Round Each Decimal Answer To Two Digits Or You Will Get Inco

Round Each Decimal Answer To Two Digits Or You Will Get Incorrect Res

Round Each Decimal Answer To Two Digits Or You Will Get Incorrect Res

Use the following information to complete the Source table for a One-Way Independent Samples ANOVA and indicate if there is a significant treatment effect. The study was a test of a new treatment for depression. Twenty four subjects were randomly assigned to three treatment conditions.

For items 2-8 you will need to fill in the values that go in each of the following uncompleted source table cells:

  • SS (Sum of Squares)
  • df (degrees of freedom)
  • MS (Mean Square)
  • F (F-ratio)

Given:

  • Between: 784.75
  • Within: 363.87
  • Total: To be calculated

Remaining cells to fill:

  • Between: Degrees of freedom (df) = 3
  • Within: Degrees of freedom (df) = 8
  • Total: Degrees of freedom (df) = 11
  • Between: MS = 6.58
  • Within: MS = 6.58 (calculate or check)
  • F = 1.49 (calculate accordingly)

Paper For Above instruction

The purpose of this analysis is to examine whether different treatment conditions have a significant effect on the depression scores of subjects. The study involved 24 participants randomly assigned to three treatment groups, with treatment effects assessed via a one-way ANOVA. The available data provides sum of squares and degrees of freedom for both between-group and within-group variations, essential for calculating the mean squares and testing for significance.

First, by analyzing the provided sum of squares, the total variability in the data combines both differences among the treatment groups and variability within them. The total sum of squares (SST) is obtained by summing the between-group sum of squares (SSB) and the within-group sum of squares (SSW). From the given data, SS Between is 784.75 and SS Within is 363.87. Consequently, the total sum of squares (SST) is:

SST = SSB + SSW = 784.75 + 363.87 = 1148.62

The degrees of freedom (df) associated with these sums of squares are critical for calculating mean squares. The between-groups degrees of freedom (dfB) are given as 3, and within-groups degrees of freedom (dfW) as 8, which sum to a total df (dfT) of 11, aligning with the total variability among all subjects.

The mean squares (MS) are derived by dividing the sum of squares by their respective degrees of freedom. For the between-group MS (MSB):

MSB = SSB / dfB = 784.75 / 3 ≈ 261.58

Similarly, the mean square within groups (MSW) is:

MSW = SSW / dfW = 363.87 / 8 ≈ 45.48

The F-ratio evaluates the ratio of variability between the groups to the variability within the groups:

F = MSB / MSW ≈ 261.58 / 45.48 ≈ 5.75

Given these calculations, the F-value is approximately 5.75. Usually, for a significance level of 0.05 and degrees of freedom (3,8), the critical F-value from F-distribution tables is around 4.07. Since 5.75 > 4.07, there is a statistically significant difference among the treatment groups, indicating a significant treatment effect on depression scores.

In conclusion, based on the completed ANOVA table and calculated F-ratio, the analysis provides evidence that the new depression treatment has a significant effect. Post hoc analyses could further specify which groups differ significantly.

References

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