ANOVA, the analysis of variance

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xuhag87

Mathematics

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Please answer all questions to the best of knowledge and show work if needed.

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WEEK 8 - HOMEWORK 8 LANE CHAPTER 15; ILLOWSKY CHAPTER 13 This week we finish up with ANOVA, the analysis of variance. Here we can deal with THREE or more variables at a time. The intent is to see if there is a significant difference among them. You use the word “between” when comparing two items (and use the t-test) , but use “among” when talking about three or more items (and use the F-test). Sounds good, but these tests will tell you if there is a difference (at the significance level chosen as usual), but NOT which mean is different. For ANOVA we use yet another Distribution: the F Distribution involving the F-test. A problem using this test will likely be on the final exam. This is all about knowing the why and when about this test. #1 What are the FIVE (5) basic assumptions that must be made to perform a ONE-WAY ANOVA ?There are five basic Assumptions that must be fulfilled in order to perform a One-Way ANOVA test. What are they? #2 A One-Way ANOVA test involving FOUR (4) groups would have what NULL Hypothsis (Ho)? #3 A One-Way ANOVA test involving FOUR (4) groups would have what ALTERNATE Hypothsis (Ha)? #4 An ANOVA test is used when? #5 Why not just compute t-tests among all pairs of means instead computing an analysis of variance? #6 How is it that estimates of variance can be used to test a hypothesis about means? #7 An experiment has 5 conditions (e.g., different diseases) and 6 subjects in each condition, what are dfn and dfe? #8 Data from a hypothetical study on the effects of age and time on scores on a test of reading comprehension: Compute the analysis of variance summary table. Fill in the ANOVA Table, calculate the F test statistic, determine the critical F statistic and compare them to see if we accept or reject Ho. (Feel free to use software to find the P-value and compare that to an alpha of your choice to see if it agrees with your test/critical F-statistic conclusion. (If it doesn’t, something went wrong). #9 These are the WEIGHTS of three groups (call these “conditions”) of men from three different States. Do a One-Way ANOVA test to determine the statistics below: FILL IN THE TABLE BELOW WITH THESE VALUES: (a) Sum of Squares factor (b) Sum of Squares Error (c) df for the Numerator (d) df for the Denominator (e) Mean Square Factor (f) Mean square Error (g) The F-test statistic (h) The F- critical value (assume alpha = 5%) CITE HERE: ________ (i) the P-value (software OK) (j) Accept or Reject Ho ? ( if test/critical F statistic conclusion differs from P-value conclusion, something is wrong.) AND EXPLAIN WHAT THIS MEANS SOURCE CONDITION ERROR TOTAL df (c) (d) SSQ (a) (b) MS (B&E) (e) (f) XXXXX F (g) P (i) XXXXX XXXXX (h) is the critical F-value from a Table of your choice. See if you can figure it out.
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Explanation & Answer

Hi there!Attached please find the completed assignment in the Word doc below. Work for all calculations is shown, and all questions have been thoroughly answered. I have also included the Excel spreadsheet I used to fill in the various ANOVA tables. Thanks again!Selenica

WEEK 8 - HOMEWORK 8 LANE CHAPTER 15; ILLOWSKY CHAPTER 13
This week we finish up with ANOVA, the analysis of variance. Here we can deal with THREE or more variables
at a time. The intent is to see if there is a significant difference among them. You use the word “between”
when comparing two items (and use the t-test) , but use “among” when talking about three or more items
(and use the F-test). Sounds good, but these tests will tell you if there is a difference (at the significance level
chosen as usual), but NOT which mean is different. For ANOVA we use yet another Distribution: the F
Distribution involving the F-test. A problem using this test will likely be on the final exam.
This is all about knowing the why and when about this test.
#1 What are the FIVE (5) basic assumptions that must be made to perform a ONE-WAY ANOVA ?There are five
basic Assumptions that must be fulfilled in order to perform a One-Way ANOVA test. What are they?
The population from which samples are drawn is assumed to be normal
Factor is a categorical variable
The response is a numerical variable
Samples are selected at random and independently
All populations have an equal standard deviation
#2 A One-Way ANOVA test...


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