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ANOVA: Analysis of Variance

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The original concepts of analysis of variance came from the work of Sir Ronald A. Fisher, an English statistician. This technique, better known as ANOVA, has become one of the most commonly used research methods for testing differences among several population means. If only two populations are in question, ANOVA can be used; however, a two-sample t test would be much easier to test for equality of two population means.

Now suppose five populations are in question. If the two-sample t test were used, we would need to test ten possible combinations (five items taken two at a time). This would be possible; however, if we chose ? = 0.05 for each test, this means the probability of committing a Type I error in any particular test is 0.05. What can we conclude about the hypothesis that all means are equal if each of the ten individual tests has a 0.05 probability of a Type I error?

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An analysis of variance for ANOVA are determined.

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What can we conclude about the hypothesis that all means are equal if each of the ten individual tests has a 0.05 ...

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  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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