To fill in the missing results in the ANOVA summary table, we need to understand the concepts and calculations involved in analysis of variance (ANOVA).
ANOVA is used to test whether the means of multiple groups are significantly different from each other. It breaks down the total variation into variation between groups and variation within groups.
Let's go through each row of the ANOVA summary table and fill in the missing results step-by-step:
1A) Source: "Among Groups"
1B) Degrees of Freedom: c - 1, where c represents the number of groups. In this case, there are four groups, so c - 1 = 4 - 1 = 3.
1C) Sum of Squares: SSA
1D) Mean Square (Variance): MSZ = SSA / (c - 1) = 80 / 3
1E) F-statistic: FSTAT
2A) Source: "Within Groups"
2B) Degrees of Freedom: n - c, where n represents the total number of observations and c represents the number of groups. In this case, there are four groups with eight values in each, so n - c = 4 * 8 - 4 = 24.
2C) Sum of Squares: SSW = 560
2D) Mean Square (Variance): MSW = SSW / (n - c) = 560 / 24
3A) Source: "Total"
3B) Degrees of Freedom: n - 1, where n represents the total number of observations. In this case, there are four groups with eight values in each, so n - 1 = 4 * 8 - 1 = 31.
3C) Sum of Squares: SST
To calculate the missing sum of squares (SSA) and total sum of squares (SST), we need the formula:
SST = SSA + SSW
Now, let's calculate the missing values:
1C) SSA = SST - SSW = ? - 560
1D) MSZ = 80 / 3
1E) FSTAT
2D) MSW = 560 / 24
3C) SST = ?
To determine the missing values, you will need additional information or data. Please provide the value of SST, or any other details or data you have, in order to calculate the missing results in the ANOVA summary table.