You intend to conduct an ANOVA with 3 groups in which each group will have the same number of subjects:n=20. (This is referred to as a "balanced" single-factor ANOVA.)

What are the degrees of freedom for the numerator?

d.f.(treatment) =

What are the degrees of freedom for the denominator?

d.f.(error) = __________________________________________________________________________

The following data represent the results from an independent-measures experiment comparing three treatment conditions withn=4 in each sample. Conduct an analysis of variance with=0.05 to determine whether these data are sufficient to conclude that there are significant differences between the treatments.

Treatment A	Treatment B	Treatment C
10	11	12
6	9	7
10	9	9
6	7	12

F-ratio =

p-value =

Conclusion:

• These data do not provide evidence of a difference between the treatments
• There is a significant difference between treatments
• n2=

The results above were obtained because the sample means are close together. To construct the data set below, the same scores from above were used, then the size of the mean differences were increased. In particular, the first treatment scores were lowered by 2 points, and the third treatment scores were raised by 2 points. As a result, the three sample means are now much more spread out.

Before you begin the calculation, predict how the changes in the data should influence the outcome of the analysis. That is, how will theF-ratio for these data compare with theF-ratio from above?

Treatment A	Treatment B	Treatment C
8	11	14
4	9	9
8	9	11
4	7	14

F-ratio =

p-value =

Conclusion:

• There is a significant difference between treatments
• These data do not provide evidence of a difference between the treatments
• 2=

__________________________________________________________________________

Note that a significantlylargeF-ratio is evidence against equal population means. Thus, ANOVA hypothesis tests are always ____-tailed.

• one
• left
• right
• two

One of the choices is better than the others

__________________________________________________________________________

ANOVA is a statistical procedure that compares two or more treatment conditions for differences in variance.

• True
• False

__________________________________________________________________________

You intend to conduct an ANOVA with 5 groups in which each group will have the same number of subjects:n=23. (This is referred to as a "balanced" single-factor ANOVA.)

What are the degrees of freedom for the numerator?

d.f.(treatment) =

What are the degrees of freedom for the denominator?

d.f.(error) =

__________________________________________________________________________

You intend to conduct an ANOVA with 56 subjects, which will be divided into 7 treatment groups.

What are the degrees of freedom for the numerator?

d.f.(treatment) =

What are the degrees of freedom for the denominator?

d.f.(error) =

__________________________________________________________________________

A researcher uses an ANOVA to compare five treatment conditions with a sample size of n = 14 in each treatment. For this analysis find the degrees of freedom.

What is df(treatment)?

This is sometimes referred to as the "numerator degrees of freedom."

What is df(error)?

This is sometimes referred to as the "denominator degrees of freedom."

If the scenario was changed so that there were still five treatments, but there were different sample sizes for each treatment (a.k.a. an unbalanaced design), which of the following degrees of freedom would NOT change?

1. df(treatment)
2. df(error)
3. both change
4. neither change

__________________________________________________________________________

You conduct a one-factor ANOVA with 8 groups and 10 subjects in each group (a balanced design) and obtainF=2.13. Find the requested values.

dfbetween=

dfwithin=

Google Sheets can be used to find the critical value for an F distribution for a given significance level. For example, to find the critical value (the value above which you would reject the null hypothesis) for=0.05 withdfbetween=5 anddfwithin=78, enter=FINV(0.05,5,78)

Enter this into Google Sheets to confirm you obtain the value 2.332.

You conduct a one-factor ANOVA with 3 groups and 7 subjects in each group (a balanced design). Use Google Sheets to find the critical values for=0.1 and=0.01

(report accurate to 3 decimal places).

F0.1=

F0.01=

Given the following ANOVA output, calculate2.

	SS	df	MS	F-ratio	p-value
Between	76	4	2.38	F = 1.118 F=1.118	p = 0.365 p=0.365
Within	68	32	2.13
TOTAL	144	36

2=SS/SStotal=