To find the degrees of freedom for the total sum of squares (SST) in a production data analysis, you first need to determine how the data is structured. Specifically, we are looking at the shifts as groups, with multiple observations for each shift.

Steps to calculate the degrees of freedom for the total sum of squares:

1. Number of groups (k): In this case, the groups are the three shifts (First Shift, Second Shift, and Third Shift), so $k = 3$.

2. Total number of observations (n): You have 12 days of production data for each shift. Since there are three shifts for each day, the total number of observations is:

   $n = 12 \text{ days} \times 3 \text{ shifts/day} = 36 \text{ observations in total}.$

3. Degrees of freedom for the total sum of squares (DFT): The degrees of freedom for the total sum of squares is simply $n - 1$. This is because the total degrees of freedom represents the variation across all observations.

   $\text{DFT} = n - 1 = 36 - 1 = 35.$

Thus, the value for the degrees of freedom for the total sum of squares is 35.

Would you like more details on how this connects to other types of sum of squares, or any further clarification?

Related Questions:

1. How do you calculate the between-groups sum of squares in this scenario?
2. What is the degrees of freedom for the within-groups sum of squares?
3. How would you find the mean squares for between and within groups?
4. How do you interpret the F-statistic in the context of production shifts?
5. How does an ANOVA test help in understanding production differences between shifts?

Tip:

The degrees of freedom are a critical part of variance analysis. They indicate how much data is available to estimate parameters and are used to compute test statistics in hypothesis testing.