QMB3250 EXAM 3 QUESTIONS WITH ACCURATE
SOLUTIONS
One-Way Anova Assumptions -- Answer ✔✔ • Equal Variance - roughly equal
population standard deviations.
• Independence - Random and independent samples
• Normally distributed response variables - Check boxplots for outliers, histograms for
each group to be symmetric, normal quantile plot to look linear, and histogram of
residuals.
Connecting Letters Report (Tukey) -- Answer ✔✔ When 2 common letters, means
they are not different.
Confidence intervals (Tukey) -- Answer ✔✔ If 0 is in the interval, not significantly
different.
Bonferroni CI -- Answer ✔✔ The confidence interval is calculate with 1 - (alpha/j)
j = number of comparisons.
j= a(a-1)/2
a = number of treatments
alpha = probability of a type 1 error from the family error rate.
, Individual error rate -- Answer ✔✔ alpha/j
family error rate / # of comparisons
Bonferroni confidence level -- Answer ✔✔ 1-(aplha/j)
100% -the individual error rate (%)
family error rate -- Answer ✔✔ alpha
probability of a type 1 error from the family error rate
Two way ANOVA assumptions -- Answer ✔✔ • Equal Variance - roughly equal
population standard deviations.
• Independence - Random and independent samples
• Normally distributed response variables (or large enough sample sizes)
Nonparametric Tests -- Answer ✔✔ • Response Variable is quantitative
• The assumption of normality is not met
• Small sample size with unknown population distribution
• There may be outliers
• Rather than testing population means (like in t-tests), nonparametric tests compare
medians/ distributions
SOLUTIONS
One-Way Anova Assumptions -- Answer ✔✔ • Equal Variance - roughly equal
population standard deviations.
• Independence - Random and independent samples
• Normally distributed response variables - Check boxplots for outliers, histograms for
each group to be symmetric, normal quantile plot to look linear, and histogram of
residuals.
Connecting Letters Report (Tukey) -- Answer ✔✔ When 2 common letters, means
they are not different.
Confidence intervals (Tukey) -- Answer ✔✔ If 0 is in the interval, not significantly
different.
Bonferroni CI -- Answer ✔✔ The confidence interval is calculate with 1 - (alpha/j)
j = number of comparisons.
j= a(a-1)/2
a = number of treatments
alpha = probability of a type 1 error from the family error rate.
, Individual error rate -- Answer ✔✔ alpha/j
family error rate / # of comparisons
Bonferroni confidence level -- Answer ✔✔ 1-(aplha/j)
100% -the individual error rate (%)
family error rate -- Answer ✔✔ alpha
probability of a type 1 error from the family error rate
Two way ANOVA assumptions -- Answer ✔✔ • Equal Variance - roughly equal
population standard deviations.
• Independence - Random and independent samples
• Normally distributed response variables (or large enough sample sizes)
Nonparametric Tests -- Answer ✔✔ • Response Variable is quantitative
• The assumption of normality is not met
• Small sample size with unknown population distribution
• There may be outliers
• Rather than testing population means (like in t-tests), nonparametric tests compare
medians/ distributions
