the problem asks to complete an ANOVA table and report the relevant SS, df, MS, and F values, and find the critical value for the F-values. I found my F values: they were 3 and 16. I do not understand how to find the critical value.

http://www.itl.nist.gov/div898/handbook/eda/section3/eda3673.htm

The critical value is found in a table, it is a measure of the probability density function.

I'm not quite sure what you are asking, but I will give you an example and hope it helps.

Suppose we have the following table with the values included:

Source.....SS.....df.....MS.....F
Between....8.13....2.....4.065..5.57
Within.....8.8.....12....0.73
Totals.....16.93...14

To get some of these values, we can do a few things:

SS total = SS between + SS within = 16.93 (from the table).

To calculate df between:
k - 1 = 3 - 1 = 2
Note: k = number of levels.

To calculate df within:
N - k = 15 - 3 = 12
Note: N = total number of values in all levels.

df total = df between + df within = 14 (from the table).

To calculate MS between:
SS between/df between = (8.13)/2 = 4.065

To calculate MS within:
SS within/df within = (8.8)/12 = 0.73

To calculate F-ratio:
MS between/MS within = (4.065)/(0.73) = 5.57

I hope this will help.

thank you

To find the critical value for the F-values, you need to consult the F-distribution table or use a statistical software package.

First, let's understand what the F-value represents. In ANOVA (Analysis of Variance), the F-value is used to test the null hypothesis by comparing the variation between different groups (treatments) to the variation within each group.

To find the critical value, you will need two pieces of information: the significance level (α) and the degrees of freedom associated with the numerator (dfn) and denominator (dfd) of the F-value.

1. Significance level (α): This is the probability of making a Type I error, which is rejecting the null hypothesis when it is actually true. Commonly used significance levels are 0.05 (5%) and 0.01 (1%).

2. Degrees of freedom: In ANOVA, there are two sets of degrees of freedom – dfn (degrees of freedom numerator) and dfd (degrees of freedom denominator). The dfn represents the number of groups minus 1, and the dfd represents the total number of observations minus the number of groups.

Once you have the α and the degrees of freedom values, follow these steps:

1. Look up the significance level (α) in the F-distribution table.
2. Find the row corresponding to the dfn (numerator degrees of freedom).
3. Find the column corresponding to the dfd (denominator degrees of freedom).
4. The intersection of the row and column will give you the critical F-value.

Alternatively, if you are using statistical software like R or Excel, you can directly calculate the critical value using functions such as qf or FINV, respectively. Just provide the significance level, dfn, and dfd as inputs to the function, and it will return the critical F-value.

Remember, the critical value determines the threshold above which you reject the null hypothesis. If your calculated F-value is higher than the critical value, you reject the null hypothesis; otherwise, you fail to reject it.