Stat

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	df	SSQ	MS (B&E)	F	P
CONDITION	(c)	(a)	(e)	(g)	(i)
ERROR	(d)	(b)	(f)
TOTAL			XXXXX	XXXXX	XXXXX

(h) is the critical F-value from a Table of your choice. See if you can figure it out.