Research Question
Will subjects instructed to complete null matches while viewing the MüllerLyer illusion make different settings than subjects ask to set the variable component to be the same physical length as the fixed component of the illusion?
Experimental Design
Two groups of subjects complete several tasks with a computerized version of the MüllerLyer illusion using the method of adjustment . The data for one group of subjects is recorded when "null matching" instructions are used (n = 9). Data for the other group of subjects is recorded when "set to same physical length" instructions are used (n = 14).
20 trials are collected from each subject. The average "equality" setting is calculated.
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} = 21 degrees of freedom.
TypeI Error rate
We'll use a 5% TypeI error rate.
Decision Rule
Data 
Descriptive Statistics 



ANOVA Source Table
Source of Variation  SS  df  MS  F  
Numerator of F  Between Groups  753.127337  1  753.127337  4.465473381 
Denominator of F  Within Groups  3541.76875  21  168.6556548  
Total  4294.896087  22 
Statistical Decision
Since the Fvalue we got from the experiment (4.465) is greater than the critical value (4.38), we reject Ho. There is evidence the independent variable effected the mean setting.
Interpretation
There is evidence that subjects make different mean settings when the "matching" instructions were altered. Since the mean setting for instructions to set the variable stimulus to "physical equality" are closer to the length of the standard stimulus (130 pixels), we can conclude that subjects who know the manner in which the illusion affects settings can adjust the setting more toward physical equality.
Calculations for ANOVA (optional)
SS_{Total}: Calculate the est sigma for all 23 scores in the data set. Square the value and multiply by 22 to get the Total SS. [est. sigma = 13.9722; n = 23; SS_{Total} = (13.9722)^{2} X (23  1 ) = 4294.896]
SS_{Within Groups}: Calculate the SS for each group. Add the separate SS values together.
[SS_{W/I} = 3003.454 + 538.315 = 3541.769]
SS_{Between Groups} = SS_{Total}  SS_{Within Groups}
_{MS = SS ÷ df }[Remember: mean square (aka "Variance") is SS divided by df ].
F = MS_{Bet} ÷ MS_{W/I}