Exercise 1:

1) Test Set-Up

General Cereals is a large manufacturer of pre-sweetened, ready-to-eat children's cereals. One of its oldest brands is Super Golden Sweeties. As part of its marketing efforts, General Cereals has been running a test market for new package designs for Super Golden Sweeties. The test of the three designs ran for 52 weeks.The research question:Are sales for the three package designs unequal? And, if they are, which of the pairs are unequal? Here are the results based on cases sold per week in the test markets for each of the three package designs:

2) Select a Level of Significance,

A 5 percent significance level has been selected. What is the Critical Value of F?Please Note:You will not find the critical value on a standard F-distribution table. Use Excel's F.INV.RT function. Excel's "Anova: Single Factor" tool also reports the critical value of F.Do not show the ANOVA Table here.

3) State the Null and Alternate Hypotheses

H0:
H1:

Follow the examples shown inClear-Sighted Statistics.You must use the appropriate Greek letters and mathematical symbols.

=			>		<
	2			2	2

4) Compose a Decision Rule

Follow the examples shown inClear-Sighted Statistics. Base your decision rule on the critical value of F. Do not use p-values.

5) Data Analysis. Create an ANOVA table. Calculate and interpret the eta-square Effect Size. Calculate Statistical Power and the probability of a Type II error. When necessary, conduct a complete LSD Confidence Intervalpost hocanalysis. Do not use any otherpost hocmethod. All of your calculations must go here. Do not use any software other than Microsoft Excel.

ANOVA Table:

Effect Size, Statistical Power, and the Probability of a Type II Error:

Effect Size and Interpretation:

Statistical Power:

Probability of a Type II Error:

Interpretation of Statistical Power:

LSD Confidence IntervalPost HocAnalysis:

6) Decide and Report. Conduct a post hoc analysis if you reject the Null Hypothesis

Please Note:You report must be framed in the context of the research question. Merely stating that you rejected or failed to reject the Null Hypothesis is not sufficient. You must consider the issues of statistical power, Effect Size, and practical significance in your report.

data set

Statistical Power for a One-Way ANOVA Test
Enter the vales in the cells in RED cells.
Use Excel's Paste Special ==> Value command to paste this data
Level of Significance,	0.05	User entered
SS Between Groups, (SSB)		User entered from ANOVA table
Mean Square Within Groups, (MSW)		User entered from ANOVA table
Lambda,	#DIV/0!	=C5/C6
df1		User entered from ANOVA table, (k - 1)
df2		User entered from ANOA table, (n - k)
Total (SS Total)		User entered
Effect Size (Eta-Squared, 2)	#DIV/0!	=SSB/Total (C5/C10)
Interpretation of 2 Effect Size	#DIV/0!
Effect Size (Cohen's f)	#DIV/0!	=SQRT(C11/(1-C11))
Interpretation of Cohen's f Effect Size	#DIV/0!
e	2.7183	=EXP(1)
CV for F	#NUM!	=F.INV.RT(C4,C8,C9))
Post Hoc Statistical Power	#DIV/0!
P(Type II or Error)	#DIV/0!	=1-C12
Eta-Squared ES Thresholds
<0.010: Negligible
0.010: Small
0.059: Medium
0.138: Large
Cohen's f Thresholds	Note:
<0.10: Negligible	Cohen's f ES is required by G*Power & Statistical Kingdom
0.10: Small
0.25: Medium
0.40: Large

xcel

Eta-Squared ES		Effect Size Thresholds
#DIV/0!		<0.01	Negligible
#DIV/0!		0.010	Small
		0.059	Medium
Eta-Square = SSB/Total	0.138	Large
Significance Level
#NUM!
=IF.INV.RT(SignificanceLevel,DF_Numerator,DF_Demonator)
Important Note: Set OUTPUT RANGE at $F$1