A researcher conducts an experiment comparing three treatment conditions with a separate sample n = 8 in each treatment. An analysis of variance is used to evaluate the data, and the results of the ANOVA are presented in the table below. Complete all missing values in the table (Hint: Begin with the df values.)


Source SS df MS F
Between 12 2.00
Within
Total

Your ANOVA summary table has the following setup:

Source.....SS.....df.....MS.....F
Between
Within
Total

Fill in the data with what you know, then find what you don't know.

Here are a few hints:
SS total = SS between + SS within

To calculate df between:
k - 1
Note: k = number of levels or groups.

To calculate df within:
N - k
Note: N = total number of values in all levels or groups.

df total = df between + df within

To calculate MS between:
SS between/df between

To calculate MS within:
SS within/df within

To calculate F-ratio:
MS between/MS within

I hope this brief summary will get you started.

Source SS df MS F

Between 12 2 6 2.00
Within 24 21 1.14
Total 36 23

To complete the missing values in the table, we need to understand the components of an analysis of variance (ANOVA) table.

1. Source: This column lists the sources of variability in the data. In this case, we have "Between" and "Within" sources.

2. SS (Sum of Squares): This column represents the sum of squared deviations from the mean. It quantifies the variability in the data associated with each source.

3. df (Degrees of Freedom): This column represents the degrees of freedom, which indicate the number of independent pieces of information available for estimating a population parameter.

4. MS (Mean Square): This column represents the mean sum of squares, which is calculated by dividing the sum of squares by the degrees of freedom.

5. F (F-value): This column represents the F-ratio, which is calculated by dividing the mean square for the "Between" source by the mean square for the "Within" source.

Now, let's complete the missing values in the table:

Source S S df MS F
Between 12 2 6 2.00
Within W k-1 n-k W/(k-1)
Total T n-1

To calculate the missing values:

1. Degrees of Freedom (df):
The degrees of freedom for the "Between" source is calculated as k-1, where k is the number of treatment conditions. Here, we have 3 treatment conditions, so the df for the "Between" source is 3-1=2.

2. Sum of Squares (SS):
The total sum of squares (SS_Total) is the sum of squared deviations from the grand mean. It represents the total variability in the data. In this case, it is not given, so we cannot determine the value.

The SS for the "Between" source is calculated as SS_Between = MS_Between * df_Between. Using the given F-value (2.00) and df for "Between" (2), we can calculate the missing SS for "Between" as 2.00 * 2 = 4.00.

The SS for the "Within" source is calculated as SS_Within = MS_Within * df_Within. Since both SS_Within and df_Within are missing, we cannot determine the exact values.

3. Mean Square (MS):
The MS for the "Between" source is already given as 2.00.

The MS for the "Within" source is calculated as MS_Within = SS_Within / df_Within. Since both MS_Within and df_Within are missing, we cannot determine the exact values.

4. F-value:
The F-value is already given as 2.00.

To calculate the missing values, we will need more information about the SS and df.

Therefore, we cannot complete the missing values in the table without additional information.

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