Which statistic measures the total variability around the overall mean?

Which statistic measures the total variability around the overall mean?

• A. Test statistic
• B. Tolerance
• C. Total sum of squares
• D. Transformation

Answer: (C)

Total variability around the grand mean is captured by the total sum of squares. It is computed by summing the squared differences between each observation and the overall mean, reflecting how spread out all the data are around that central value. This single value represents all the variability in the response before any partition into explained or unexplained parts. In ANOVA, SST is the total variability, and it can be divided into the part due to the model (explained variance) and the residual part (unexplained variance). Note that a test statistic is a value used to decide about a hypothesis, tolerance is a measure related to allowable deviation or multicollinearity in regression contexts, and transformation refers to changing the data to meet analysis assumptions. The total sum of squares best answers the idea of measuring the overall dispersion around the mean.

Total variability around the grand mean is captured by the total sum of squares. It is computed by summing the squared differences between each observation and the overall mean, reflecting how spread out all the data are around that central value. This single value represents all the variability in the response before any partition into explained or unexplained parts. In ANOVA, SST is the total variability, and it can be divided into the part due to the model (explained variance) and the residual part (unexplained variance). Note that a test statistic is a value used to decide about a hypothesis, tolerance is a measure related to allowable deviation or multicollinearity in regression contexts, and transformation refers to changing the data to meet analysis assumptions. The total sum of squares best answers the idea of measuring the overall dispersion around the mean.