Is the Immediate Memory Span for Digits and Letters different?
Experimental Design
Immediate memory span letters and digits was measured for 56 persons. This data was collected in January 1998.
Statistical Hypothesis
Are the mean settings of the two groups sampled from the same population or different populations? Is µ_{1} = µ_{2}?
Hypothesis Testing Model
Ho: µ_{1} = µ_{2}
Ha: µ_{1} <> µ_{2}
The Test Statistic
The test statistic is the Fstatistic (aka "variance ratio")
The Sampling Distribution
If the Ho is true then the F value from the experiment will be drawn from the sampling distribution of F with n_{1 }= 1 and n_{2} = 55 degrees of freedom.
TypeI Error rate
We'll use a 5% TypeI error rate.
Decision Rule
Data 
Descriptive Statistics 



ANOVA Source Table
Concerning the Dependent Groups ANOVA Table:
ANOVA Summary Table  
Source 
SS 
df 
MS 
F 

Subjects In Excel this row is labeled "Rows" Numerator of F 
99.7477679 
55 
1.81359578 
3.46760301 
This F "tells" whether or not some subjects had memory spans different from other subjects. Irrelvant or trivial in this instance.  
Treatment In Excel this row is labeled "Columns" Numerator of F 
31.609375 
1 
31.609375 
60.4372624 
This F "tells" whether or not the independent variable had an effect on the value of the dependent variable.  
Error Denominator of F 
28.765625 
55 
0.5230 

Total 
160.122768 
111 
MSs do not Total 
Statistical Decision
Since the Fvalue we got from the experiment (60.437) is greater than the critical value (4.08), we reject Ho. There is evidence the independent variable affected the mean setting.
Interpretation
There is evidence the letter and digit spans are different. Since the mean digit span is larger than the mean letter span, we can say that digit span is larger than digit span.
Calculations for ANOVA (optional)