Question 1 – ANOVA
Problem Description:
The goal of this statistical analysis homework was to investigate the effect of different interventions on well-being. The analysis involved using ANOVA to examine the impact of interventions, followed by post hoc tests for pairwise comparisons.
Solution:
The Levene's test indicated a violation of the homogeneity of variances assumption, but given our sample size, ANOVA remains robust. The change scores were normally distributed across the three groups.
- Control group (n=100) had a mean change score of 10.00 (SD = 2.04).
- Mindfulness intervention group (n=100) had a mean change score of 16.89 (SD = 1.40).
- Growth mindset intervention group (n=100) had a mean change score of 8.9 (SD = 2.11).
ANOVA revealed a significant effect (F(2,297) = 529.802, p = 0.000), and post hoc Dunnett's T3 test was conducted for non-normally distributed data with unequal variances. Results showed that the mindfulness group had a significantly higher change score than the growth mindset and control groups (p < 0.05).
Question 2 – Chi-Squared Goodness of Fit
Problem Description:
This homework aimed to assess the distribution of symptom severity in a sample of First Nations people compared to expected values.
Solution:
Out of 200 participants, 119 had mild symptoms (59.5%), 64 had moderate symptoms (32%), 9 had severe symptoms without ventilator (4.5%), and 8 had severe symptoms with ventilator (4%). The observed frequencies did not significantly differ from the expected frequencies (χ^2(3,N = 200) = 7.338, p = 0.062).
Question 3 – Simple Linear Regression
Problem Description:
This homework involved predicting future earnings based on undergraduate performance and examining the relationship between the two.
Solution:
A simple regression model was used to predict future earnings from undergraduate performance. The model was statistically significant (F(1,98) = 65.333, p < 0.01) with an R^2 of 0.4. The positive effect of grade on future earnings (b = 2.00) suggests that a unit increase in undergraduate performance doubles future earnings. Assumptions of normality and linearity were met.
Question 4 – 2 Ways Factorial ANOVA
Problem Description:
This homework explored the effects of factors, including the presence of an app and video quality, on recall scores.
Solution:
Factor 1 (app presence) was not significant (F(1,96) = 1.207, p > 0.01). Factor 2 (video quality) had a significant effect (F(1,96) = 61.952, p < 0.01). The interaction effect was also significant (F(1,96) = 1.22, p < 0.05). Results indicated that good video quality significantly improved recall scores compared to bad quality video.
Question 5 – Multiple Regression
Problem Description:
This homework aimed to build an efficient model for predicting performance based on several predictor variables.
Solution:
Multiple regression with resilience, years of education, years served in the army, and age as predictors showed a significant model (F(4,95) = 219.773, p < 0.01, R^2 = 0.902). However, only resilience was a statistically significant predictor (p > 0.01), leading to a simplified model using only resilience as the predictor.
Question 6 – One Way Repeated Measures ANOVA
Problem Description:
This homework assessed the impact of different couple's activities on marriage satisfaction.
Solution:
A one-way repeated measures ANOVA revealed a significant effect of couple's activities (F(2,38) = 545.465, p < 0.01). Post hoc analysis found that couples in the cycling program had significantly higher marriage satisfaction scores compared to those in the military boot-camp exercise and pottery class. Violation of sphericity was addressed.
Question 7 – Chi-Squared Test of Independence
Problem Description:
This homework examined the association between vaccine type and heart attack in a group of 300 participants.
Solution:
Chi-squared test showed no significant association between vaccine type and heart attack (χ^2(1, N = 300) = 0.785, p = 0.376), with all cells having expected counts greater than 5. The type of vaccine did not influence the occurrence of heart attacks.
Question 8 – Multiple Linear Regression
Problem Description:
The homework aimed to understand the relationship between suicidality and predictor variables, such as alcohol consumption, income, and number of close friends.
Solution:
Alcohol consumption had a significant effect on suicidality (p < 0.01), while income and the number of close friends were not significant predictors. Together, these variables explained a significant portion of variance in suicidality (R^2 = 0.101, F(3,1996) = 74.899). The research suggests a strong association between alcohol consumption and increased suicide risk.
Question 9 – Fisher Exact Test
Problem Description:
This homework investigated the relationship between class attendance mode and final grade in a sample of 34 students.
Solution:
Using Fisher’s exact test, no significant association was found between class attendance mode and final grade (p = 1.000). All cells had fewer than 10 observations, and the two categorical groups were mutually exclusive.
Question 10 – One Way Independent ANOVA
Problem Description:
This homework assessed the impact of depressive disorder groups on changes in depression scores, despite the assumption of homogeneity of variances being violated.
Solution:
ANOVA indicated a significant effect (F(2,297) = 140.93, p < 0.001), and Dunnett's T3 post hoc test was used due to the violation of the homogeneity of variances. Results showed significant differences in change in depression scores among the groups. The high-dose group had the highest score, followed by the low-dose group, and the placebo group had the lowest scores (p < 0.05 for all comparisons).