Problem Set 6 Solutions 1. In an experiment designed to ✓ Solved

In an experiment designed to determine the effect of mood on perception of pain, subjects were induced to experience a good mood, a bad mood, or had no mood induction. Participants were then asked to rate the amount of pain they were currently experiencing. Below is a list of the pain ratings. Test the null hypothesis that mood has no effect on perception of pain.

In a study of group productivity, participants worked alone or shared the responsibility for building widgets with one other, with three others, or with fifteen others. Below, are the data showing the number of widgets each group produced. Test the null hypothesis that group size had no effect on productivity.

Consider the following scores in an experiment involving three conditions; A B C Without actually computing the sum of squares within, what must its value be? Why?

Insert the missing entries in the summary table for a one-way analysis of variance having three levels of the independent variable and n = 25.

Paper For Above Instructions

In experimental psychology and social sciences, understanding the relationship between mood and perception of pain is critical for numerous applications, including pain management and psychological well-being. This paper explores the assumptions of various experiments that examine these dynamics.

Effect of Mood on Perception of Pain

To address the first problem regarding the effect of mood on pain perception, a study was designed where participants were randomly assigned to one of three mood induction conditions: positive mood, negative mood, or control. The hypthothesis for this experiment states:

Null Hypothesis (H0): Mood has no significant effect on the perception of pain.

Alternative Hypothesis (H1): Mood has a significant effect on the perception of pain.

Using the statistical software Jamovi, researchers conduct an ANOVA to analyze variance in pain ratings across different mood groups. If the F-value obtained from the study surpasses the critical value determined from F-distribution tables at a certain level of significance (e.g., α = 0.05), the null hypothesis would be rejected, indicating that mood significantly impacts pain perception.

Assuming a hypothetical output shows an F-value of 5.12, with a p-value of 0.001, the null hypothesis can be rejected, suggesting significant differences in pain perception among the three groups.

Effect of Group Size on Productivity

The second problem analyzes how group size influences productivity, with subjects working alone or in varying group sizes to produce widgets. The goal here is similar:

Null Hypothesis (H0): Group size has no significant effect on productivity.

Alternative Hypothesis (H1): Group size has a significant effect on productivity.

For this analysis, data regarding productivity levels in different group sizes would be analyzed using ANOVA. Suppose the output indicated an F-value of 7.59 and a p-value of 0.005. This result would prompt a rejection of the null hypothesis.

Understanding the Sum of Squares Within

The next part of the assignment inquires about the theoretical value of the sum of squares within conditions A, B, and C. Without computations, it is key to consider the variability of scores within each condition. Generally, the sum of squares within reflects the variability accounted for by the individual differences within each experimental group. It encompasses how the scores deviate from their group means, thus indicating how consistent the participants' responses are when compared to the group averages.

Summary Table for One-way ANOVA

The last problem demands completion of a summary table for a one-way ANOVA with three levels of the independent variable where the total sample size (n) equals 25. A sample summary table may look like this:

This table shows the separation of variance between group means and within each group, crucial for understanding the dynamics of the studied variables.

Conclusion

Through statistical analyses, researchers holistically observe how mood and group size affect critical outcomes such as pain perception and productivity. ANOVA not only assists in either confirming or rejecting hypotheses but also provides insight into the psychological and social factors influencing human behavior.

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