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Analysis of Results in a One-Way ANOVA Experiment - Coggle Diagram
Analysis of Results in a One-Way ANOVA Experiment
To conduct a One-Way ANOVA, several steps are followed to decompose the total variability into explanatory and error components.
Step 1: Model Formulation
The statistical model for One-Way ANOVA is:
yij = μ + αi + εij
yij is the observed response for the j-th subject in the i-th group.
μ is the overall mean.
αi is the effect of the i-th treatment.
εij is the random error
Step 2: Hypotheses Formulation
Null hypotheses (H0)
(μ1=μ2=…=μk)
Alternative Hypothesis (Ha)
At least one of the means is different.
Step 3: Variability Decomposition
Total Sum of Squares (SST): measures the total variability in the data relative to the overall mean.
Sum of Squares Between Groups (SSB): measures the variability between the means of different groups.
Sum of Squares Within Groups (SSW): measures the variability within each group.
SST=SSB+SSW
Step 4: Calculation of Degrees of Freedom (df)
For SSB: dfSSB = k−1
For SSW: dfSSW = N−k
For SST: dfSST = N−1
where k is the number of groups and N is the total number of observations.
Step 5: Calculation of Mean Squares (MS)
Mean Square Between Groups (MSB): MSB = SSB / dfSSB
Mean Square Within Groups (MSW): MSW = SSW / dfSSW
Step 6: Calculation of the F Statistic
F = MSB / MSW
Step 7: Decision Making
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