ANOVA Problem Set

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ANOVA Problems

The situation:

You have completed a research project. You've entered the data into Excel, mumbled the proper incantations, moved your hands in the movements of power. Excel outputs the summary table for the Analysis of Variance that will enable you to determine whether or not the independent variable was effective.

Worthwhile points to consider:

Sketch out a figure that shows what the data set looks like.
- How many columns of data?
- Were the same subjects used in the different columns?
What is the independent variable?
What is the dependent variable?
Was this an independent or dependent groups design?
Explicitly proceed through the 8 or 9 steps necessary to complete any inferential statistical test
- It is very important to write out the decision rule.

Problem 1

The 24 students enrolled in PS201 in the Spring of 2000 measured immediate memory span on themselves for letters and digits per the lab project. The descriptive statistics were as follows:

	Letter Span	Digit Span
Mean	5.98	7.31
est sigma	0.972	1.325
n	24	24

One of the following ANOVA summary tables is appropriate to determine whether or not the independent variable was effective. I've deleted some of the values in the summary tables to help you master the relationships among the values. Fill in the missing values in both tables. Determine which is the appropriate analysis. Is there evidence digit and letter spans differ?

Candidate Summary Table 1 for ANOVA
Source	SS	DF	MS	F
Rows			1.87952899
Columns		1		25.938326
Error	18.9166667	23	0.822464377
Total	83.4791667	47	MS's don't total.

Candidate Summary Table 2 for ANOVA
Source	SS	DF	MS	F
Between		1
Within			1.350996377
Total	83.47916667	47	MS's don't total.

Problem 2

Given below are the descriptive statistics and ANOVA summary table for the Letter Span data collected by the four teams of students during Spring 2000. Again, I've deleted some of the values of the source table Excel provides. You have the information you need to complete the table. Is there evidence the independent variable was effective? Note: The entire data set is given in the Key

Descriptive Statistics for Letter Span for Volunters
Group	Count	Sum	Average	Variance
Red	18	110	6.11	1.0458
Green	18	120	6.67	0.7647
Blue	18	109.6	6.06	0.7908
Yellow	18	118.5	6.58	1.2838

Source Table for ANOVA
Source	SS	DF	MS	F
Between		3
Within			0.94628268
Total	69.7187575		MSs don't total

Key