smellmovinglz

2021-11-14

Six researchers at different universities agree to carry out exactly the same social psychology experiment involving three treatment conditions. When the studies are complete, they pool their data to study outcome variable Y, and they carry out a two-way ANOVA. Assuming that 10 subjects were randomly assigned to each of the treatments at each of the sites, what are the degrees of freedom associated with each of the variance components outlined in the ANOVA Table shown below?

Two versions of the analysis are planned. In the first analysis, the researchers restrict their interest to the six specific sites included in the joint research. In the second analysis they consider the six universities to be a sample from the population of American universities. For each analysis, look up the critical F values for a =.05, and enter them into the table below. (The critical value is the number the F statistic must exceed to be considered statistically significant at the .05 level.) Also indicate the degrees of freedom for each F.

soniarus7x

Beginner2021-11-15Added 17 answers

Step 1

The six researchers carry out same experiment for treatments=3 and assign randomly 10 subjects to each of the three treatments. The analysis are planned for six specified sites for both of the versions.

Two version of analysis contain the same sample size.

Step 2

Number of treatments =3

df for treatments =3-1=2

Total number of sites =6

df for site =6-1=5

Interaction =(3-1)*(6-1)

df for interaction =10

within treatments group =3*6*(10-1)=162

adjusted total =(30)(6)-1=179

Since, the sample size is same for both of the analysis. We compute the F statistics for above values of df at 0.05 level of significance.

$$\begin{array}{|cccc|}\hline sources\text{}of\text{}variance& df& critical\text{}F& values\\ & & specific\text{}site& random\text{}site\\ treatment& 2& 3.051819187& 3.051819187\\ site& 5& 2.26996016& 2.26996016\\ treatment\text{}by\text{}site& 10& 1.889561475& 1.889561475\\ within\text{}treatment\text{}group& 162& & \\ adjusted\text{}total& 179& & \\ \hline\end{array}$$

The six researchers carry out same experiment for treatments=3 and assign randomly 10 subjects to each of the three treatments. The analysis are planned for six specified sites for both of the versions.

Two version of analysis contain the same sample size.

Step 2

Number of treatments =3

df for treatments =3-1=2

Total number of sites =6

df for site =6-1=5

Interaction =(3-1)*(6-1)

df for interaction =10

within treatments group =3*6*(10-1)=162

adjusted total =(30)(6)-1=179

Since, the sample size is same for both of the analysis. We compute the F statistics for above values of df at 0.05 level of significance.