To assess the effects of instructor and student gender on...

To assess the effects of instructor and student gender on student course scores, an experiment was conducted in 11 sections of managerial accounting classes ranging in size from 25 to 66 students. The factors were instructor gender $(M, F)$ and student gender $(M, F)$. There were 11 instructors ( 7 male, 4 female). Steps were taken to eliminate subjectivity in grading, such as common exams and sharing exam grading responsibility among all instructors so no one instructor could influence exam grades unduly. (a) What type of ANOVA is this? (b) What conclusions can you draw? (c) Discuss sample size and raise any questions you think may be important. $$ \begin{array}{lrrrrr} \hline {\text { Analysis of Variance for Students' Course Scores }} & & & \\ \hline \begin{array}{l} \text { Source of } \\ \text { Variation } \end{array} & \begin{array}{c} \text { Sum of } \\ \text { Squares } \end{array} & \begin{array}{c} \text { Degrees of } \\ \text { Freedom } \end{array} & \begin{array}{l} \text { Mean } \\ \text { Square } \end{array} & \text { F Ratio } & \text { p-Value } \\ \hline \text { Instructor gender (I) } & 97.84 & 1 & 97.84 & 0.61 & 0.43 \\ \text { Student gender }(S) & 218.23 & 1 & 218.23 & 1.37 & 0.24 \\ \text { Interaction (IXS) } & 743.84 & 1 & 743.84 & 4.66 & 0.03 \\ \text { Error } & 63,358.90 & 397 & 159.59 & & \\ \quad \text { Total } & 64,418.81 & 400 & & & \\ \hline \end{array} $$

To assess the effects of instructor and student gender on student course scores, an experiment was conducted in 11 sections of managerial accounting classes ranging in size from 25 to 66 students. The factors were instructor gender $(M, F)$ and student gender $(M, F)$. There were 11 instructors ( 7 male, 4 female). Steps were taken to eliminate subjectivity in grading, such as common exams and sharing exam grading responsibility among all instructors so no one instructor could influence exam grades unduly. (a) What type of ANOVA is this? (b) What conclusions can you draw? (c) Discuss sample size and raise any questions you think may be important.
$$
\begin{array}{lrrrrr}
\hline {\text { Analysis of Variance for Students' Course Scores }} & & & \\
\hline \begin{array}{l}
\text { Source of } \\
\text { Variation }
\end{array} & \begin{array}{c}
\text { Sum of } \\
\text { Squares }
\end{array} & \begin{array}{c}
\text { Degrees of } \\
\text { Freedom }
\end{array} & \begin{array}{l}
\text { Mean } \\
\text { Square }
\end{array} & \text { F Ratio } & \text { p-Value } \\
\hline \text { Instructor gender (I) } & 97.84 & 1 & 97.84 & 0.61 & 0.43 \\
\text { Student gender }(S) & 218.23 & 1 & 218.23 & 1.37 & 0.24 \\
\text { Interaction (IXS) } & 743.84 & 1 & 743.84 & 4.66 & 0.03 \\
\text { Error } & 63,358.90 & 397 & 159.59 & & \\
\quad \text { Total } & 64,418.81 & 400 & & & \\
\hline
\end{array}
$$

Key Concepts

Two-Way Factorial ANOVA

This concept involves analyzing the effects of two independent categorical variables on a continuous dependent variable, as well as their interaction. In a two-way factorial design, the main effects of each factor are tested separately, and any combined effect (interaction) between the factors is also evaluated. This method is especially useful when experiments involve multiple factors that might have overlapping or interacting influences on the outcome.

Main Effects

Main effects refer to the isolated influence of each independent variable on the dependent variable in an ANOVA. In a factorial design, the analysis separates the individual impact of each factor, providing an understanding of how, for example, one factor contributes to variability regardless of the levels of the other factor. Assessing main effects is crucial to determine if each individual factor exerts a statistically significant effect.

Interaction Effects

Interaction effects occur when the effect of one independent variable on the dependent variable differs depending on the level of another independent variable. In this context, it means that the combination of two categorical variables creates a joint effect that is not predictable from their individual effects. Detecting an interaction can indicate that the factors influence each other in impacting the outcome, which may have important implications for interpretation and subsequent research.

Sample Size and Experimental Design Considerations

Understanding sample size is essential for ensuring adequate power and representativeness in statistical experiments. Small sample sizes or uneven distribution across groups can affect the reliability of the ANOVA results. Additionally, experimental design considerations include the control of potential confounding variables (such as standardizing grading practices) and ensuring random assignment where possible to minimize biases. These factors collectively contribute to the validity and generalizability of the study's conclusions.

Transcript

00:01 For a, the population of interest is all college students in the us.

00:14 For b, this study is an experiment, specifically a factorial experiment, because the researchers are manipulating the ceiling arrangements and measuring the effect on students ' feeling -at -ease scores.

00:30 Now, for c, the response variable is the feeding -at -ease score, which is quantitative.

00:42 The explanatory variables are gender and seeding arrangements, and both are qualitative.

01:01 Now for d, we're going to compute the mean and standard deviation for the scores in the male u -shaped cell.

01:09 Cell, and here i have decoding python to calculate the mean and standard deviation, which turned out to be mean of 19 .825 and standard deviation of 0 .580.

01:32 0 .580.

01:37 Now for e, we're going to calculate the probability given that u -shaped layout are normally distributed with mean of 19 and standard deviation of 0 .8 for males.

02:00 Now we can calculate the z statistic which is just the average minus the mean over the standard deviation over square root n so here mean have been found here and the true mean is given as 19 .8 and the standard deviation or the sigma is given as 0 .8 so here i have calculated the z -statistic, and it turned out to be 1 .812.

02:40 And so we're just going to find the probability that the normal distribution with 0 ,1 is larger than 1 .812.

02:53 2, and here is the coding python to calculate this probability, and it turned out to be 0 .035.

03:09 Now, this is a small probability, but it is not impossible to have this average...

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