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F-Test

An F-test is a form of hypothesis testing used for comparing variances using the F-distributions, with varying degrees of freedom. F-distributions were developed by George W. Snedecor in honour of R.A. Fisher. F-tests are used to test whether the variances of two samples are equal; this is the null hypothesis. The advantage of the F-test is that it can be used to compare multiple samples at the same time. Another way to think of the F-test is that it tests how well a particular regression fits the data set. In this case the F-statistic can be calculated by:

F = explained variance / unexplained variance,

or

F = between-group variability / within-group variability

After calculating the F-statistic we can compare it to the critical value to determine whether the null hypothesis can or cannot be rejected at the specified significance level. The explained variance is calculated by taking the sum of the square of the difference between the means for each group of data and the overall mean of the data set multiplied by the number of observations, and divided by one less the number of groups. Hence, it is known as the between-group variability because it compares the variability of each group to the overall level. The unexplained variance is the sum of every group's differences between each observation of each group and that group's mean squared, and then divided by the number of observations less the number of groups. It is the within-group variability because it compares the variance between the observations and the means within each group. Formally the explained and unexplained variances are shown below respectively where: n is the number of observations for the specific group, i is the counter for the groups, j is the counter for observations, Y is the specific observation, Ῡ is the mean, N is the overall sample size, and K is the number of groups.

 

Hypotheses for Two-Sample Tests: Independent Samples vs Dependent Samples

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Phatmaceutical Test Groups

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True or False

Identify each of the following statements as true or false, explain why: A. A parameter is a population characteristic that is estimated by a coefficient derived from a sample of data. B. A one-tailed t-test is used to indicate whether the independent variables as a group explain a significant share of demand variation. C. G

ANOVA and Turkey test

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Statistics: F Test for equality of variance

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ANOVA analysis: Treatment conditions, F-ratio, Migrating birds,

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F test for equality of variance of two populations

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Statistics: Values of the F-statistic

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Assumptions for the F Test

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Post Hoc Analysis for an F-Test

What are post hoc comparisons, and why do researchers make them? Why do researchers not use the Bonferroni procedure of procedures for post hoc comparisons? What is the advantage over the Bonferroni procedure of procedures such as the Tukey and Scheffe tests? Is Scheffe preferred over others if so, why and what are the advant

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P value for F test

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Critical Value for F-Test

a) Given the significance level 0.01, the F-value for the degrees of freedom, d.f. = (7,3) is? b) In a completely randomized design for ANOVA, the number of degrees of freedom for the numerator and denominator are 4 and 25, respectively. The total number of observations must equal?

Hypothesis Testing for Variances: F Test

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Independent Sample/F Distribution/Type I Error

a. What is an independent sample? What is a related sample? When should researchers use different hypothesis tests for independent and related samples? Is one type of sample preferable over the other? b. What is a Type I error? Explain how the cumulative Type I error affects your decision making. How is the two independent sa

Hypothesis testing :F test for Variance

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Comparing two population variances (F-test)

The following hypotheses are given: Ho: s2 sub 1 = s2 sub 2 H1: s2 sub 1 = s2 sub 2 A random sample of five observations from the first population resulted in a standard deviation of 12. A random sample of seven observations from the second population showed a standard deviation of 7. At the .01 significance level, is t