we will evaluate an example of hypothesis testing for a single proportion.
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In this section we will evaluate an example of hypothesis testing for a single mean.
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In this section we will evaluate an example of hypothesis testing for a single variance.
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To compare two means or two proportions, one works with two groups.
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To compare independent samples, both populations are normally distributed with the population means and standard deviations unknown.
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If two estimated proportions are different, it may be due to a difference in the populations or it may be due to chance.
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In a hypothesis test for matched or paired samples, subjects are matched in pairs and differences are calculated.
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In order to compare two variances, we must use the
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A common problem is calculating the sample size required to yield a certain power for a test, given a predetermined type I error rate
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An F-test is any statistical test in which the test statistic has an F-distribution under the null hypothesis.
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The
The
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Most
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ANOVA is a statistical tool used in several ways to develop and confirm an explanation for the observed data.
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Many statisticians base ANOVA on the design of the experiment, especially on the protocol that specifies the random assignment of treatments to subjects.
The results of a one-way ANOVA can be considered reliable as long as certain assumptions are met.