Exhibit 7-11: in a 2 $\times$ 3 Experimental Design Three Kinds of Treatments (A, B, and Kinds

question 79

Multiple Choice

Exhibit 7-11: In a 2 $\times$ 3 experimental design three kinds of treatments (A, B, and C) were used with two groups of subjects (M and N) .The number of subjects and the mean of each group are as follows:
$\begin{array}{lll}&&&\text { Treatments }\\&&\mathrm{A} & \mathrm{B} & \mathrm{C} \\&\mathrm{~M}&\mathrm{X}=20 & \mathrm{X}=18 & \mathrm{X}=16 \\&&\mathrm{~N}=5 & \mathrm{~N}=5 & \mathrm{~N}=5 \\\text { subjects } \\&\mathrm{~N}&\mathrm{X}=12 & \mathrm{X}=14 & \mathrm{X}=16 \\&&\mathrm{~N}=5 & \mathrm{~N}=5 & \mathrm{~N}=5\end{array}$
The following is the incomplete summary table of multifactor analysis of variance.Complete the table and answer the following questions.
$\begin{array}{ll}\text { Source of variation } & S S & \underline { \text { df }} & \underline { \text { MS}} & \underline { \text { F}}\\\hline \text { Between columns } & 0 \\\text { Between rows } & 120 \\\text { Interaction } & \\\hline \text { Between groups } & 200 \\\text { Within groups } & \\\hline \text { Tntal } & 454\end{array}$
-Refer to Exhibit 7-11.Assume that the F ratios for between rows and interaction are statistically significant, but the F ratio for between columns is not statistically significant.In accepting these results, is it possible that

• A) we make only Type I errors.
• B) we make only Type II errors.
• C) we make both Type I and Type II errors.
• D) we make neither Type I nor Type II errors.

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Definitions:

Dependent Variables

Dependent variables are the outcomes or responses that researchers are trying to explain or predict, which change based on other variables.

Indicator Variable

A dummy variable that assigns a value of 0 or 1 to categorical data for use in regression analysis.

Dummy Variable

A binary variable used in statistical models to represent the presence or absence of a characteristic or effect.

Significance Level

The probability of rejecting the null hypothesis in a statistical test when it is actually true, serving as a critical value for decision-making in hypothesis testing.